# yield curve

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Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues by Alain Ruttiens

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As a result, except for the USD yield curve, market practitioners prefer to start from a swap yield curve and, for each maturity, deduct some spread to obtain the corresponding risk-free yield curve, or add a spread to quote corporate bonds of other issuers of lower rating, or to penalize a restricted liquidity. However, the market nowadays tends to favor a variant of the swap curve called the OIS swap curve (OIS swaps are explained in Chapter 6, Section 6.7.2). In addition, we will see that interpolating rates between two points of a yield curve is much easier and grounded on a swap curve than on a government bonds yield curve. We will therefore present the building of both yield curves, but in more detail for the swap curve. Theoretically, interest rates as data points may form a yield curve in various ways.

Swaps and swap rates are studied in Chapter 6. 2. Yield curves are studied in Chapter 2. Here we just compare “rough” curves of joined discount factors and of zeroes. 3. Although in the practice, the minimum period for an interest period is a day. 4. In some cases, the reasoning is unfortunately not possible, for example, with credit derivatives. The valuation of such instruments is, therefore, more questionable. 2 The term structure or yield curve 2.1 INTRODUCTION TO THE YIELD CURVE A term structure or yield curve can be defined as the graph of spot rates or zeroes1 in function of their maturity. Since most of the time interest rates are higher with longer maturities, one talks of a “normal” yield curve if it is going upwards, and of an “inverse” yield curve if and when longer rates are lower than shorter rates.

pages: 1,088 words: 228,743

Expected Returns: An Investor's Guide to Harvesting Market Rewards by Antti Ilmanen

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The implications of two hypotheses about yield curve behavior Pure expectations hypothesis Risk premium hypothesis What is the information in forward rates (yield curve steepness)? Market’s rate expectations Required bond risk premia What future events should forward rates forecast? Future interest rate changes Near-term return differentials across bonds What is the best predictor of a 5-year zero-coupon bond’s 1-year return? The 1-year riskless spot rate The 5-year zero’s “rolling yield” (which is also the 1-year forward rate after 4 years) What is the best predictor of next year’s spot yield curve? Implied spot yield curve one year forward Current spot yield curve Roll or slide is another nuanced aspect of carry. The random walk hypothesis assumes that the current yield curve is the best predictor of the future yield curve.

The rate expectation component can be expressed either in terms of expected multi-year changes in the 1-year yield over the next decade or, alternatively, as the expected next-year change in the 10-year yield, scaled by its (end-of-horizon) duration. The first yield curve equation focuses on gradual changes in short rates and the yield-based BRPY while the second equation focuses on near-term changes in long yields and the return-based BRPH. Alternative theories Which of the two components has a larger influence on the yield curve shape? To interpret the yield curve, one can usefully contrast the classic pure expectations hypothesis (PEH) with the random walk hypothesis. The PEH makes the extreme assumption that risk premia are zero and is consistent with the idea of investor risk neutrality. One can then virtually read the market’s rate expectations off the yield curve (specifically, off the forward rate curve). Suppose a particularly steep yield curve indicates that, according to the PEH, the market expects short rates to rise quickly over time (to exactly offset longer bonds’ initial yield advantage; thus all bond investments have the same expected return).

The random walk hypothesis assumes that the current yield curve is the best predictor of the future yield curve. If an upward-sloping yield curve remains unchanged over the next year, a long-term bond’s yield income advantage over the one-year bond will be augmented by capital gains through a “rolldown” effect. For example, if the current 4-year rate is 20 bp lower than the current 5-year rate, the assumption of an unexpected yield curve implies that the bond’s yield will fall by 20 bp simply as a result of aging and rolling down the yield curve. The consequent “rolldown return” gives roughly a 0.8% capital gain (a 4-year duration times a 20 bp yield decline) even if the constant maturity yield curve is unchanged. We can calculate a broader carry measure that incorporates both yield income and rolldown return; it is called “rolling yield” and reflects return in an unchanged curve scenario.

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Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined by Lasse Heje Pedersen

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• Bond carry trade: A bond’s carry is its yield-to-maturity in excess of the financing rate. For example, a 10-year Japanese government bond has a high carry if the Japanese yield curve is steep. Some macro investors trade on bond carry across countries, buying bonds in countries with high carry while shorting bonds in countries with low carry. Such trades can be implemented with cash bonds (financed in repo), bond futures, or interest-rate swaps. • Yield-curve carry trade: Macro investors also trade bonds of different maturities within the same country. This is called a yield-curve trade. Chapter 14 provides more sophisticated measures of bond carry (that include a so-called roll-down effect) and discusses in more detail how to implement bond and yield-curve trades. • Commodity carry trade: The carry of a commodity futures contract is the amount of money one makes if the spot commodity price does not change.

An example of a classic fixed-income arbitrage trade is to sell short newly issued on-the-run bonds against long positions in older off-the-run bonds. Other classic trades include yield curve trades called butterflies, swap spread trades, mortgage trades, and fixed-income volatility trades. Before we get into the details of these trades, we first consider the fundamentals of bond yields and bond returns. The collection bond yields across all maturities are called the “yield curve” or the “term structure of interest rates.” Fixed-income arbitrage traders are obsessed with the yield curve. We discuss how the yield curve is characterized by its level, slope, and curvature, where the level is set by the central bank, and the slope and curvature are determined by expected future central bank rates and risk premiums.

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My Life as a Quant: Reflections on Physics and Finance by Emanuel Derman

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The traders were aware of their need for a better model, and as such were at the forefront of the impetus to replace it. We knew that we had to model the future behavior of all Treasury bonds, that is, the evolution of the entire yield curve. How to set about it was neither obvious nor easy. A stock price is a single number, and when you model its evolution, you project only one number into an uncertain future. In contrast, the yield curve is a continuum, a string or rubber band whose every point, at any instant, represents the yield of a bond with corresponding maturity. As time passes and bond prices change, the yield curve moves, as illustrated in Figure 10.3. To evolve the entire yield curve forward in time is a much more difficult task: Just as you cannot move the different points on a string completely independently of each other, because the string must stay connected, so bonds close to each other must stay connected, too.

We were building a model for traders, and we wanted it to be simple, consistent, and reasonably realistic. Simple meant that only one random factor drove all changes. Consistent meant that it had to value all bonds in agreement with their current market prices; if it produced the wrong bond prices, it was pointless to use it to value options on those bonds. Finally, realistic meant that the model's future yield curves should move through ranges similar to those experienced by actual yield curves. Figure 10.3 Yield curves can vary during the day. When physicists build models, they often first resort to a toy representation of the world in which space and time are discrete and exist only at points on a lattice-it makes picturing the mathematics much easier. We built our model in the same vein. We imagined a world in which the shortest investment you could make lasted exactly one year, and was represented by the one-year Treasury bill interest rate.

But, since the value of the current three-year yield is known, you can use it to deduce the distribution of one-year rates two years hence. Continuing in this way, you can use the current yield curve at any instant to pin down the range of all future one-year rates, as illustrated in Figure 10.5. This was the essence of our model. When Bill and I programmed it, it seemed to work-we could extract the market's expectation of the distributions of future one-year rates from the current yield curve and its volatility. There was nothing holy about the one-year time steps we started with. Once the model worked, we used monthly, weekly, or sometimes even daily steps on a lattice, determining the market's view of the distribution of future short-term rates at any instant from the current yield curve. A typical lattice (or tree, as we called it, because of the way an initial interest rate forked out into progressively wider branches) had hundreds or thousands of equally spaced short periods, as illustrated in Figure 10.6.

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The Investopedia Guide to Wall Speak: The Terms You Need to Know to Talk Like Cramer, Think Like Soros, and Buy Like Buffett by Jack (edited By) Guinan

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Related Terms: • Accrual Accounting • Cost of Goods Sold—COGS • Inventory • Asset Turnover • Gross Profit Margin Inverted Yield Curve Yield What Does Inverted Yield Curve Mean? An interest rate environment in which long-term debt instruments have lower yields than do short-term debt instruments of the same credit quality. This type of yield curve is the rarest of the three main curve types and is considered a predictor of economic recession. Maturity Copyright © 2006 Investopedia.com Partial inversion occurs when only some of the short-term Treasuries (5 or 10 years) have higher yields than the 30-year Treasuries; an inverted yield curve sometimes is referred to as a negative yield curve. Investopedia explains Inverted Yield Curve Historically, inversions of the yield curve have preceded many U.S. recessions. Because of this historical correlation, the yield curve often is seen as an accurate indicator of the turning points of the business cycle.

An SEC yield is the percentage yield on a mutual fund based on a 30-day period. 323 324 The Investopedia Guide to Wall Speak Related Terms: • Annual Percentage Yield—APY • Dividend Yield • Yield to Maturity—YTM • Current Yield • Yield Curve Yield Curve Yield What Does Yield Curve Mean? The line on a chart that plots the interest rates, at a set point in time, of bonds that have equal credit quality but different maturity dates. The most frequently reported yield curve compares 3-month, 2-year, 5-year, and 30-year U.S. Treasury debt. This yield curve is used as a benchmark for other debt in the market, such as mortgage rates and bank lending rates. The curve also can be used to predict changes in economic output and growth. Maturity Copyright © 2006 Investopedia.com Investopedia explains Yield Curve The shape of the yield curve is scrutinized closely because it can indicate future changes in interest rates and economic activity. There are three main types of yield curve shapes: (1) normal, (2) inverted, and (3) flat (or humped). (1) A normal yield curve (pictured here) is one in which longer-maturity bonds have a higher yield than do shorter-term bonds because of the risks associated with time. (2) An inverted yield curve is one in which the shorter-term yields The Investopedia Guide to Wall Speak 325 are higher than the longer-term yields; this can be a sign of an upcoming recession. (3) A flat (or humped) yield curve is one in which the shorter-term and longer-term yields are very close to each other; this is also a predictor of an economic transition.

There are three main types of yield curve shapes: (1) normal, (2) inverted, and (3) flat (or humped). (1) A normal yield curve (pictured here) is one in which longer-maturity bonds have a higher yield than do shorter-term bonds because of the risks associated with time. (2) An inverted yield curve is one in which the shorter-term yields The Investopedia Guide to Wall Speak 325 are higher than the longer-term yields; this can be a sign of an upcoming recession. (3) A flat (or humped) yield curve is one in which the shorter-term and longer-term yields are very close to each other; this is also a predictor of an economic transition. The slope of the yield curve also is considered important: the greater the slope, the greater the gap between short-term and long-term rates. Related Terms: • Corporate Bond • Inverted Yield Curve • U.S. Treasury • Interest Rate • Risk-Free Rate of Return Yield to Maturity (YTM) What Does Yield to Maturity Mean?

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Frequently Asked Questions in Quantitative Finance by Paul Wilmott

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If the model couldn’t even get bond prices right, how could it hope to correctly value bond options? Thomas Ho and Sang-Bin Lee found a way around this, introducing the idea of yield curve fitting or calibration. See Ho and Lee (1986). 1992 Heath, Jarrow and Morton Although Ho and Lee showed how to match theoretical and market prices for simple bonds, the methodology was rather cumbersome and not easily generalized. David Heath, Robert Jarrow and Andrew Morton took a different approach. Instead of modelling just a short rate and deducing the whole yield curve, they modelled the random evolution of the whole yield curve. The initial yield curve, and hence the value of simple interest rate instruments, was an input to the model. The model cannot easily be expressed in differential equation terms and so relies on either Monte Carlo simulation or tree building.

First, the spot rate does not exist, it has to be approximated in some way. Second, with only one source of randomness the yield curve is very constrained in how it can evolve, essentially parallel shifts. Third, the yield curve that is output by the model will not match the market yield curve. To some extent the market thinks of each maturity as being semi independent from the others, so a model should match all maturities otherwise there will be arbitrage opportunities. Models were then designed to get around the second and third of these problems. A second random factor was introduced, sometimes representing the long-term interest rate (Brennan & Schwartz), and sometimes the volatility of the spot rate (Fong & Vasicek). This allowed for a richer structure for yield curves. And an arbitrary time-dependent parameter (or sometimes two or three such) was allowed in place of what had hitherto been constant(s).

The time-dependent parameter a(t) is chosen so that the theoretical yield curve matches the market yield curve initially. This is calibration. Hull and White There are Hull and White versions of the above models. They take the formsdr = (a(t) − b(t)r)dt + c(t)dX, ordr = (a(t) − b(t)r)dt + c(t)r1/2dX . The functions of time allow various market data to be matched or calibrated. There are solutions for bonds of the form exp(A(t; T) − B(t; T)r). Black-Karasinski In this model the risk-neutral spot-rate process isd(ln r) = (a(t) − b(t) ln rdt + c(t)dX. There are no closed-form solutions for simple bonds. Two-factor models In the two-factor models there are two sources of randomness, allowing a much richer structure of theoretical yield curves than can be achieved by single-factor models.

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The Financial Crisis and the Free Market Cure: Why Pure Capitalism Is the World Economy's Only Hope by John A. Allison

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What is sad, however, is that even though at some level Bernanke knew that the Fed had made major mistakes, this is not what he discussed publicly. He said repeatedly that the inverted yield curve would not cause a recession, but would simply slow the rate of inflation. While he mentioned the housing market occasionally, mostly by claiming that there was no bubble,15 his focus was primarily on commodity prices. He held the inverted yield curve for more than a year (from July 2006 to January 2008), one of the longest yield-curve inversions ever. The subsequent Great Recession, which lasted through June 2009 (and, practically speaking, continues in December 2011), began in December 2007. As mentioned, history reveals that there is a very high correlation between inverted yield curves and recessions. Bernanke denied this correlation and was adamant that things were different this time because of globalization.

The inflation rate using the “old” CPI is significantly higher than that using Greenspan’s calculation.13 Could the Fed be making improper decisions based on miscalculating the CPI? At best, the calculation of the CPI is more art than science. After he became chairman of the Federal Reserve in early 2006, Bernanke rapidly raised interest rates and created an inverted yield curve. An inverted yield curve is one in which short-term rates are higher than long-term rates, and even Fed researchers acknowledge that an inverted yield curve tends to trigger recessions.14 Because bankers had been misled by Greenspan’s often-spoken concern about deflation, many of them had extended their bond portfolios, as this was one of the few areas where they could make long-term profits based on Greenspan’s deflation scenario. (Greenspan based his assumptions on his belief in “excess” global savings driven by the Chinese.)

The rapid increase in interest rates was far more destructive than the level of rates. Also, the unanticipated pace and magnitude of rising interest rates left bankers in a very difficult position. Inversions of yield curves are an unusual phenomenon. Typically, investors will invest for a longer duration only if they can earn a higher interest rate, because, other things being equal, the longer the investment, the greater the risk and the lower the liquidity. Markets practically never invert yield curves. It is interesting that Bernanke’s decision to both raise short-term interest rates (to a peak of 5.25 percent) and invert the yield curve must have reflected his realization that Greenspan’s policies had been inflating the economy and leading to misinvestment (overinvestment in housing). Greenspan himself seemed to have realized it, since as chairman he had raised the fed funds rate from 1 percent in 2004 to 4.5 percent before leaving office in early 2006.

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Inside the House of Money: Top Hedge Fund Traders on Profiting in a Global Market by Steven Drobny

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We had other trades on that were doing well. We also hung on to that trade for so long because it was so outstandingly good. I have never seen a yield curve that was as mispriced as the yen curve at that time. Other great trades over the years were curvature and conditional steepener type trades on the U.S. yield curve back in 2001 when nobody understood them. Now everyone understands them so there is not much juice left in it. The trade is where you buy a receiver swaption or a call on the oneyear interest rate one-year forward, and sell the same on the 10-year interest rate.There is a slight macro bias to this trade as it is a pure curve trade, which I consider more macro than RV. We built models of the whole yield curve out to 30 years to see what we thought the shape of the curve would be at any given rate level, how convex we thought the curve should be, why it should be that convex, and so on.

When you understand the process, then the whole out-of-control process is oddly very much in control. Because as a control freak, you’re always looking out ahead of you, you’re looking out ahead for trouble, and that’s exactly what you have to do in markets, is try to look forward. So much of market talk, market analysis, and trading is based on what’s happened in the past.“The yield curve is flat, therefore it tells you it’s a recession,” or “The yield curve is steep, which tells you there’s going to be a recovery.”Those types of historical examples are of very little value, so a control freak is always trying to look forward and trying to look ahead. What do you think differentiates a good analyst and a good trader? The good trader knows how to actively manage the risk and run a position. A good analyst should help find the trade or look for pitfalls in the trade.

Our risk is not limited to Barclays’ outstanding liabilities.We are actively managing risk and seeking a positive absolute return while being limited by the firm’s value at risk (VAR) model, regulatory capital limits, and balance sheet limits. We look to maximize current income for a given unit of risk. As a result, we tend to be in the front end of the yield curve as opposed to the back end because it’s better to roll one billion one-year notes for 10 years than to buy 100 million 10-year bonds ceteris paribus.The VAR would be the same if they had the same volatility but with the one-year notes, you get much more current income. By concentrating risk in the front end of the yield curve, the only thing that can really make me right or wrong is a central bank. A central bank has the ability to enhance or diminish my carry, and we want carry. Everything else is just noise. Our area of core expertise is the one-year, one-year interest rate forwards.

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A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber

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Plotting these payouts forms the well-known yield curve. Although the prices of the bonds and their respective yields vary as circumstances change—inflation, recession, war—each interest rate along the yield curve is flexibly but securely tethered to its neighboring rates in a way that can be described mathematically. CRUNCH TIME AT MORGAN STANLEY The job of the quants descending on Wall Street was to exploit the relationships along the yield curve, to develop mathematical models that would tease a higher return out of a bond portfolio or a bond trading operation than the green-eyeshade gang could. By the early 1980s, a number of other firms were already riding the number crunching wave. Marty Leibowitz at Salomon had built a strong team that was at the top of the heap for fixed income portfolio strategy and yield-curve trading.

Meanwhile, in Orange County, California, treasurer Robert Citron had been structuring trades with the help of friends at Merrill Lynch to borrow on the short end of the yield curve to finance positions in the usually higher-yielding intermediate-term rates. Citron’s strategy depended on short-term interest rates remaining relatively low when compared with medium-term interest rates. This they did in the early 1990s, so Citron’s yield curve bet made money and everyone was happy, with no questions asked. Even in early 1994, when his strategy began to go south, he survived an election that focused attention on his financial management, convincing voters that the criticisms were just so much politically motivated rhetoric. Then the Fed started raising rates in February 1994, and the yield curve started to move the wrong way. Orange County got crushed. A succession of hikes saddled Citron’s fund with losses of approximately \$1.7 billion, around 20 percent of its value.

The trade might have just happened to be getting cheaper at the same time interest rates were dropping. Markets either go up, go down, or stay the same, so if you are losing money in one there are bound to be others that will be losing at the same time. That does not mean the two are functionally linked. Another possibility was that the arb model did not pick up all of the factors affecting interest rates. The model was a proprietary yield curve model dubbed the “two plus” because it looked at the yield curve as two factors, plus a parameter to signal the effects of Federal Reserve policy shifts. The two-plus model was the citadel of intellectual capital for the group. It was a closely guarded secret, although, despite the group’s best efforts, it found its way to a number of other firms as talent was periodically bid away. 85 ccc_demon_077-096_ch05.qxd 2/13/07 A DEMON 1:45 PM OF Page 86 OUR OWN DESIGN The model was developed by Bill Krasker in the mid-1980s shortly after he came to Salomon from a brief stint teaching at Harvard.

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Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives by Satyajit Das

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P & G lost (from increases in the spread) if rates increased at either point in the yield curve. P & G had, knowingly or unknowingly, sold six month put options on the five year CMT rates and on the 30 year Treasury bond price. The premium received lowered the cost of borrowing. The structure had greater exposure to the five year CMT rate. The five year CMT rate was multiplied by 17.04 (in the simplified version of the formula) to convert the five year CMT rate into a price. After adjustment for this, the five year CMT was around four times the 30 year position in terms of amount and around two times in price sensitivity terms. Nero would have instantly recognized the leverage in the structure. The trade was very sensitive to interest rates. If rates increased across the yield curve, then the spread increased. If the yield curve flattened (the difference in rates between the five year CMT and the 30 year Treasury bond decreased), then the spread increased.

It was invented by traders in agricultural futures and is generally attributed to Holbrook Working. Swaps? They are simply a collection of forwards. There are subtle problems. Is the income on the asset a known known? In the case of shares, dividends are a known unknown and tend to cause heartache. Also we need a yield curve; that is, the interest rates for borrowing and lending for different dates. Interest rates are frequently not available for every maturity. Quants have elaborate models for creating ‘complete’ and ‘parsimonious’ yield curves. I have no idea why the yield curve has to be stingy, that is, parsimonious. The rocket scientists emphasize that this is important, citing Occam’s razor. Occam was a fourteenth century logician and Franciscan friar in the English county of Surrey. The principle states that: ‘Entities should not be multiplied unnecessarily.’

The arrangement was that OCM paid dollar LIBOR minus 40 basis points (that is, 0.40% pa),’ I explained. ‘Yes, yes. Cheaper cost. We get cheaper funding. Save 40 basis points. Cheap money.’ Budi’s excitement was palpable. ‘Bank advise us,’ Adewiko added quickly. ‘Bank give us detail presentation. They say dollar yield curve very steep. Get value from steep curve using arrears swap.’ Adewiko displayed surprising animation. ‘Bank know Greenspan. Play tennis with him.’ I must have looked surprised. ‘Bank advise us,’ Adewiko said gloomily, remembering the script. I referred to my notes. ‘Then, you terminated the arrears swap.’ ‘Take profit, take profit,’ Budi interrupted. ‘Dollar yield curve flatten. We take profit.’ DAS_C01.QXD 5/3/07 11:45 PM Page 7 P ro l o g u e 7 I could imagine what had happened. The dealers had played these guys for the I could imagine what had suckers they were. OCM had entered into happened.

The Concepts and Practice of Mathematical Finance by Mark S. Joshi

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Develop an analytic formula for its price if the forward rate follows geometric Brownian motion. 14 The pricing of exotic interest rate derivatives 14.1 Introduction The critical difference between modelling interest rate derivatives and equity/FX options is that an interest rate derivative is really a derivative of the yield curve and the yield curve is a one-dimensional object whereas the price of a stock or an FX rate is zero-dimensional. One might be tempted to think that as most movements of the yield curve are up and down it is unnecessary to model the one-dimensional behaviour. However, the yield curve can and does change shape over time, and we shall see that for certain options these changes are the source of most of the option's value. From time to time, yield curves also undergo qualitative changes in shape. For example, the UK yield curve changed from being upward-sloping to being humped in the early 1990s. The fact that we are modelling the changes of a curve makes life considerably more complicated but also much more interesting.

This is a distortion for a number of reasons but is nevertheless a reasonable way to proceed: in this section we explain why. There are, in fact, many yield curves for each currency whose levels depend on the riskiness of the instruments involved. We discuss the curves for sterling but the issues are essentially the same for the euro and US dollar curves. We will generally talk about constructing discount curves rather than yield curves, as the discount curve is just the price of a zero-coupon bond as a function of maturity which is what we generally want. On the other hand, the yield curve is a notional measure of the effective annual interest rate which we would receive for investing in such a bond. The yield curve is useful from a qualitative point of view as it strips out redundant information by converting everything to interest rates, but to work mathematically with the yield curve is simply annoying. With all the discount curves, one thing to bear in mind is that the theoretical curve will not actually represent a price one can obtain in the market.

Pricing a reversing pair is trivial: we just decompose it into a sum of two forward-rate agreements, which we already know how to price, and we are done. The interesting thing about the reversing pair is that its value is very insensitive to changes in the overall level of the yield curve. If interest rates go up by 1%, then we gain on the first forward-rate agreement but lose a similar amount on the 319 320 The pricing of exotic interest rate derivatives second. If, however, the shape of the yield curve changes so that the first rate goes down and the second rate goes up, then we lose on the first and lose on the second. Thus the value of the reverse contract reflects changes in the shape but not the level of the yield curve. In particular, the reverse contract is sensitive to the slope of the curve: a change in slope means money won or lost. We can extend the reverse contract to a double reverse contract by taking two reverse contracts over adjacent periods of time which go in opposite directions.

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What's Next?: Unconventional Wisdom on the Future of the World Economy by David Hale, Lyric Hughes Hale

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However, the hawkishness of Asia’s central banks also means that while OECD yield curves are steep and likely to remain so for the foreseeable future, Asian yield curves are now flattening rapidly all across the board. One amazing development is that the US (and German) yield curves have, since 2009, continued to shift lower in spite of the economic recovery. In Asia, we are seeing exactly the opposite, with yield curves flattening (in Malaysia, Indonesia, China, Thailand, Australia, etc.) or shifting higher (India), a divergence in trend that can only logically be explained by the differences in monetary policy. And, of course, this should logically have an impact on currency markets since steep yield curves often weaken currencies, while flat or inverted yield curves strengthen them (cash becomes harder to find, thereby inviting companies and individuals to repatriate capital from abroad, etc.).

Indeed, most Asian equity indices are typically comprised of 20–25 percent of exporting stocks (which should struggle as Asian currencies move higher) and 30–35 percent of Asian financials (for whom the flattening yield curves could prove a headwind). In other words, investors into Asia who decide to solely get exposure through benchmark ETFs are likely investing more than half of their money in what should prove to be “dead money.” Asia’s very different cyclical and policy outlook argues against investing in indices and instead for concentrating on the parts of the market that will benefit from the higher currencies and lower long-term interest rates. This of course includes long-dated Asian government bonds, high-dividend yield-paying stocks (which tend to always outperform when yield curves flatten and/or invert), utility stocks, local consumption stocks, and all the “stable growth” stocks, whether pharmaceuticals, consumer staples, software and tech stocks, and so on.

But what is interesting is that since 2009, stocks linked to local consumption, which one would expect to hold up decently as yield curves flatten, have done precisely that. In a sign of unprecedented maturity for the Chinese market, most of the sectors listed above are actually trading at higher levels than they did when the Chinese market peaked in August 2009! Figure 6.2 Outperformers since Market Peaked in August 2009 Source: Thomson Reuters The Second Challenge: A Structural Shift? We would be remiss to mention the outperformers in China’s current bear market without highlighting the sectors that have brought the index down. And here, one finds mostly the sectors one would expect to see penalized by a flatter yield curve, whether financials, steel and cement (since there should be less construction), mining, oil and gas, real estate, and so on.

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The Crisis of Crowding: Quant Copycats, Ugly Models, and the New Crash Normal by Ludwig B. Chincarini

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Box 2.2 Salomon Arb Group Interview Question Question: Your portfolio group strongly believes that the yield curve is going to flatten very soon. It could be that short-term rates will rise or long-term rates will fall or some combination of the two. Suppose also that you have three instruments available: a 30-year zero-coupon bond, a 1-year Treasury bill, and a cash account. Suppose the modified duration of the 30-year is 28 and the modified duration of the 1-year is 1. What strategy should you pursue to benefit from your beliefs? Suggested Solution: The investor would ideally like to have no interest-rate exposure, but take a view on the flattening yield curve. Thus, one would like to hedge parallel yield curve shifts, but take advantage of the nonparallel moves. One way to do this would be to buy long bonds and to short short-term notes (e.g., buy the 30-year Treasury and short the 1-year note).

PGAM, JWMP, and other funds had this trade on in 2008. They could implement it with government securities or swaps, but typically executed it with swaps. The trade is short the 30-year and 5-year areas of the yield curve and long the 10-year part of the curve. It’s constructed to eliminate interest-rate risk (duration neutral) and eliminate curve-slope risk. This position lost quite a bit in 2008. PGAM (and others) had a large position in this trade across a variety of different currencies. For PGAM, this was a hedge position, designed to diversify its holdings. This trade should have done well in a crisis, when the yield curve typically steepens and the 10- to 30-year part of the curve steepens more than the 5- to 10-year area. When monetary authorities lower interest rates, natural long-term debt buyers such as pension funds shy away from the long end of the curve, and higher risk aversion means that investors shorten durations, moving away from longer-dated securities.

A Primer for the Mathematics of Financial Engineering by Dan Stefanica

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BONDS. 72 which is equivalent to flB ~ -fly D. (2.59) B In other words, the percentage change in the price of the bond can be approximated by the duration of the bond multiplied by the parallel shift in the yield curve, with opposite sign. For very small parallel shifts in the yield curve, the approximation formula (2.59) is accurate. For larger parallel shifts, convexity is used to better capture the effect of the changes in the yield curve on the price of the bond. Definition 2.5. The convexity C of a bond with price B and yield y is 1 82 B C=B8 y 2· 2.8. NUMERICAL IMPLEMENTATION OF BOND MATHEMATICS 73 From (2.62) and (2.64), we conclude that y = r(O, T). In other words, the yield of a zero coupon bond is the same as the zero rate corresponding to the maturity of the bond. This explains why the zero rate curve r(O, t) is also called the yield curve. As expected, the duration of a zero coupon bond is equal to the maturity of the bond.

(J" Thus, the implied volatility approximate value is within 0.015% of the volatility used to price the call option, which is remarkably good accuracy. 0 I(J" - (J"imp,approxl CHAPTER 5. TAYLOR'S FORMULA. TAYLOR SERIES. 170 5.6 Connections between duration and convexity Recall from section 2.7 that bond duration measures the change in the price of a bond with respect to changes in the yield curve, while bond convexity measures the change of the duration of a bond with respect to changes in the yield curve, i.e., D= 1 82B C = B 8 y 2' 1 8B and B 8y (5.94) Also, recall that the value B of a bond with yield y paying cash-flows Ci and time t i , i = 1 : n, is B = 2:7=1 Cie-yti. To emphasize that the value of the bond is a function of its yield, we denote B by B (y), i.e., n B(y) = L Cie- yti . (5.95) 5.6. CONNECTIONS BETWEEN DURATION AND CONVEXITY 171 for the function f(x) = B(y), and for the points x = y + ~y and a = y: B(y + ~y) ~ B(y) + ~y B'(y) + (~y)2 BI/(y). (5.97) 2 Let ~B = B(y + ~y) - B(y).

For continuously compounded interest, the value at time t of B(O) currency units (e.g., U.S. dollars) is where exp(x) = eX. The value at time of B(t) currency units at time t is r(t) = lim ~ . B(t + dt) - B(t) = B'(t). dt-70 dt B(t) B(t) ----------------------2We note, and further explain this in section 2.7.1, that r(O,t) is the yield of a zero~ coupon bond with maturity t. The zero rate curve is also called the yield curve. r(T) dT), V t > 0; (2.39) from (2.39) is called the discount factor. r(O, t) = ~ t rt r(T) dT. (2.40) 10 In other words, the zero rate r(O, t) is the average of the instantaneous rate r (t) over the time interval [0, t] . If r( t) is continuous, then it is uniquely determined if the zero rate curve r(O, t) is known. From (2.40), we obtain that 1'r(T) dT = t ·r(O, t). (2.41) By differentiating (2.41) with respect to t, see, e.g., Lemma 1.2, we find that r(t) = r(O, t) (2.36) The instantaneous rate r(t) at time t is the rate of return of deposits made at time t and maturing at time t + dt, where dt is infinitesimally small, i.e., J~ r(T) dT) (-1' From (2.35) and (2.38), it follows that (2.35) ° B(O) = exp( -t r(O, t)) B(t)

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Wall Street: How It Works And for Whom by Doug Henwood

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For traders in global firms, the trading day begins in Tokyo; they "pass the book" at about 4 or 5 in the afternoon Tokyo time to London, where it is 7 or 8 in the morning, and pass it westwards at 1 PM to New York, where it is 8 in the morning. The trading day ends when New York closes. Treasury debt falls into three categories — bills, with maturities running from three months to one year; notes, one year to 10; and bonds, over 10. Most trading occurs in the two- to seven-year range. Shown on p. 26 are three "yield curves," plots of interest rates at various maturities. Normally the yield curve slopes gently upward, with interest rates rising as maturities lengthen. The reason for this is pretty simple — the longer a maturity, the more possibility there is for something to go wrong (inflation, financial panic, war), so investors require a sweeter return to tempt them into parting with their money. It's rare, however, that a bondholder would actually hold it to maturity; holding periods of weeks and hours are more common than years.

After a few months of declining rates — usually encouraged by the Federal Reserve — the stock market begins reponding to one of its favorite stimuli, lower rates. At business cycle peaks, the process is thrown into reverse gear, with interest rates steadily rising and the stock market flattening and finally sinking. Note that short-term rates move far more dramatically in both directions than long-term rates; the yield curve normally flattens or even goes negative as the economy approaches recession, then turns steeply positive as the slowdown ends. In fact, the yield curve "significantly outperforms other financial and macroeconomic indicators in predicting recessions two to six quarters ahead" (Estrella and Mishkin 1996) — and not only in the U.S., but in most of the rich industrial countries (Bernard and Gerlach 1996). It outdoes the stock market and composite leading indicators at this distance, with stocks and the composites having a forward vision of only about a single quarter.^ The bond market's fear of economic strength, and its love of weakness, used to be something of a Wall Street secret, at least until around 1993, when it became a more open secret.

In the early 1980s, the curve was negative, as Volcker's Fed drove rates up to record levels to kill inflation; in the early 1990s, it was quite steep, and Greenspan's Fed forced rates down to keep the financial system from imploding. It's likely that investors assumed that both extremes were not sustainable, and that short rates would return to more "normal" levels, which is why the longer end of the curve never got so carried away. 16% 14% 12% 10% 8% 6% 4% 2% 0% U.S. Treasury yield curves Jan 1997 Dec 1980 Oct 1992 3-mo 1 2 3 5 7 10 30 years to maturity mums Federal government bonds aren't the only kind, of course. Cities and states sell tax-exempt municipal bonds, which help retired dentists to shelter income and local governments to build sewers and subsidize shopping malls in the name of "industrial development." The muni bond market is smaller than the U.S. Treasury market — at the end of 1997, state and local governments had \$1.1 trillion in debt outstanding, compared to \$3.8 trillion for the Treasury and another \$2.7 trillion for government-related financial institutions — and trading is usually sleepy and uninteresting.

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Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander

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What is our best guess of data that are outside our range of observations? For instance, suppose the monthly spot rates from 1 month to 36 months are as shown in Figure I.5.6. How should we ‘extrapolate’ these data to obtain the spot rates up to 48 months? Since the yield curve is not a straight line, we need to fit a quadratic or higher order polynomial in order to extrapolate to the longer maturities. UK Short Spot Curve, 31 May 2002 5.50 5.25 5.00 4.75 4.50 4.25 4.00 3.75 3.50 0 4 m 8 m 12 m 16 m 20 m 24 m 28 m 32 m 36 m 40 m 44 m Figure I.5.6 Extrapolation of a yield curve I.5.3.1 Linear and Bilinear Interpolation Given two data points, x1 y1 and x2 y2 with x1 < x2 , linear interpolation gives the value of y at some point x ∈ x1 x2 as x − x1 y1 + x − x1 y2 y= 2 (I.5.11) x2 − x1 7 See http://en.wikipedia.org/wiki/Conjugate_gradient_method. 194 Quantitative Methods in Finance For an example of linear interpolation, consider the construction of a constant maturity 30-day futures series from traded futures.

If further data on 10-delta strangles and risk reversals are available, two more points can be added to the implied volatility smile: 10 = 50 + ST10 + 21 RR10 90 = 50 + ST10 − 21 RR10 (I.5.13) A more precise interpolation and extrapolation method is then to fit a quartic polynomial to the ATM, 25-delta and 10-delta data: this is left as an exercise to the reader. I.5.3.3 Cubic Splines: Application to Yield Curves Spline interpolation is a special type of piecewise polynomial interpolation that is usually more accurate than ordinary polynomial interpolation, even when the spline polynomials have quite low degree. In this section we consider cubic splines, since these are the lowest degree splines with attractive properties and are in use by many financial institutions, for instance for yield curve fitting and for volatility smile surface interpolation. We aim to interpolate a function fx using a cubic spline. First a series of knot points x1 xm are fixed. Then a cubic polynomial is fitted between consecutive knot points.

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The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money by Steven Drobny

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For example, we were ahead of the game in predicting that the yield curve would invert during the Greenspan conundrum era (see box on page 276). We realized that the world had switched from one of supply constriction in commodities to one of demand pull, and that a bull market in commodities (with the associated switch from backwardation into contango in commodity futures curves) would be reflected in an inverted yield curve. In a deflationary consumer environment with an inflationary real asset environment, the real asset inflationary aspects affect the short end of the curve, but the long end remains locked down. With productivity gains and no real inflation feeding through to core CPI—because core excludes food and energy—we bought bonds on the long end and put on yield curve inversion trades, which practically everyone scoffed at.

For an example of an asymmetric bet available today, look at Sweden. The central bank of Sweden, the Riksbank, has announced they do not plan to raise rates before June 2010. The one-year interest rate is currently 87 basis points, whereas the one-year interest rate in one year’s time is 2.52 percent, and the one-year interest rate in two years’ time is 3.50 percent. Right now, due to the steep upward sloping forward yield curve, you can buy receiver swaptions on one-year interest rates struck at 1.8 percent that will increase in value six times if one-year interest rates remain unchanged. This is not a bad payout for a world with very low rates because the global economy remains weak or stock markets have sold off again. These examples call for real money investment committees to widen their search for risk premia beyond the usual assets covered, and be willing to use option-like derivatives to purchase potential upside for a portfolio that works especially well during periods of crisis.

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The New Science of Asset Allocation: Risk Management in a Multi-Asset World by Thomas Schneeweis, Garry B. Crowder, Hossein Kazemi

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First, the signals must make economic sense; that is, one should be able to explain in simple terms why the model is able to forecast relative performance of various asset classes. For example, one of the most reliable signals about future performance of equities relative to fixed income instruments has been the slope of the yield curve. An upward sloping yield curve is generally consistent with a period of rising stock prices. The reason behind this is that an upward sloping yield curve is generally observed at the beginning of economic expansion. By examining the economic foundation of the signal, one can avoid using results that have resulted from data mining, that is, the generated signals that are not likely to perform well out of sample. So what are the economic foundations of a sensible signaling model of a TAA?

For many, risk is defined as any factor that may lead to the possibility of losing some or all of an investment as well as the magnitude and duration of that loss, while portfolio standard deviation centers on the probability of loss. However, for those who focus on risk measures beyond standard deviation of return, risk analysis at the portfolio level includes a wide range of analysis, including:9 34 ■ ■ ■ ■ ■ ■ THE NEW SCIENCE OF ASSET ALLOCATION Market Risk Analysis (changes in the yield curve or other marketrelated variables) on the performance of the portfolio as well as the primary asset sectors. Changes in factors such as interest rate movements, yield curve shifts, and other economic factors provide additional information on the macro sensitivity of the portfolio to economic factors. Performance Attribution: Attribution analysis, which measures the sources of return on an asset class as well as sector selection as a percentage of total return. Correlation Analysis: Correlation within an asset class (e.g., strategies, security sectors, geographical regions) and across asset classes.

How they could or should be priced in a single-factor or even a multi-factor model framework was explored, but a solution was rarely found.9 Option Pricing Models and Growth of Futures Markets We have spent a great deal of time focusing on the equity markets. During this period of market innovation, considerable research also centered on direct arbitrage relationships. Arbitrage relationships in capital and A Brief History of Asset Allocation 11 corporate markets were explored during the 1930s (forward interest rates implied in yield curve models)10 and in the 1950s (corporate dividend policy and debt policy). Similarly, cost of carry arbitrage models had long been the focal point of pricing in most futures based research. In the early 1970s Fischer Black and Myron Scholes (1973) and Merton (1973) developed a simple-to-use option pricing model based in part on arbitrage relationships between investment vehicles. Soon after, fundamental arbitrage between the relative prices of a put option (the right to sell) and a call option (the right to buy) formed a process to become known as the Put-Call Parity Model, which provided a means to explain easily the various ways options can be used to modify the underlying risk characteristics of existing portfolios.

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Asset and Risk Management: Risk Oriented Finance by Louis Esch, Robert Kieffer, Thierry Lopez

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If we describe P (s) as the issue price of a zero-coupon bond with maturity s and R(s) as the rate observed on the market at moment 0 for this type of security, called the spot rate, these two values are clearly linked by the relation P (s) = (1 + R(s))−s . The value R(s), for all the values of s > 0, constitutes the term interest-rate structure at moment 0 and the graph for this function is termed the yield curve. The most natural direction of the yield curve is of course upwards; the investor should gain more if he invests over a longer period. This, however, is not always the case; in practice we frequently see ﬂat curves (constant R(s) value) as well as increasing curves, as well as inverted curves (decreasing R(s) value) and humped curves (see Figure 4.4). R(s) R(s) s R(s) s R(s) s s Figure 4.4 Interest rate curves 13 A detailed presentation of these concepts can be found in Bisière C., La Structure par Terme des Taux d’intérêt, Presses Universitaires de France, 1997. 14 This justiﬁes the title of this present section, which mentions ‘interest rates’ and not bonds. 130 Asset and Risk Management 4.3.2 Static interest rate structure The static models examine the structure of interest rates at a ﬁxed moment, which we will term 0, and deal with a zero-coupon bond that gives rise to a repayment of 1, which is not a restriction.

xix xix xxi PART I THE MASSIVE CHANGES IN THE WORLD OF FINANCE Introduction 1 The Regulatory Context 1.1 Precautionary surveillance 1.2 The Basle Committee 1.2.1 General information 1.2.2 Basle II and the philosophy of operational risk 1.3 Accounting standards 1.3.1 Standard-setting organisations 1.3.2 The IASB 2 Changes in Financial Risk Management 2.1 Deﬁnitions 2.1.1 Typology of risks 2.1.2 Risk management methodology 2.2 Changes in ﬁnancial risk management 2.2.1 Towards an integrated risk management 2.2.2 The ‘cost’ of risk management 2.3 A new risk-return world 2.3.1 Towards a minimisation of risk for an anticipated return 2.3.2 Theoretical formalisation 1 2 3 3 3 3 5 9 9 9 11 11 11 19 21 21 25 26 26 26 vi Contents PART II EVALUATING FINANCIAL ASSETS Introduction 3 4 29 30 Equities 3.1 The basics 3.1.1 Return and risk 3.1.2 Market efﬁciency 3.1.3 Equity valuation models 3.2 Portfolio diversiﬁcation and management 3.2.1 Principles of diversiﬁcation 3.2.2 Diversiﬁcation and portfolio size 3.2.3 Markowitz model and critical line algorithm 3.2.4 Sharpe’s simple index model 3.2.5 Model with risk-free security 3.2.6 The Elton, Gruber and Padberg method of portfolio management 3.2.7 Utility theory and optimal portfolio selection 3.2.8 The market model 3.3 Model of ﬁnancial asset equilibrium and applications 3.3.1 Capital asset pricing model 3.3.2 Arbitrage pricing theory 3.3.3 Performance evaluation 3.3.4 Equity portfolio management strategies 3.4 Equity dynamic models 3.4.1 Deterministic models 3.4.2 Stochastic models 35 35 35 44 48 51 51 55 56 69 75 79 85 91 93 93 97 99 103 108 108 109 Bonds 4.1 Characteristics and valuation 4.1.1 Deﬁnitions 4.1.2 Return on bonds 4.1.3 Valuing a bond 4.2 Bonds and ﬁnancial risk 4.2.1 Sources of risk 4.2.2 Duration 4.2.3 Convexity 4.3 Deterministic structure of interest rates 4.3.1 Yield curves 4.3.2 Static interest rate structure 4.3.3 Dynamic interest rate structure 4.3.4 Deterministic model and stochastic model 4.4 Bond portfolio management strategies 4.4.1 Passive strategy: immunisation 4.4.2 Active strategy 4.5 Stochastic bond dynamic models 4.5.1 Arbitrage models with one state variable 4.5.2 The Vasicek model 115 115 115 116 119 119 119 121 127 129 129 130 132 134 135 135 137 138 139 142 Contents 4.5.3 The Cox, Ingersoll and Ross model 4.5.4 Stochastic duration 5 Options 5.1 Deﬁnitions 5.1.1 Characteristics 5.1.2 Use 5.2 Value of an option 5.2.1 Intrinsic value and time value 5.2.2 Volatility 5.2.3 Sensitivity parameters 5.2.4 General properties 5.3 Valuation models 5.3.1 Binomial model for equity options 5.3.2 Black and Scholes model for equity options 5.3.3 Other models of valuation 5.4 Strategies on options 5.4.1 Simple strategies 5.4.2 More complex strategies PART III GENERAL THEORY OF VaR Introduction vii 145 147 149 149 149 150 153 153 154 155 157 160 162 168 174 175 175 175 179 180 6 Theory of VaR 6.1 The concept of ‘risk per share’ 6.1.1 Standard measurement of risk linked to ﬁnancial products 6.1.2 Problems with these approaches to risk 6.1.3 Generalising the concept of ‘risk’ 6.2 VaR for a single asset 6.2.1 Value at Risk 6.2.2 Case of a normal distribution 6.3 VaR for a portfolio 6.3.1 General results 6.3.2 Components of the VaR of a portfolio 6.3.3 Incremental VaR 181 181 181 181 184 185 185 188 190 190 193 195 7 VaR Estimation Techniques 7.1 General questions in estimating VaR 7.1.1 The problem of estimation 7.1.2 Typology of estimation methods 7.2 Estimated variance–covariance matrix method 7.2.1 Identifying cash ﬂows in ﬁnancial assets 7.2.2 Mapping cashﬂows with standard maturity dates 7.2.3 Calculating VaR 7.3 Monte Carlo simulation 7.3.1 The Monte Carlo method and probability theory 7.3.2 Estimation method 199 199 199 200 202 203 205 209 216 216 218 viii Contents 7.4 Historical simulation 7.4.1 Basic methodology 7.4.2 The contribution of extreme value theory 7.5 Advantages and drawbacks 7.5.1 The theoretical viewpoint 7.5.2 The practical viewpoint 7.5.3 Synthesis 8 Setting Up a VaR Methodology 8.1 Putting together the database 8.1.1 Which data should be chosen?

As the second-degree term C(r)2 /2 of the approximation formula is always positive, it therefore appears that when one has to choose between two bonds with the same return (actuarial rate) and duration, it will be preferable to choose the one with Bonds 129 the greater convexity regardless of the direction of the potential variation in the rate of return. 4.3 DETERMINISTIC STRUCTURE OF INTEREST RATES13 4.3.1 Yield curves The actuarial rate at the issue of a bond, as deﬁned in Section 4.1.2 is obviously a particular characteristic to the security in question. The rate will vary from one bond to another, depending mainly on the quality of the issuer (assessed using the ratings issued by public rating companies) and the maturity of the security. The ﬁrst factor is of course very difﬁcult to model, and we will not be taking account of it, assuming throughout this section 4.3 that we are dealing with a public issuer who does not carry any risk of default.

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Derivatives Markets by David Goldenberg

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We are in the world of interest-rate swaps which is a LIBOR world. So we need the current (t=0) spot LIBOR yield curve. It gives the rates to be applied to zero-coupon Eurobonds for alternative maturities. Assume that it is as in Table 8.8. Our long position in the ﬁxed-rate bond can be decomposed as the sum of three zero-coupon bonds, and one NP repayment bond as indicated in the multi-level cash ﬂow diagram, Figure 8.15. 304 TRADING STRUCTURES BASED ON FORWARD CONTRACTS TABLE 8.8 LIBOR Yield Curve (Spot Rates) Maturity Zero-Coupon Bond Yields 1 year 6.0% 2 years 6.5% 3 years 7.0% FIGURE 8.15 The Implicit Fixed-Rate Bond in a Swap, Written in Terms of Zero-Coupon Bonds Bond 4 NP Bond 3 R * NP Bond 2 R * NP Bond 1 R * NP t=0 1.0 2.0 3.0 = T The LIBOR zero-yield curve says that the appropriate discount rate to apply to the cash ﬂow from Bond 1 is 6.00%, the appropriate discount rate to apply to the cash ﬂow from Bond 2 is 6.5%, and the appropriate discount rate to apply to the cash ﬂows from Bond 3 and from Bond 4 is 7.0%.

The weights add up to 1.0 and are the current prices of 1, 2, and 3-year unit discount LIBOR bonds each expressed as a percentage of the sum of the values of those bonds, R= B0′ ,1 B0′ ,1 + B0′ ,2 + B0′ ,3 + * LIBOR1,0 + B0′ ,3 B0′ ,1 + B0′ ,2 + B0′ ,3 B0′ ,2 B0′ ,1 + B0′ ,2 + B0′ ,3 * IFR1,1 * IFR1,2 Interpretation 2 This representation is equivalent to that given in section 8.9.4 of the par swap rate as 1.0 − B0′ ,3 B0′ ,1 + B0′ ,2 + B0′ ,3 To establish this equivalence, all we have to do is to show that, 1.0 − B0′ ,3 = LIBOR1,0 * B0′ ,1 + IFR1,1 * B0′ ,2 + IFR1,2 * B0′ ,3 Re-write LIBOR1,0 as r1 ,where r1 is the LIBOR zero yield curve rate used to price B′0,1, r2 is the LIBOR zero yield curve rate used to price B′0,2, and r3 is the LIBOR zero yield curve rate used to price B′0,3. Using the deﬁnitions of the IFRs we obtain that the right hand side of the required equality, LIBOR1,0*(B′0,1)+[IFR1,1]*(B′0,2)+[IFR1,2]*(B′0,3), is equal to, ⎤ ⎛ 1 ⎞ ⎡(1 + r )2 ⎤ ⎛ 1 ⎞ ⎡ (1 + r )3 r1 3 2 +⎢ − 1.0⎥ * ⎜ − 1 . 0 ⎟ ⎟+ ⎢ ⎥* ⎜ 2 2 3 (1 + r1 ) ⎣ (1 + r1 ) ⎦ ⎝ (1 + r2 ) ⎠ ⎣(1 + r2 ) ⎦ ⎝ (1 + r3 ) ⎠ = ⎡ 1 r1 1 ⎤ ⎡ 1 1 ⎤ +⎢ − + − ⎢ ⎥ ⎥ (1 + r1 ) ⎣(1 + r1 ) (1 + r2 )2 ⎦ ⎣(1 + r2 )2 (1 + r3 )3 ⎦ = r1 1 1 + − (1 + r1 ) (1 + r1 ) (1 + r3 )3 = r1 + 1 1 − (1 + r1 ) (1 + r3 )3 = 1 − B0′ ,3 314 TRADING STRUCTURES BASED ON FORWARD CONTRACTS This is what we wanted to demonstrate because it is the left side of 1.0–B′0,3=LIBOR1,0*B′0,1+IFR1,1*B′0,2+IFR1,2*B′0,3 Interpretation 3 There is a third useful interpretation of the par swap rate that follows from basic bond ﬁnance.

The IFR1,1 is given by, IFR1,1 = (1 + LIBOR 2,0 )2 (1 + LIBOR1,0 ) − 1.0 Similarly, the Implied Forward Rate on one-year loans two years from today, denoted by IFR1,2, is deﬁned as the artiﬁcial rate such that, (1 + LIBOR 3,0 )3 = (1 + LIBOR 2,0 )2 (1 + IFR1,2 ) or IFR1,2 = (1 + LIBOR 3,0 )3 (1 + LIBOR 2,0 )2 − 1.0 Implied Forward Rates are obtained from the LIBOR yield curve, or from the prices of Eurodollar futures contracts. For example, based on the LIBOR yield curve given in Table 8.8, we can imply 1-year forward rates one year from today and two years from today. n CONCEPT CHECK 6 a. Calculate, based upon Table 8.8, the IFR for 1-year loans one year from today, IFR1,1. b. Also, calculate the IFR for 1-year loans two years from today, IFR1,2. Implied Forward Rates are useful because, under certain assumptions, they are unbiased estimates of future 1-year LIBOR.

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Investing Demystified: How to Invest Without Speculation and Sleepless Nights by Lars Kroijer

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That being the case, although this risk can also lead to you making money it is not a risk you get compensated for taking in the form of higher expected returns. 7 By adding other safe bonds to your minimal risk bonds you are also diversifying your interest rate risk away from that of just one currency (you have exposure to a couple of different yield curves), but for the purposes of keeping the portfolio simple I don’t think this diversification is worth the added complexity and currency risk of those bonds. 8 We have left out the large and broad market of financial institution debt. This includes interbank debt, but also various obligations issued by financial institutions. This is less of a transparent market for the rational investor and someone with the broad exposures discussed in this book already have a lot of the same exposures via the existing bond and equity positions in their portfolio. 9 Occasionally the yield curve is inverted (long-term yields are lower than short-term ones). This is when the market is expecting the interest rate to drop in the future. 10 The straight line between minimal risk, point T, and up to the right assumes that the investor can borrow at the same rate as the minimal risk bond.

As a reward for taking the interest rate risk associated with the longer-term bonds they typically yield more than the short-term bonds, as illustrated in Figure 4.1.2 So if you need a product that will not lose money over the next year, pick short-term bonds to match that profile. However, if you – like most people – are after a product that will provide a secure investment further into the future, pick longer-term bonds and accept the attendant interest-rate risk. Figure 4.1 The typical bond yield curve You should therefore consider the time horizon of your portfolio and select the maturity of your minimal risk bonds accordingly. If you are matching needs far in the future (like your retirement spending) there is certainly merit in adding long-term bonds or even inflation-protected bonds (see below) to your portfolio. Long-term bonds compensate investors for interest-rate risks by offering higher yields and you have the further benefit of matching the timing of your assets and needs.

You will have to accept interest rate risk even if you avoid inflation risk by buying inflation-adjusted bonds. 1 For those who don’t think government bonds can default I would encourage you to read This Time is Different: Eight Centuries of Financial Folly by Carmen Reinhart and Kenneth Rogoff (Princeton University Press, 2011). The authors make a mockery of the belief that governments rarely default and that we are somehow now protected from the catastrophic financial events of the past. 2 There are cases where the yield curve is reversed and shorter-term bonds yield more than longer-term ones, but these cases are less frequent. 3 Imagine the scenario where you want to hold one-month government bonds. Tomorrow the bonds are no longer one-month to maturity, but 29 days. Is this ok? How about 2 days hence? How much you are willing for the maturity to deviate from exactly 30 days is up to you, but in reality there is a trading and administrative cost associated with trading bonds.

How I Became a Quant: Insights From 25 of Wall Street's Elite by Richard R. Lindsey, Barry Schachter

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If the men on the trading floor had had any idea that this activity would evolve from a small P&L source to a major business, or be as “sexy” as the M&A business, then I would have not been given the chance. We hired an academic to build a pricing model. The model provided Black-Scholes type prices, but with a couple of simplifications. To be able to obtain real-time prices at the beginning of each day, the head trader (me) had to select the values to assign to each of two parameters. The first parameter was yield-curve shape, and the choices of parameter values were “relatively flat” and “relatively steep.” The second parameter was spot volatility (no JWPR007-Lindsey 90 May 28, 2007 15:39 h ow i b e cam e a quant vol surface here!). The choices were “relatively high” and “relatively low.” This model was more sophisticated at the time than models used elsewhere in the bank and among our competitors for cap pricing.

I believe that I was the first in the industry to answer this question with the delta-gamma approach (see Wilson (1994b)), based on the observation that a quadratic form of normal variables is distributed as the sum of noncentral chi-squared variables for which numerical solutions are available. How many independent factors are practically required to capture the risk of a multicurrency fixed income trading book? The dimensionality of VaR calculations for a global trading book quickly becomes too large to be calculated efficiently, especially if each point on the yield curve is modeled separately. A logical place to look for a reduction in the dimensionality was therefore in the modeling of multicurrency interest rates. My answer (see Wilson (1994a)) compared both factor analysis and eigenvalue decompositions of multicurrency term structures and attempted to characterize the required number of factors and the stability of the parameter estimates over time. What happens to the tails of our VaR calculations if we have only estimates of volatilities and correlations and not their exact values?

It was an exciting project, and he had put together a strong team for the job. I guess it was for most of us the first time that we had been involved in building what amounted to a whole derivatives pricing JWPR007-Lindsey 174 May 18, 2007 21:24 h ow i b e cam e a quant system from scratch. Everything had to be coded from the ground up: ISDA day counting and accrual conventions, holiday calendar handling, volatility quotation conventions, settlement delays, yield curve stripping, simple analytical convexity corrections, a whole host of simple option analytics (the usual suspects: baskets, barriers, etc.), number generators, multithreaded Monte Carlo simulation, variance reduction techniques, multidimensional tree solvers for diffusion-based models, general finite differencing solvers for jump-diffusion based models, multifactor HullWhite models, LIBOR market models with global calibration, Bermudan Monte Carlo techniques, serialization of any of model or product objects for possible storage or distribution, distributed valuation framework, etc.

All About Asset Allocation, Second Edition by Richard Ferri

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Most of the time, a 10-year Treasury note has had a higher yield than the 1-year T-bill. These are periods with a “normal” yield curve, so called because under normal conditions short-term T-bills are expected to yield less than intermediate-term Treasury notes. A “flat” yield curve occurs when the yield on T-bills and T-notes is the same. If T-bills have a higher yield than Treasury notes, this is known as an “inverted” yield curve. There is a school of thought that believes that when the curve is inverted, the economy is slowing and the stock market will likely go down. There appears to be some support for this theory, although CHAPTER 8 152 FIGURE 8-3 Treasury Term Spread, 1-Year T-Bills, and 10-Year Treasury Notes 4.0 Normal yield curve (long-term rates higher than short-term rates) 3.0 Yield difference 2.0 1.0 0.0 Feb. 89 ⫺1.0 Apr. 00 Jan. 06 ⫺2.0 ⫺3.0 Dec-10 Dec-05 Dec-00 Dec-95 Dec-90 Dec-85 Dec-75 Dec-70 Dec-65 Dec-60 Dec-55 ⫺4.0 Dec-80 Inverted yield curve (short-term rates higher than long-term rates) the timing is sketchy at best.

There appears to be some support for this theory, although CHAPTER 8 152 FIGURE 8-3 Treasury Term Spread, 1-Year T-Bills, and 10-Year Treasury Notes 4.0 Normal yield curve (long-term rates higher than short-term rates) 3.0 Yield difference 2.0 1.0 0.0 Feb. 89 ⫺1.0 Apr. 00 Jan. 06 ⫺2.0 ⫺3.0 Dec-10 Dec-05 Dec-00 Dec-95 Dec-90 Dec-85 Dec-75 Dec-70 Dec-65 Dec-60 Dec-55 ⫺4.0 Dec-80 Inverted yield curve (short-term rates higher than long-term rates) the timing is sketchy at best. Sometimes the curve becomes inverted a couple of years before stocks correct during a recession, and sometimes it inverts after the market has already started to pull back. CREDIT RISK Credit risk is illustrated on the vertical axis in Figure 8-1. Bonds that have more credit risk should pay a higher interest rate than bonds with low credit risk. Table 8-1 shows how three different credit-rating agencies categorize bonds by creditworthiness. Investment-grade bonds have an S&P and Fitch rating of BBB or higher and a Moody’s rating of Baa or higher. Direct and indirect obligations of a government agency, such as Treasury bonds and federal agency bonds, have the least credit risk and yield the least.

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Hedge Fund Market Wizards by Jack D. Schwager

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For example, after liquidity dried up in the money markets in August 2007, O’Shea expected rates to be cut. Instead of expressing this trade idea only through long short-term interest rate instrument positions, O’Shea also implemented the trade as a yield curve spread: long short-term rate instruments/short long-term rate instruments. His reasoning was that the yield curve at the time was relatively flat, implying that a rate decline would most likely be concentrated on the short-term end of the yield curve. If, however, rates went up, the flat yield curve implied that long-term rates should go up at least as much as short-term rates and probably more. The yield curve spread provided most of the profit potential with only a fraction of the risk. In essence, it provided a much better return-to-risk ratio than a straight long position in short-term rates alone.

What did Greenspan do after the 1987 crash? He injected liquidity. Right. Add liquidity and cut rates. That was the policy response we expected. So that was our trade at the time: Rates would go lower and the yield curve would steepen. So you put on long positions in short-term rate instruments? Yes, but we coupled it with short positions on the long end because it was a better risk/reward trade. The yield curve was flat at the time and priced to stay flat. The market wasn’t pricing in any risk that there would be a major problem. So you bet on lower short-term rates through a yield curve spread rather than a long position in short-term rate instruments because you felt it was a safer way to do the trade. Yes, because what I am trying to do is find trades that won’t lose much money even if I am wrong.

Bull markets ignore any bad news, and any good news is a reason for a further rally. Can you think of an example where the market response to the news was counter to what you expected and impacted your trade? In 2009, I was long 2-year notes/short 10-year notes one-year forward, looking for the yield curve to widen, and a lot of news came out that I thought would hurt me. One news item after another, I saw the screen and thought, I am going to get screwed in this position. But I didn’t. After a number of these instances, I thought, the yield curve just can’t get any flatter no matter what comes out. So I quadrupled my position. It was a great trade. The spread went from 25 basis points to 210, although I got out at 110. Any other examples where the market action was the catalyst for a trade? When the whole debt fiasco in Europe started to unfold, the euro plunged from 1.45 to 1.19.

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Valuation: Measuring and Managing the Value of Companies by Tim Koller, McKinsey, Company Inc., Marc Goedhart, David Wessels, Barbara Schwimmer, Franziska Manoury

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In practice, forward rate curves derived from the yield curve will rarely follow the smooth patterns of Exhibit 34.11. Small irregularities in the current yield curve can lead to large spikes and dents in the forward rate curves, which 776 BANKS EXHIBIT 34.11 Yield Curve and Future Interest Rates Interest rate, % Current yield curve Forward 1-year rates Forward 3-year rates Forward 5-year rates Forward 10-year rates 6 5 4 3 2 1 0 2015 2020 2025 2030 2035 2040 would produce large fluctuations in net interest income forecasts. As a practical solution, use the following procedure. First, obtain the forward one-year interest rates from the current yield curve. Then smooth these forward oneyear rates to even out the spikes and dents arising from irregularities in the yield curve. Finally, derive the two-year and longer-maturity forward rates from the smoothed forward one-year interest rates.

Following this theory, it is necessary to ensure that our expectations for interest rates in future years are consistent with the current yield curve. Exhibit 34.11 shows an example of a set of future one-, three-, five-, and ten-year interest rates that are consistent with the yield curve as of 2014. The forecasts for a bank’s interest income and expenses should be based on these forward rates, which constitute the matched-opportunity rates for the different product lines. For example, if the bank’s deposits have a three-year maturity on average, you should use the interest rates from the forward three-year interest rate curve minus an expected spread for the bank to forecast the expected interest rates on deposits in your DCF model. The rates are all derived from the current yield curve. To illustrate, the expected three-year interest rate in 2016 follows from the current three- and six-year yield: [ r2016−2019 ] 13 [ ] 13 (1 + 2.82%)6 = −1 = − 1 = 4.0% (1 + Y2016 )3 (1 + 1.66%)3 (1 + Y2019 )6 where r2016–2019 is the expected three-year interest rate as of 2016, Y2016 is the current three-year interest rate, and Y2019 is the current six-year interest rate.

Suppose general inflation is expected to be 4 percent and unit prices for the company’s products are expected to increase at one percentage point less than general inflation. Overall, the company’s prices would be expected to increase at 3 percent per year. If we assume a 3 percent annual increase in units sold, we would forecast 6.1 percent annual revenue growth (1.03 × 1.03 – 1). 14 U.S. Department of the Treasury, Daily Treasury Yield Curve Rates, November 24, 2014. 254 FORECASTING PERFORMANCE EXHIBIT 11.14 Expected Inflation vs. Growth in the Consumer Price Index % 6 5 4 Implicit expected inﬂation as derived using 10-year U.S. TIPS bonds 3 2 Annualized growth in the consumer price index 1 0 2000 2002 2004 2006 2008 2010 1 2012 2014 –1 –2 –3 Source: Bloomberg and the Federal Reserve Bank of St. Louis. higher expectations, as the market predicted a stronger recovery than actually occurred.

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After the Music Stopped: The Financial Crisis, the Response, and the Work Ahead by Alan S. Blinder

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The Fed’s hawks went along kicking and screaming (internally). The dire outlook was overwhelming their usual zeal for tighter money. The good news was that Bernanke and the FOMC doves were firmly in control. The bad news was that the Fed was nearly out of bullets. Eyes would now turn to fiscal policy. THE EXPECTATIONS THEORY OF THE YIELD CURVE The idea that intermediate-and long-term interest rates depend on beliefs (or expectations) about what overnight interest rates (like the federal funds rate) will be in the future is called the expectations theory of the yield curve. It is the basis for Federal Reserve policies that make implicit or explicit commitments about future interest rates. Here’s a simple example: If one-day money costs 2 percent (annualized) today, and the market expects one-day money to cost 3 percent tomorrow, how much should two-day money cost today?

There were three main candidates: The first was more conventional open-market policy. While the federal funds rate was already down to a superlow 1 percent, the FOMC could lower it still further. The markets thought a 50-basis-point cut most likely. Second, the Committee could try to reduce longer-term interest rates by committing to holding its overnight rate low for a long time. Some called that “open-mouth policy.” The idea is based on the expectations theory of the yield curve, which is explained in the accompanying box. Third, the Fed could keep on expanding its balance sheet, which had already soared from \$924 billion the week before Lehman to \$2,262 billion on December 11. Which option would the Fed choose? It turned out to be all of the above. In the FOMC’s own language, it decided to use “all available tools” to fight the recession. Of course, Bernanke was inventing tools as he went along.

See European Central Bank (ECB) euro, problem of, 418–19, 425–26 financial leadership countries, 417–19 Greece as problem, 380–83, 413–18 as sovereign crisis, 169, 409, 412, 419, 425–26 U.S. economy, impact on, 381–83, 409 European Stability Mechanism, 426 Evans, Charles, 383–84 Excess reserves, reducing rate on, 246–47, 386 Exchange Stabilization Fund (ESF), 146, 180 Exchange-traded derivatives, 61, 281, 436 Executive compensation, 81–84 AIG bonuses after bailout, 137–38, 297 Dodd-Frank provisions, 309 golden parachute to O’Neal (Stan), 152 regulatory efforts, rejection of, 83–84 regulatory needs for, 283–85, 297, 437 risk-based rewards, 81–83, 284 TARP restrictions, 183, 188–91, 202 Exit strategy of Fed, 367–79 European crisis and delay of, 381–83, 409 excess reserves, dealing with, 369–72, 378, 431 and inflation level, 374–75, 378 interest rates, normalizing, 372–74, 378, 431 timing of, 374–75, 378–79 unconventional policy, continuation of, 384–86 Expectations theory of yield curve, 221–23 Fannie Mae/Freddie Mac, 115–19 competitive edge of, 116 conservatorship, 118–19, 287n federal safety net for, 115–16, 118 financial crisis, role in, 117–18 functions of, 115, 324 future view for, 287–88, 297–98, 309 mortgage default, low rate, 72 QE1 asset-purchase, 206–7, 251 in shadow banking system, 60 and subprime mortgages, 71–72, 116–17 vulnerabilities of (2007), 116–17 Farkas, Lee, 355 Federal budget deficit, 387–408 and Bush administration actions, 388–91, 394 and creditworthiness of U.S., 395–96, 400, 401 economic danger of, 395 future view for, 400–408, 430 growth in dollars, 387–88, 392–93 and health care costs, 390, 398, 404, 406 national debt ceiling, raising, 400 Obama attempts to address, 396–400 public opinion of, 393–95 and recovery programs, 234–36, 350–51, 359–61, 392–93 Simpson-Bowles plan, 397, 401–2, 405–8, 430 Federal Deposit Insurance Act (1991), 162 Federal Deposit Insurance Corporation (FDIC) history of, 144, 146–47 marketable debt guarantee, 161–62 money market funds, not insured, 144 receivership authority of, 298, 306, 310 regulatory failure of, 58 systemic risk exception invoked, 162–63 Temporary Liquidity Guarantee Program (TLGP), 161–62, 208, 242 Federal Deposit Insurance Corporation Improvement Act, 306 Federal Housing Finance Agency (FHFA), 118 home price index, 17–18, 18n, 34 Federal Open Market Committee (FOMC) communication problems of, 373–74 funds rate cuts (2007), 96–97, 172 funds rate cuts (2008), 221–23, 244 growth versus exit actions (2011), 381–85 initial response to crisis, 91–93, 95, 171 landmark meeting (2008), 221–23 Operation Twist, 383–84 Federal Reserve anti-Fed sentiments, 276–77, 293–94, 348–49, 352–53, 358–59 bailouts, 105–19, 136–40 balance sheet (2007–2011), 368–72, 431 and bond bubble burst, 44–45 chairman during crisis.

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The Only Game in Town: Central Banks, Instability, and Avoiding the Next Collapse by Mohamed A. El-Erian

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El-Erian, “What We Need from the IMF/World Bank Meetings,” Financial Times, October 6, 2013, http://blogs.ft.com/the-a-list/2013/10/06/what-we-need-from-the-imfworld-bank-meetings/. CHAPTER 23: THE BELLY OF THE DISTRIBUTION OF POTENTIAL OUTCOMES 1. “The World in 2015,” Economist, December 2014. 2. Michael J. Casey, “Flattening Yield Curve Latest Complication for Fed,” Wall Street Journal, April 12, 2015, http://blogs.wsj.com/moneybeat/2015/04/12/flattening-yield-curve-latest-complication-for-fed/?mod=WSJ_hps_MIDDLE_Video_Third. 3. Mohamed A. El-Erian, “The Instability in Central Bank Divergence,” Financial Times, February 26, 2014, http://blogs.ft.com/the-a-list/2014/02/26/the-instability-in-central-bank-divergence/. CHAPTER 24: A WORLD OF GREATER DIVERGENCE (I): MULTI-SPEED GROWTH 1.

In the span of a few weeks, the Swiss National Bank would suddenly dismantle a key element of its exchange rate system, and do so in what proved to be an incredibly disruptive manner for markets; Singapore would alter its own exchange rate system; and Denmark would declare that it would refrain from issuing any more government bonds. The next few weeks would also witness a market collapse in government yields, including negative levels all the way out to the nine-year point in the German yield curve and the benchmark ten-year bond there trading at just five basis points (that is, 0.05 percent). They would see investors rush to buy many newly issued bonds directly from some European governments, agreeing to pay (rather than receive) interest income for doing so. And they would witness large banks actively discourage depositors from keeping money with them. These were just some of the many unthinkables.

This discomfort relates to the growing difficulties that both national economies and the global system face (and will face) in reconciling in a relatively stable manner five trends that I believe will become more pronounced in the period ahead—namely: • Multi-speed growth; • Multi-track central banking policies; • Growing pricing anomalies, from negative nominal interest rates to the unusual position of having “the U.S. yield curve…now shaped as much by foreign monetary policy as the Fed’s”;2 • Non-economic headwinds; and • The impact of certain disruptive innovations going macro. Together they suggest that, as opposed to the consensus view of a relatively stable low-growth world, we are looking at increasing economic and policy divergences among countries, which, together with prospects for national political and geopolitical disruptions, will make the belly of the distribution a lot less stable.

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Financial Modelling in Python by Shayne Fletcher, Christopher Gardner

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+ccy+".hw" mr = env.retrieve constant(key) if mr <> 0: term var *= (math.exp(2.0*mr*t)-1.0)/(2.0*mr) else: term var *= t return math.sqrt(term var) The Hull–White Model 101 def local vol(self, t, T, ccy, env): assert t <= T key = "cv.mr."+ccy+".hw" mr = env.retrieve constant(key) return math.exp(-mr*t)-math.exp(-mr*T) The requestor class uses the class environment implemented in the ppf.market.environment module. The purpose of this class is to provide access to market data objects such as yield curves, volatility surfaces, correlation surfaces, etc. Refer to section 5.3 for the details. The following code snippets illustrate how to construct a requestor and make a request for a discount factor and a term volatility: >>> import math >>> import ppf.market >>> from ppf.math.interpolation import loglinear >>> times = [0.0, 0.5, 1.0, 1.5, 2.0] >>> factors = [math.exp(-0.05*t) for t in times] >>> c = ppf.market.curve(times, factors, loglinear) >>> env = ppf.market.environment() >>> key = "zc.disc.eur" >>> env.add curve(key, c) >>> r = requestor() >>> t = 1.5 >>> print r.discount factor(t, "eur", env) 0.927743486329 >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> 0.1 import math import ppf.market from numpy import zeros expiries = [0.1, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0] tenors = [0, 90] values = zeros((8, 2)) values.fill(0.04) surf = ppf.market.surface(expiries, tenors, values) env = ppf.market.environment() key = "ve.term.eur.hw" env.add surface(key, surf) key = "cv.mr.eur.hw" env.add constant(key, 0.0) r = requestor() t = 0.25 print r.term vol(t, "eur", env) 8.1.2 State When pricing a financia instrument we frequently need to know about the state of the world – the world being both define and modelled by the chosen model.

The explanatory variables are then returned to the client. class cle exercise: def init (self, l): self. leg = l 116 Financial Modelling in Python def num explanatory variables(self): return 2 def call (self, t, fill, state, requestor, env): # harvest active flows all flows = self. leg.flows() flows = [] for flow in all flows: accrual start days = env.relative date( flow.accrual start date()) if accrual start days >= t*365.0: flows.append(flow) if len(flows) < 1: raise RuntimeError, "no active flows remaining" # explanatory variables num sims = state.shape[0] evs = numpy.zeros((num sims, self.num explanatory variables())) pv01 = numpy.zeros(num sims) notl exchange = numpy.zeros(num sims) cnt = 0 for flow in flows: Ts = env.relative date(flow.accrual start date())/365.0 Te = env.relative date(flow.accrual end date())/365.0 Tp = env.relative date(flow.pay date())/365.0 dfp = fill.numeraire rebased bond(t, Tp, flow.pay currency()\ , env, requestor, state) pv01 += flow.year fraction()*dfp if cnt == 0: dfs = fill.numeraire rebased bond(t, Ts, flow.pay currency()\ , env, requestor, state) notl exchange = dfs dfe = fill.numeraire rebased bond(t, Te, flow.pay currency()\ , env, requestor, state) evs[:, 0] = (dfs/dfe-1.0)/flow.year fraction() elif cnt == len(flows)-1: notl exchange -= fill.numeraire rebased bond(t, Te, flow.pay currency(), env, requestor, state) cnt = cnt+1 evs[:, 1] = notl exchange/pv01 return evs Note that the above component is model independent and therefore could be re-used for other models. Unit tests for the exercise component are provided in the module ppf.test.test hull white. The method test explanatory variables on the class exercise tests checks that the computed explanatory variables, the LIBOR and swap rates, The Hull–White Model 117 match the corresponding rates taken from the yield curve for the case when the Hull–White volatilities are all zero. def test explanatory variables(self): from ppf.math.interpolation import loglinear times = [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0] factors = [math.exp(-0.05*t) for t in times] c = ppf.market.curve(times, factors, loglinear) expiries = [0.0, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0] tenors = [0, 90] values = numpy.zeros((8, 2)) surf = ppf.market.surface(expiries, tenors, values) from ppf.date time \ import date, shift convention, modified following, basis act 360, months pd = date(2008, 01, 01) env = ppf.market.environment(pd) key = "zc.disc.eur" env.add curve(key, c) key = "ve.term.eur.hw" env.add surface(key, surf) key = "cv.mr.eur.hw" env.add constant(key, 0.0) r = ppf.model.hull white.requestor() s = ppf.model.hull white.monte carlo.state(10) sx = s.fill(0.25, r, env) f = ppf.model.hull white.fill(3.0) flows = ppf.core.generate flows( start = date(2008, 01, 01) , end = date(2010, 01, 01) , duration = months , period = 6 , shift method = shift convention.modified following , basis = "ACT/360" , pay currency = "EUR") lg = ppf.core.leg(flows, ppf.core.PAY) ex = ppf.model.hull white.monte carlo.cle exercise(lg) t = env.relative date(flows[1].accrual start date())/365.0 T = env.relative date(flows[1].accrual end date())/365.0 ret = ex(t, f, sx, r, env) dft = c(t) dfT = c(T) expected libor = (dft/dfT-1.0)/flows[1].year fraction() pv01 = 0.0 for fl in flows[1:]: T = env.relative date(fl.pay date())/365.0 dfT = c(T) pv01 += fl.year fraction()*dfT T = env.relative date(flows[-1].accrual end date())/365.0 dfT = c(T) expected swap = (dft-dfT)/pv01 118 Financial Modelling in Python expected libors = numpy.zeros(10) expected libors.fill(expected libor) expected swaps = numpy.zeros(10) expected swaps.fill(expected swap) actual libors = ret[:, 0] actual swaps = ret[:, 1] assert seq close(actual libors, expected libors) assert seq close(actual swaps, expected swaps) 8.2 THE MODEL AND MODEL FACTORIES The model class brings all the components from the preceding sections together into one place.

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The Simple Path to Wealth: Your Road Map to Financial Independence and a Rich, Free Life by J L Collins

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Generally speaking, short-term bonds pay less interest as they are seen as having less risk since your money is tied up for a shorter period of time. Accordingly, long-term bonds are seen as having higher risk and pay more. If you are a bond analyst, you’ll graph this on a chart and create what is called a yield curve. The chart on the left is fairly typical. The greater the difference between short, mid and long-term rates, the steeper the curve. This difference varies and sometimes things get so wacky short-term rates become higher than long-term rates. The chart for this event produces the wonderfully named Inverted Yield Curve and it sets the hearts of bond analysts all aflutter. You can see what that looks like in the illustration on the right. Stage 7 Inflation is the biggest risk to your bonds. As we’ve discussed, inflation occurs when the cost of goods is rising.

When you lend your money by buying bonds, during periods of inflation when you get it back it will buy less stuff. Your money is worth less. A big factor in determining the interest rate paid on a bond is the anticipated inflation rate. Since some inflation is almost always present in a healthy economy, long-term bonds are sure to be affected. That’s a key reason they typically pay more interest. So, when we get an Inverted Yield Curve and short-term rates are higher than long-term rates, investors are anticipating low inflation or even deflation. Stage 8 Here are a few other risks: Credit downgrades. Remember those rating agencies we discussed above? Maybe you bought a bond from a company rated AAA. This is the risk that sometime after you buy the company gets in trouble and those agencies downgrade its rating. The value of your bond goes down with it.

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How to Speak Money: What the Money People Say--And What It Really Means by John Lanchester

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The inverse correlation of bond prices and yields is one of those principles that is difficult to get your head around, and I find myself reexplaining it to myself almost every time I come across it. From the point of view of listening to the news, the thing to remember is that yields going up means the debt is being seen as more risky. yield curve The yield projected into the future. If you lend money, the general rule is that longer you’re lending it for, the more your money is at risk. This means that longer loans should offer a higher yield: more risk means the yield has to be more tempting to get you to lend money. The graph of time plotted against risk is called the yield curve, and over time, it goes up, as the risk and yield go up. Sometimes, though, when things are weird and the economy is hitting hard times, investors think that the long-term rates currently on offer are better than the ones they’ll be getting in a few months’ time.

Sometimes, though, when things are weird and the economy is hitting hard times, investors think that the long-term rates currently on offer are better than the ones they’ll be getting in a few months’ time. They pile into long-term debt, taking the opportunity to get these good rates while they’re still available. The price of those long-term debts goes up. Because price and yield are inversely correlated, the rising price makes the yield on those debts go down: that can mean that the longer-term debt ends up with a lower yield than short-term debt. This is known as an inverted yield curve, and it is a sure sign that the market thinks there is severe trouble just ahead. yuan and renminbi Observers of China refer to both the renminbi and the yuan in talking about the country’s currency. They’re the same thing: renminbi means “the people’s currency,” and it was the name given the new currency at the foundation of the People’s Republic of China in 1949. Yuan means “dollar” and is the unit of the currency; so renminbi is like sterling and yuan is like pound.

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The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interaction by Richard Bookstaber

I have seen this issue repeatedly in risk management, and it is one reason any risk management model will not cover all risks. Once the model is specified, the traders will try to find a way around it. Are you measuring interest rate risk? Well, fine, then I will do a trade that is interest rate neutral but bets on the slope of the yield curve. Now you’re measuring yield curve risk? Fine, then I will do a trade that is both interest rate and yield curve neutral, but rests on the curvature of the yield curve—a butterfly trade. And as this game is being played, the complexity and thus endogenous risk is increasing with each iteration. One of the problems with the standard risk measures is that they become exposed to multiple dimensions for such gaming, and for gaming in a way that is harder to detect. In fact, it was largely reliance on these measures (such as value at risk) that allowed for the ballooning of risks in the banks pre-2008.

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The Four Pillars of Investing: Lessons for Building a Winning Portfolio by William J. Bernstein

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On the other hand, the excess return earned by extending bond maturities is minimal, as shown by the “yield curve” for the U.S. Treasury market I’ve plotted in Figure 13-2. Notice that you get about 4% of extra return by extending your maturity from 30 days out to 30 years. This is about as “steep” as the yield curve gets. Much of the time, the curve is much less steep—perhaps 1% to 1.5% difference between long and short yields—and there are even times when the yield curve is “inverted,” i.e., when long rates are lower than shorter rates. Table 13-4. Bond and Bond Index Funds Figure 13-2. U.S. Treasury yield curve. (Source: The Wall Street Journal, 3/14/02.) In Figure 13-2, note that you get the most “bang for the buck” by about a five-year maturity. This is the steepest part of the yield curve—the part that rewards you the most. Beyond that, the extra return diminishes, with continually increasing risk.

Investment: A History by Norton Reamer, Jesse Downing

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Fixed income hedge funds differ fairly widely in the riskiness of the strategies employed. Some are rather risk averse, seeking to buy attractive debt securities that deliver healthy and uninterrupted payments. Others have far more complicated schemes to garner returns, such as exploiting aberrations in yield curves. This can occur when the yield curve adopts an unusual geometry (often a ﬂat or steep slope at the extreme) and managers place long and short positions that proﬁt when the yield curve shifts. One of the most common ﬁxed income strategies is the “swap spread,” which involves collecting the difference between Treasury rates and the swap rate. Others invest in mortgage-backed securities, like those packaged by Fannie Mae and Freddie Mac. Macro hedge funds seek to anticipate major structural changes in an economy, either because of natural market forces (perhaps the market is grossly overheated and is due for a correction) or because of political circumstances.

Quant funds use quantitative factors in models to develop, buy, or sell signals for stocks, commodities, or currencies. These models have a wide spectrum of sophistication. Some of them are simple, trying to capitalize on well-studied sources of risk premium in the stock market like momentum, value, and small market capitalization. Others are more complicated, analyzing convergence-divergence patterns, steepness or ﬂatness of yield curves or futures curves, or even sifting through press releases and conference calls for information on a stock that the market has neglected. The quant fund faces a few difficulties that the best groups are able to overcome. The ﬁrst is to ensure that the models are not overﬁtted to historical patterns. In other words, if a strategy is designed or tweaked using historical price behavior, there is a temptation to retroﬁt a strategy that worked well in the past but may not be capturing the underlying dynamics that would cause it to be successful in the future.

(Rozanov), 128 whole life insurance, 132 Wickham, Richard, 46–47 Wiggin, Albert, 190–91 William and Flora Hewlett Foundation, 127 William III (king of England), 73, 97 William of Orange (stadtholder of Dutch Republic), 86 Williams, John Burr, 4, 232–33 Williams, Ted, 311–12 Wilsonian internationalism, 199 Wisselbank, 85 “World’s Largest Hedge Fund Is a Fraud, The” (Markopolos), 152 World War I: impacts of, 95, 162; inﬂation during, 198; transition out of, 197–98 436 Investment: A History World War II: bull market after, 92, 143; economy and, 275; impacts of, 96; mutual funds during postwar period, 142–44; price and wage ﬁxing of, 110 Wujinzang (Buddhist temples’ wealth), 29 Wu Zetian, 29 Xenophon, 18 Yale University, 257, 296, 328, 332 yield curves, aberrations in, 266 Zarossi, Luigi, 156 Zhiku lending institution, 29–30

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Getting a Job in Hedge Funds: An Inside Look at How Funds Hire by Adam Zoia, Aaron Finkel

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Fixed Income Arbitrage A fund that follows this strategy aims to profit from price anomalies between related interest rate securities. Most managers trade globally with a goal of generating steady returns with low volatility. This category includes interest rate swap arbitrage, U.S. and non-U.S. government bond arbitrage, forward yield curve arbitrage, and mortgage-backed securities (MBS) arbitrage. The mortgage-backed market is primarily U.S.-based, over-the-counter (OTC), and particularly complex. Note: Fixed income arbitrage is a generic description of a variety of strategies involving investments in fixed income instruments, and weighted in an attempt to eliminate or reduce exposure to changes in the yield curve. Risk Arbitrage Sometimes called merger arbitrage, this involves investment in event-driven situations such as leveraged buyouts (LBOs), mergers, and hostile takeovers. Normally, the stock c01.indd 6 1/10/08 11:00:55 AM Getting Started 7 of an acquisition target appreciates while the acquiring company’s stock decreases in value.

Everyone else who works at this fund came out of a banking program, and I was told that the reason they don’t normally hire consultants is that consultants typically don’t have any idea about finance. I believe I was able to make a case for myself because I knew the theory behind finance and had also taught myself the technical aspects. A lot of bankers know the technical part of finance and are Excel experts, but they don’t have the business intuition that consultants do. In my view, and I’m biased, I’d say a consultant who can understand yield curves, do a DCF analysis, and build a cash flow statement is in great shape to be a hedge fund candidate. My primary advice to someone aspiring to work at a hedge fund is to work to be at the top of your consulting or invest“People have to understand ment banking analyst class. Taking the time to invest in pubwhat each fund does before just lic securities will be a major differentiating factor. After that, saying that they are interested in if you can discuss the rationales of two or three investments hedge funds.” you’ve made, are comfortable with finance, and understand the macro issues affecting the markets, you will be in good shape.

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Nerds on Wall Street: Math, Machines and Wired Markets by David J. Leinweber

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—OGDEN NASH T his chapter is based on a number of ever-evolving dinner and lunch talks I have given over many years, all called “Nerds on Wall Street” irrespective of their actual subject. Many financial conference speakers, including those talking to mixed professional/spousal audiences after open-bar events, are deadly dull; hardly anyone really wants to see yield curves over dessert and that last glass of wine. I started collecting photographs about markets and technology in the early 1990s, and tried to mix in some actual informative content. That, along with the natural sensibilities of a borscht belt comic, made me a popular alternative to the yield curve guys. Given the 20-minute rule for these talks, none of them were as voluminous as this chapter. Still, this is not intended in any way to be a complete history of market technology, but rather an easily digestible introduction. I occasionally still do these talks on what remains of greater Wall Street.

Note that these percentages are not referring to total energy consumption, but to the level of total power (the rate of delivering energy) that has to be provided over the year. In the electric world, this is called lowering the peak of the load duration curve. Understanding load duration curves is the first lecture in Power 101 class. If you want to understand bonds, you need to know about the yield curve. The load duration curve is equally important if you want to understand electricity. Figure 14.1 shows a load duration curve and how it would shift with the use of the technologies discussed in this chapter. Lowering the peaks on these curves is important economically, environmentally, and geopolitically, because the plants needed to meet them are expensive, and often oil fueled. Software applied to the electric grid offers unprecedented flexibility in reshaping the load duration curve.

The state of both means that there are likely to be more than 330 Nerds on Wall Str eet 1 2 Hourly MW Load Reduce Customers’ Peak Loads ⭈ Utility-Controlled Circuit-level Management Discharge Stored Power During Peak ⭈ Clean, Reliable, Efficient ⭈ Targeted Deployments 3 4 Offer Value-Added Optimize Generation Services and T&D Assets ⭈ Online Energy Management ⭈ Charge Energy Storage ⭈ Renewables Integration and PHEVs Off-peak 2 1 3 4 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 Hours Per Year Load duration curve. Result of stored power deployed during peak and charging power during off-peak. Result of reducing customers’ peak loads and energy conservation. ENVIRONMENTAL LEADERSHIP AND GRID RELIABILITY Figure 14.1 Reshaping the load duration curve. Bonds have the yield curve. Power has this. Source: GridPoint. a few readers contemplating this transition. This last chapter is a gentle introduction to and a survey of more in-depth resources on this topic. Accelerating Innovation There are over a million hybrid Toyota Prius vehicles on the road, and in Berkeley, California, it often seems that they are all parked on the same street. With only one model and a handful of colors, you need a distinctive bumper sticker to find yours.

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Financial Market Meltdown: Everything You Need to Know to Understand and Survive the Global Credit Crisis by Kevin Mellyn

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All other borrowers going to the bond market should, for any given tenor, have to pay bond buyers more for their money than the risk-free government rate. How much more depends on their specific credit rating but most critically on current market sentiment about risk in general. The effective rate that the government has to pay to borrow money for any given tenor can be plotted as a line called the ‘‘yield curve.’’ Normally, the curve should run from left to right, with rates going up with tenor. However, at times, we can have what is called an ‘‘inverted’’ yield curve, where shorter rates are higher than longer rates. This is because bond rates are set by the market, which is to say by you and me. Although you can buy government debt directly from the treasury, very few people do so. However, all institutional investors, from pension funds to banks and insurance companies are big buyers of government bonds.

Analysis of Financial Time Series by Ruey S. Tsay

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Using the modern econometric terminology, if one assumes that the two interest rate series are unit-root nonstationary, then the behavior of the residuals of Eq. (2.40) indicates that the two interest rates are not co-integrated; see Chapter 8 for discussion of co-integration. In other words, the data fail to support the hypothesis that there exists a long-term equilibrium between the two interest rates. In some sense, this is not surprising because the pattern of “inverted yield curve” did occur during the data span. By inverted yield curve, we mean the situation under which interest rates are inversely related to their time to maturities. 1970 1980 year 1990 2000 ACF 0.0 0.2 0.4 0.6 0.8 1.0 Series : res 0 5 10 15 Lag 20 25 30 Figure 2.14. Residual series of linear regression (2.40) for two U.S. weekly interest rates: (a) time plot, and (b) sample ACF. 69 REGRESSION MODELS WITH TIME SERIES ERRORS -2 per. chg. -1 0 1 2 (a) Change in 1-year rate 1970 1980 year 1990 2000 1990 2000 -2 per. chg. -1 0 1 2 (b) Change in 3-year rate 1970 1980 year Figure 2.15.

Write down the biases and weights of the network in the estimation subsample. • Suppose that we are interested in forecasting the direction of the 1-month ahead stock movement. Fit a 6-5-1 feed-forward neural network to the return series using a Heaviside function for the output node. Compute the 1-step ahead forecasts in the forecasting subsample and compare them with the actual movements. 5. Because of the existence of inverted yield curves in the term structure of interest rates, the spread of interest rates should be nonlinear. To verify this, consider the weekly U.S. interest rates of (a) Treasury 1-year constant maturity rate, and (b) Treasury 3-year constant maturity rate. As in Chapter 2, denote the two interest rates by r1t and r3t , respectively, and the data span is from January 5, 1962 to September 10, 1999. The data are in files “wgs3yr.dat” and “wgs1yr.dat” on the Web. • Let st = r3t − r1t be the spread in log interest rates.

ISBN: 0-471-41544-8 Index ACD model, 197 Exponential, 197 generalized Gamma, 199 threshold, 206 Weibull, 197 Activation function, see Neural network, 147 Airline model, 63 Akaike information criterion (AIC), 37, 315 Arbitrage, 332 ARCH model, 82 estimation, 88 normal, 88 t-distribution, 89 Arranged autoregression, 158 Autocorrelation function (ACF), 24 Autoregressive integrated moving-average (ARIMA) model, 59 Autoregressive model, 29 estimation, 38 forecasting, 39 order, 36 stationarity, 35 Autoregressive moving-average (ARMA) model, 48 forecasting, 53 Back propagation, neural network, 149 Back-shift operator, 33 Bartlett’s formula, 24 Bid-ask bounce, 179 Bid-ask spread, 179 Bilinear model, 128 Black–Scholes, differential equation, 234 Black–Scholes formula European call option, 79, 235 European put option, 236 Brownian motion, 224 geometric, 228 standard, 223 Business cycle, 33 Characteristic equation, 35 Characteristic root, 33, 35 CHARMA model, 107 Cholesky decomposition, 309, 351, 359 Co-integration, 68, 328 Common factor, 383 Companion matrix, 314 Compounding, 3 Conditional distribution, 7 Conditional forecast, 40 Conditional likelihood method, 46 Conjugate prior, see Distribution, 400 Correlation coefficient, 23 constant, 364 time-varying, 370 Cost-of-carry model, 332 Covariance matrix, 300 Cross-correlation matrix, 300, 301 Cross validation, 141 Data 3M stock return, 17, 51, 58, 134 Cisco stock return, 231, 377, 385 Citi-Group stock return, 17 445 446 Data (cont.) equal-weighted index, 17, 45, 46, 73, 129, 160 GE stock return, 434 Hewlett-Packard stock return, 338 Hong Kong market index, 365 IBM stock return, 17, 25, 104, 111, 115, 131, 149, 160, 230, 261, 264, 267, 268, 277, 280, 288, 303, 338, 368, 383, 426 IBM transactions, 182, 184, 188, 192, 203, 210 Intel stock return, 17, 81, 90, 268, 338, 377, 385 Japan market index, 365 Johnson and Johnson’s earning, 61 Mark/Dollar exchange rate, 83 Merrill Lynch stock return, 338 Microsoft stock return, 17 Morgan Stanley Dean Witter stock return, 338 SP 500 excess return, 95, 108 SP 500 index futures, 332, 334 SP 500 index return, 111, 113, 117, 303, 368, 377, 383, 422, 426 SP 500 spot price, 334 U.S. government bond, 19, 305, 347 U.S. interest rate, 19, 66, 408, 416 U.S. real GNP, 33, 136 U.S. unemployment rate, 164 value-weighted index, 17, 25, 37, 73, 103, 160 Data augmentation, 396 Decomposition model, 190 Descriptive statistics, 14 Dickey-Fuller test, 61 Differencing, 60 seasonal, 62 Distribution beta, 402 double exponential, 245 Frechet family, 272 Gamma, 213, 401 generalized error, 103 generalized extreme value, 271 generalized Gamma, 215 generalized Pareto, 291 INDEX inverted chi-squared, 403 multivariate normal, 353, 401 negative binomial, 402 Poisson, 402 posterior, 400 prior, 400 conjugate, 400 Weibull, 214 Diurnal pattern, 181 Donsker’s theorem, 224 Duration between trades, 182 model, 194 Durbin-Watson statistic, 72 EGARCH model, 102 forecasting, 105 Eigenvalue, 350 Eigenvector, 350 EM algorithm, 396 Error-correction model, 331 Estimation, extreme value parameter, 273 Exact likelihood method, 46 Exceedance, 284 Exceeding times, 284 Excess return, 5 Extended autocorrelation function, 51 Extreme value theory, 270 Factor analysis, 342 Factor model, estimation, 343 Factor rotation, varimax, 345 Forecast horizon, 39 origin, 39 Forecasting, MCMC method, 438 Fractional differencing, 72 GARCH model, 93 Cholesky decomposition, 374 multivariate, 363 diagonal, 367 time-varying correlation, 372 GARCH-M model, 101, 431 Geometric ergodicity, 130 Gibbs sampling, 397 Griddy Gibbs, 405 447 INDEX Hazard function, 216 Hh function, 250 Hill estimator, 275 Hyper-parameter, 406 Identifiability, 322 IGARCH model, 100, 259 Implied volatility, 80 Impulse response function, 55 Inverted yield curve, 68 Invertibility, 331 Invertible ARMA model, 55 Ito’s lemma, 228 multivariate, 242 Ito’s process, 226 Joint distribution function, 7 Jump diffusion, 244 Kernel, 139 bandwidth, 140 Epanechnikov, 140 Gaussian, 140 Kernel regression, 139 Kurtosis, 8 excess, 9 Lag operator, 33 Lead-lag relationship, 301 Likelihood function, 14 Linear time series, 27 Liquidity, 179 Ljung–Box statistic, 25, 87 multivariate, 308 Local linear regression, 143 Log return, 4 Logit model, 209 Long-memory stochastic volatility, 111 time series, 72 Long position, 5 Marginal distribution, 7 Markov process, 395 Markov property, 29 Markov switching model, 135, 429 Martingale difference, 93 Maximum likelihood estimate, exact, 320 MCMC method, 146 Mean equation, 82 Mean reversion, 41, 56 Metropolis algorithm, 404 Metropolis–Hasting algorithm, 405 Missing value, 410 Model checking, 39 Moment, of a random variable, 8 Moving-average model, 42 Nadaraya–Watson estimator, 139 Neural network, 146 activation function, 147 feed-forward, 146 skip layer, 148 Neuron, see neural network, 146 Node, see neural network, 146 Nonlinearity test, 152 BDS, 154 bispectral, 153 F-test, 157 Kennan, 156 RESET, 155 Tar-F, 159 Nonstationarity, unit-root, 56 Nonsynchronous trading, 176 Nuisance parameter, 158 Options American, 222 at-the-money, 222 European call, 79 in-the-money, 222 out-of-the-money, 222 stock, 222 strike price, 79, 222 Order statistics, 267 Ordered probit model, 187 Orthogonal factor model, 342 Outlier additive, 410 detection, 413 Parametric bootstrap, 161 Partial autoregressive function (PACF), 36 PCD model, 207 π -weight, 55 Pickands estimator, 275 448 Poisson process, 244 inhomogeneous, 290 intensity function, 286 Portmanteau test, 25.

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Investment Banking: Valuation, Leveraged Buyouts, and Mergers and Acquisitions by Joshua Rosenbaum, Joshua Pearl, Joseph R. Perella

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T-notes are issued with maturities of between one and ten years, while T-bonds are issued with maturities of more than ten years. 89 Yields on nominal Treasury securities at “constant maturity” are interpolated by the U.S. Treasury from the daily yield curve for non-inflation-indexed Treasury securities. This curve, which relates the yield on a security to its time-to-maturity, is based on the closing market bid yields on actively traded Treasury securities in the over-the-counter market. 90 Bloomberg function: “ICUR {# years} <GO>.” For example, the interpolated yield for a 10-year Treasury note can be obtained from Bloomberg by typing “ICUR10,” then pressing <GO>. 91 Located under “Daily Treasury Yield Curve Rates.” 92 The 30-year Treasury bond was discontinued on February 18, 2002, and reintroduced on February 9, 2006. 93 Morningstar acquired Ibbotson Associates in March 2006.

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Birth of the Euro by Otmar Issing

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In the short to medium term, prices are determined by non-monetary factors such as wages (unit labour costs), the exchange rate, energy and import prices, indirect taxes, etc. Indicators of developments in the real economy include data on employment and unemployment, data from surveys (such as the Ifo Business Climate Index), incoming orders, and so on. This economic analysis also encompasses financial sector data such as the yield curve, stock prices and real estate prices. Asset price trends can yield information, for example, on how the wealth effect is expected to influence the growth of demand of private households. As part of its economic analysis, the ECB takes a broad look at developments in macroeconomic demand and its structure, in costs and in the labour market. This includes taking account of the influence of fiscal policy (spending and revenue) and of external factors (the international economic environment, exports and imports).

Meltzer, ‘A theory of ambiguity, credibility, and inflation under discretion and asymmetric information’, Econometrica, 54:5 (1986). 166 • The ECB – monetary policy for a stable euro only control the (very) short end of the interest rate spectrum. The influence of monetary policy on the long end depends very largely on the markets’ expectations of the central bank’s policy actions in the future and of future inflation. If the mandate is price stability or low inflation, the evolution of interest rates all along the yield curve, and in addition the decisions of agents in virtually all markets, will hinge on how far the latter expect the central bank to fulfil its mandate. Efficient and effective communication can play a major part in influencing expectations in line with the central bank’s policy. In guiding expectations in the financial markets, two dimensions need to be distinguished. On the one hand, short-term indications can be given in advance of policy decisions.

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Understanding Asset Allocation: An Intuitive Approach to Maximizing Your Portfolio by Victor A. Canto

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This is what Victor eloquently maps out in the pages ahead. The top-down forces within an economy are many. At the very top are those that directly arise from government policy, such as taxes, money supply, and regulations. Moving down a notch, there’s the value of the dollar, foreign exchange rates, and trade balances. As noted, there’s inflation and the inflation indicators, such as gold prices and Treasury yield curves that speak to the phenomenon of the way money and goods interact. On the corporate level, there’s inventory, shipments, and retained earnings. After that, there’s employment, productivity, and wage levels. Then there’s the abstract, such as supply and demand curves, or the elasticities inherent in different industries and businesses. The list is long, and highly interrelated, which can be problematic for investors at any level of expertise.

The decline in asset prices also reduced the net capital and capital adequacy of the banks, forcing them to further curtail their loan operations. These conditions created what some called a liquidity trap. As the Japan central bank printed money to stimulate the economy, the commercial banks did not lend the extra money. Instead, the money was held as excess reserves. The abundance of bank reserves reduced short-term interest rates, while stagnation lowered long-term rates. Worse, the yield curve flattened to near zero levels, hence the liquidity trap. The Japanese economy remained stagnant for several years following this turn of events. Eventually, most of the bad loans were worked out and the banks began lending again, once their capital had increased. Rising asset prices started to generate a virtuous cycle, and climbing net worth in the Japanese private sector made the sector’s credit worthy once more.

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High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems by Irene Aldridge

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Fleming and Remolona (1999) estimate the high-frequency impact of macroeconomic announcements on the entire U.S. Treasury yield curve. Fleming and Remolona (1999) measure the impact of 10 distinct announcement classes: consumer price index (CPI), durable goods orders, gross domestic product (GDP), housing starts, jobless rate, leading indicators, non-farm payrolls, producer price index (PPI), retail sales, and trade balance. Fleming and Remolona (1999) define the macroeconomic surprise to be the actual number released less the Thomson Reuters consensus forecast for the same news release. All of the 10 macroeconomic news announcements studied by Fleming and Remolona (1999) were released at 8:30 A . M. The authors then measure the significance of the impact of the news releases on the entire yield curve from 8:30 A . M. to 8:35 A . M., and document statistically significant average changes in yields in response to a 1 percent positive surprise change in the macro variable.

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How the City Really Works: The Definitive Guide to Money and Investing in London's Square Mile by Alexander Davidson

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The Debt Management Ofﬁce (DMO), established in April 1998 as an executive agency of HM Treasury, sells one-month and three-month treasury bills (T-bills) on the government’s behalf every Friday in a tender offer to banks, and six-month bills about once a month. The T-bill is issued in sterling at a discount to face value, and the face value is later repaid, the difference being interest equivalent. The T-bill is traded less than it was because developed countries such as the UK and United States are able to borrow for longer periods, which is cheaper based on the inverted yield curve that reﬂects a decline in bond yields as the maturity extends into the future. Issuance is consequently more likely in bonds than in T-bills. The euro bill is similar to the T-bill but is issued in euros. The Bank of England issues £900 million a month in three and six-month euro bills, which helps it to fund euro liabilities. ______________________________________ INTEREST RATE PRODUCTS 83  The certiﬁcate of deposit (CD) is a money market instrument distinguished by its maturity date and its ﬁxed interest rate.

But the closer bonds are to maturity, the less inﬂuence this will have in comparison with the pull to par. On this basis, long-term bonds, particularly if undated, are more exposed to interest rates because redemption is further off. If you think interest rates will go down, you should buy long-term bonds. The yields are generally higher to compensate for a perceived greater risk, despite the inverted yield curve discussed earlier. A bond may often be callable, which means that the issuer, usually a company, may redeem it before maturity. If interest rates should decline, the issuer is likely to call the bond and reissue it at a lower rate of interest. The investor would then be left with money to reinvest in a world where interest rates are low. To compensate for this reinvestment risk, the callable bond will often pay a high coupon. 12 Credit products Introduction In this chapter, we will cover credit products, as distinct from the interest rate products covered in Chapter 11.

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The Curse of Cash by Kenneth S Rogoff

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Clearly, it would be helpful to have legal and financial experts examine every aspect of negative rates to make a transition as smooth as possible. Finally, when thinking about these hurdles, it is again important to bear in mind that part of the idea of employing negative short-term policy rates is to raise current and future expected inflation, thereby raising long-term rates and tilting the yield curve up. Even if short rates were expected to remain negative for a year or even two, one would not expect long-term nominal rates to be negative if the central bank seems determined to create inflation. Admittedly, it is difficult to know how aggressively the central bank will need to move to dislodge deflationary expectations. Especially when negative rates are a new tool, an overshoot may be necessary, but with such a powerful instrument, the central bank should be able to move the dial on expectations pretty quickly.

Chung et al. (2012), for example, argue that unemployment in the United States at the end of 2012 would have been 1.5% higher in the absence of QE, a very powerful effect. They also find, however, that most of this came from QE during the height of the crisis and not later rounds. Wu and Xia (2016) suggest that the effects found in studies such as Chung et al. (2012) may overstate the effect of QE, because it is implicitly assumed that there is a large effect across the yield curve. 29. Krishnamurthy and Vissing-Jorgensen (2011, 2013). 30. Professor James Hamilton of the University of San Diego, whose work spans both macroeconomics and econometrics, gives an extremely insightful discussion on the difficulty of discerning any long-term effect of QE in his Econbrowser column “Evaluation of Quantitative Easing,” November 2, 2014, available at http://econbrowser.com/archives/2014/11/evaluation-of-quantitative-easing. 31.

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Market Sense and Nonsense by Jack D. Schwager

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This strategy seeks to profit from perceived mispricings between different interest rate instruments. Positions are balanced to maintain neutrality to changes in the broad interest rate level, but may express directional biases in terms of the yield curve—anticipated changes in the yield relationship between short-term, medium-term, and long-term interest rates. As an example of a fixed income arbitrage trade, if five-year rates were viewed as being relatively low versus both shorter- and longer-term rates, the portfolio manager might initiate a three-legged trade of long two-year Treasury notes, short five-year T-notes, and long 10-year T-notes, with the position balanced so that it was neutral to parallel shifts in the yield curve. Fixed income arbitrage normally requires the use of substantial leverage because the relative price aberrations it seeks to exploit tend to be small. Therefore, although the magnitude of potential adverse price moves in fixed income arbitrage trades is normally small, the fact that these trades tend to be heavily leveraged can lead to occasional large losses.

Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals by David Aronson

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This transformation was used in the case study and was performed on four interest rate series: three-month treasury bills, 10-year treasury bonds, Moody’s AAA corporate bonds, and Moody’s BAA corporate bonds. Interest Rate Spreads. An interest-rate spread is the difference between two comparable interest rates. Two types of interest-rate spreads were constructed for the case study; the duration spread and the quality spread. The duration spread, also known as the slope of the yield curve, is the difference between yields on debt instruments having the same credit quality but having different durations (i.e., time to maturity). The duration spread used in the case study was deﬁned as the yield on the 10-year treasury note minus the yield on the three-month treasury bills (10-year yield minus 3-month yield). The spread was deﬁned in this way rather than 3-month minus 10-year so that an upward trend in the spread would presumably have bullish implications for the stock market (S&P 500).37 A quality spread measures the difference in yield between instruments with similar durations but with different credit qualities (default risk).

Ross, “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory (December 1976). APT says a linear Notes 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 503 model relates a stock’s returns to a number of factors, and this relationship is the result of arbitrageurs hunting for riskless, zero-investment opportunities. APT speciﬁes factors, including the rate of inﬂation, the spread between low and high quality bonds, the slope of the yield curve, and so on. In other words, the current price change is correlated with the prior change (i.e., a lag interval of 1), then with the change prior to that (lag interval = 2), and so forth. A correlation coefﬁcient is computed for each of these lags. Typically, in a random data series, the correlations drop off very quickly as a function of the lag interval. However, if the time series of price changes is nonrandom in a linear fashion, some of the autocorrelation coefﬁcients will differ signiﬁcantly from the pattern of autocorrelations of a random sequence.

., 467 Scientiﬁc method: deﬁned, 103, 332 history of, 103–108 hypothetic-deductive method, 144–147 key aspects of, 147–148 logic and, 111–124 INDEX nature of scientiﬁc knowledge and, 108–110 objectiﬁcation of subjective technical analysis, 148–151 example, 151–161 openness and skepticism in, 143, 225 philosophy of, 124–143 search bias and, 64 Secondhand information bias, 58–61 anchoring and, 360–361 information diffusion and, 365–366 Self-attribution bias, 48–49 DHS hypothesis and, 375–376 Self-interest, secondhand accounts and, 61 Shermer, Michael, 38 Shiller, Robert, 333–334, 365, 366 Shleifer, Andre, 347 Siegel, Jeremy, 84 Signals, 16–18 Simon, Barry, 259 Simon, Herbert, 42 Simplicity, principle of, 107–108, 225–227 Single-rule back-testing, versus data mining, 268–271 Skepticism, 143, 225 Slope of yield curve, 417 Slovic, Paul, 41, 470 Snelson, Jay Stuart, 71 Socioeconomics, 151 Spatial clustering, 100–101 Stale information, 340, 349, 351–354 Standard deviation, 192 Standard error of the mean, 213–215 Statement about reliability of inference, 190 Index Stationary statistical problems, 174, 188 Stationary time series, 19 Statistical analysis: descriptive statistics tools: central tendency measurements, 191 frequency distribution, 190–191 variability (dispersion) measurements, 192–193 inferential statistics: elements of statistical inference problem, 186–190 sampling example, 172–186 three distributions of, 206–207 probability, 193 Law of Large Numbers, 194–195 probability distribution, 200–202 probability distribution of random variables, 197–199 theoretical versus empirical, 196 sampling distribution and, 201–206 classical derivation approach, 209–215 computer-intensive approach, 215 used to counter uncertainty, 165–172 Statistical hypothesis, deﬁned, 220 Statistical inference: data mining and, 272–278 deﬁned, 189 hypothesis tests: computer-intensive methods of sampling distribution generation, 234–243 conﬁdence intervals contrasted to, 250–252 527 deﬁned, 217–218 informal inference contrasted, 218–223 mechanics of, 227–234 rationale of, 223–227 parameter estimation: deﬁned, 217–218 interval estimates, 218, 243, 245–253 point estimates, 218, 243–245 Statistical signiﬁcance, 23 in case study, 394 statistical signiﬁcance of observation, 171 statistical signiﬁcance of test (p-value), 232–234 Stiglitz, J.E., 343, 378 Stochastics, 401–403 Stories, see Secondhand information bias Subjective technical analysis, 5–8, 15–16, 161–163 adoption of scientiﬁc method and, 148–151 example, 151–161 chart analysis and, 82–86 conﬁrmation bias and, 62–71 erroneous beliefs and, 33–35 futility of forecasting and, 465–471 heuristic bias and, 86–93 illusion trends and chart patterns, 93–101 human pattern ﬁnding and information processing, 39–45 illusory correlations and, 72–82 overconﬁdence bias and, 45–58 secondhand information bias and, 58–61 as untestable and not legitimate knowledge, 35–38 528 Syllogisms: categorical, 112–115 conditional, 115–116 invalid forms, 118–121 valid forms, 117–118 Taleb, Nassim, 337 Technical analysis (TA), 9–11.

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House of Cards: A Tale of Hubris and Wretched Excess on Wall Street by William D. Cohan

CAYNE CAPS SPECTOR y 2004, there was no question that the businesses at the firm that reported to Warren Spector—fixed income, institutional equities, and asset management—were driving the growth of the firm. Particularly important was the exponential growth of the fixed-income business, which was without question Spector's fiefdom. Fixed-income revenue in 2004 was \$3.1 billion—nearly 45 percent of the firm's overall revenue of \$6.8 billion—and had increased some 63 percent, from \$1.9 billion in revenues, since 2002. “These businesses benefited from the low level of interest rates, a steep yield curve and narrowing of corporate credit spreads,” the firm reported in its SEC filings. “Mortgage-backed securities revenues increased significantly as residential mortgage refinancing activity reached record levels during the year, driving record new issue activity, and demand for high-quality fixed income investments continued.” The firm did not break out separately the profitability of Spector's fixed-income division, but the overall grouping of investment banking (Schwartz's bailiwick), institutional equities, and fixed income had increased its pretax income to \$2 billion in 2004, from \$1.3 billion in 2002, and it would be safe to say that much of the increase in the pretax income came from the growth in the fixed-income division.

For the past five years or so, mortgages have provided the best vehicle for asset growth.” While Bear Stearns's fixed-income revenue for the year ended November 30, 2005, declined 12 percent, to \$2.3 billion, from \$2.6 billion in 2004, the business was still humming along quite profitably. The firm's SEC filing stated that “mortgage-backed securities origination revenues declined from the robust levels of fiscal 2004 due to a flattening yield curve, shifting market conditions and changes in product mix. A decline in agency CMO volumes was offset by an increase in non-agency mortgage originations.” Regardless of the stumble in fixed income, the firm posted a record profit of \$1.5 billion in fiscal 2005, up 9 percent from the \$1.3 billion of net income the year before. Since the start of 2006, Bear's stock had risen nearly 25 percent, closing at \$143.50 on April 17.

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Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown, Eric Kim

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The reason people solve for the yield to maturity of bonds is that two bonds with similar terms and credit qualities will have similar yields, but not necessarily similar prices. Thus we can take the price of a bond we do know, convert it to a yield, and apply the yield to get the price of a similar bond whose price we do not know. We can graph bond yield versus time to maturity to get a reasonably smooth yield curve. This is both a useful economic indicator and a way to interpolate yields of other bonds. We can also graph bond yield versus credit quality with similar results. And we can take the derivative of bond price with respect to yield to get a first order idea of the volatility of a bond. The Black-Scholes-Merton model works the same way. Two options with similar terms will have similar implied volatilities, but not necessarily similar prices.

Two options with similar terms will have similar implied volatilities, but not necessarily similar prices. So we can use implied volatilities of options we know the prices of to estimate the implied volatilities, and hence the prices, of options whose prices we do not know. We can graph option implied volatility versus time or moneyness (the ratio of the strike price of an option to the underlying price) and get the same kind of insights we get from yield curves and credit curves. We can take the derivative of option price with respect to implied volatility, known as vega, which some forgotten trader thought was a Greek letter. All of this is pure mathematics; it does not require any economic assumptions. Anyway, the derivative concept in the old sense led to a fresh conflation of frequency and degree of belief. If an option price can be mathematically derived from the underlying stock price, then its price obviously does not depend on the utility function of the person evaluating it.

Culture and Prosperity: The Truth About Markets - Why Some Nations Are Rich but Most Remain Poor by John Kay

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Places The American Business Model The Future of Economics The Future of Capitalism 277 289 302 311 323 340 Appendix: Nobel Prizes in Economics Glossary Notes Bibliography Index 356 361 365 390 411 17 18 19 20 21 22 23 {part V} 24 25 26 27 28 29 {List of Figures, Tables, and Boxes} Figures 4.1 4.2 5.1 5.2 14.1 The Distribution of World Income The Dimensions of Economic Lives Rich States in Europe Rich Stares in Asia U.S. Treasury Yield Curve 34 38 65 66 167 Tables Resources per Head, U.S. The World's Richest Countries Intermediate Economies What America Spends, 2001 What America Earns, 2001 Redistribution of Income Among Households, America, 2001 4.6 What America Produces, 2001 4.7 Living Standards and Productivity, 2001 4.8 Why Material Living Standards Differ, 2001 5.1 Rich and Poor States, 1820 16.1 Lighting Efficiency 16.2 Refrigerator Features 3.1 4.1 4.2 4.3 4.4 4.5 27 32 33 39 39 40 41 46 48 68 185 186 {viii} Figures, Tables and Boxes Boxes 4.1 4.2 4.3 Inequality in World Income Distribution What GDP Is, and Isn't Work and Living Standards, United States and France, 2001 12.1 Economic Rent 18.1 Happiness and Welfare 36 42 50 145 211 {Acknowledgments} • • • • • • • • • • • • • • The background research took us from the Cro-Magnon cave paintings at Lascaux to the dot.com bubble of 1999-2000, from Auckland to Zanzibar.

The link between short and long rates is called the term structure of interest rates (Figure 14.1). It is compiled by looking at rates of interest in the bond market. Banks match borrowers and lenders and allow lenders to get their money back before the borrowers repay. Bonds are another means of handling the same problem. The bond market is a secondary market, in which the right to receive repayment of a loan can be sold to someone else. Figure 14.1 U.S. Treasury Yield Curve (September 30, 2003) 0 9 10 15 Length ofbond (years) SOURCE: U.S. Treasury (Web site) 20 25 { 168} John Kay The price of a bond in this secondary market will not necessarily be the same as the original amount of the loan. The credit risk may have changed. You can today buy the debt of many telecom companies for less than half its repayment value: these companies borrowed extravagantly and many people are now skeptical of their ability to repay.

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The End of Alchemy: Money, Banking and the Future of the Global Economy by Mervyn King

But over longer horizons still, such as a decade or more, interest rates are determined by the balance between spending and saving in the world as a whole, and central banks react to these developments when setting short-term official interest rates. Governments borrow by selling securities or bonds to the market with different periods of maturity, ranging from one month to thirty years or sometimes more. The interest rate at different maturities for such borrowing is known as the yield curve. Another important distinction is between ‘money’ and ‘real’ interest rates. Money interest rates are the usual quoted rate – if you lend \$100 and after one year receive \$105, the money interest rate is 5 per cent. If over the course of that year the price of the things that you like to buy is expected to rise by 5 per cent, then the ‘real’ rate of interest you earn is the money rate less the anticipated rate of inflation (in this example the real rate is zero).

Long-term bond rates, by contrast, as measured by yields on ten-year bonds, are still above zero. In late 2015, bond yields were around 2 per cent in the United States and most other advanced economies, apart from Germany and Japan, where rates were around 1 per cent and 0.5 per cent respectively. Only in Switzerland, of the major economies, were ten-year bond yields slightly negative. When the yield curve is completely flat, central banks may still create money by purchasing assets other than government bonds – either private sector assets, such as corporate bonds, or overseas currencies (the latter was the main strategy pursued by the Swiss National Bank in a vain attempt to prevent a sharp appreciation of the Swiss franc against the euro). But this means taking on credit risk of a very different kind from that involved in monetary policy, which is limited to buying and selling government bonds of different maturities, and has long been accepted as a legitimate role for central banks.

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Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life by Emanuel Derman

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There are sweetness and tartness, spiciness and blandness, smoothness and lumpiness, all of them different types of gustatory pleasure. And I have ignored other kinds of mentionable and unmentionable bodily pleasures, which have their pleasure premiums too. Similarly, there is more than one kind of risk and more than one kind of risk premium: stock risk and bond risk and currency risk and commodity risk and slope-of-the-yield-curve risk; and within the universe of stocks there is sector risk—health risk, technology risk, consumer durables risk, et cetera. In physics the values of the fundamental constants (the gravitational constant G, the electric charge e, Planck’s constant h, the speed of light c) are apparently timeless and universal. I doubt there will ever be a universal value for the risk premium. THE EMM AND THE BLACK-SCHOLES MODEL The best model in all of economics is the Black-Scholes Model for valuing options on stocks, an ingeniously clever extension of the EMM published in 1973 by Fischer Black and Myron Scholes.a I spent my first two years at Goldman Sachs, 1986–1987, working with Fischer Black on an extension of this model to valuing options on bonds,12 and I devoted 1993–1994 to working on an extension of Black-Scholes to stocks with variable volatility.

The Handbook of Personal Wealth Management by Reuvid, Jonathan.

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Many funds’ computer models were re-calibrated following the restrictions on shorting financials. 2009 outlook Those hedge funds that have preserved capital through 2008 will have the financial fire power to take advantage of the opportunities now arising. As distressed sellers are unloading cheap assets to unwind their over-leverage, it presents opportunities for relative value traders, who may be able to hedge out various market risks. In the commodities sector, dislocations between cash and futures prices are increasing. Macro managers may also be able to benefit from steepening yield curves following the sharp interest rate cuts of 1.5 per cent on 6 November 2008 in the UK (with other countries following suit), the further rate cut of 1 per cent in December and the possibility of further cuts to follow. Distressed managers are beginning to see a huge number of potential opportunities emerging. Corporate default rates are at current historic lows and are set to rise throughout 2009.

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Broken Markets: A User's Guide to the Post-Finance Economy by Kevin Mellyn

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If some debt instruments offer better yields than prime corporate and government bonds, you are probably taking on a lot more risk. The Fed policy is literally forcing institutional investors to take on more and more risk in search of returns, and certain exotic structured products such as collateralized debt obligations are creeping back into the market. With the central banks ﬂooding the market with liquidity, the market is too distorted and the yield curves too ﬂat (long-term and short-term rates are about the same) for ordinary investors to navigate. Also, don’t take for granted that money market funds are risk free in today’s world. Stay Debt Free Fifth, not spending money is as good as earning more money in a repressed economy. For starters, if your portfolio is doing a bit better than the market, but you are paying substantial management or advisor fees, it can cancel out.

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The Rise of the Quants: Marschak, Sharpe, Black, Scholes and Merton by Colin Read

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There, he continued to work in options and, increasingly, in improving finance’s understanding of interest rates. Black saw the description and prediction of interest rates to be a multi-faceted and challenging problem. While he had demonstrated that an options price depends on the underlying stock price mean and volatility, and the risk-free interest rate, the overall market for interest rates is much more multi-dimensional. The interest rate yield curve, which graphs rates against maturities, depends on many markets and instruments, each of which is subject to stochastic processes. His interest and collaboration with Emanuel Derman and Bill Toy resulted in a model of interest rates that was first used profitably by Goldman Sachs through the 1980s, but eventually entered the public domain when they published their work in the Financial Analysts Journal in 1990.2 Their model provided reasonable estimates for both the prices and volatilities of treasury bonds, and is still used today.

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Electronic and Algorithmic Trading Technology: The Complete Guide by Kendall Kim

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However, despite regulatory intervention, corporate bond trades are reported within a 15-minute time span and not real time.6 In July 2006, the CBOT introduced a pilot program for algorithms utilized for two- and five-year Treasury futures. The pilot program was implemented to assess the impact on trading profiles and behavior; to identify the demographics of participants pre- and post-pilot implementation; to determine whether the change in algorithm impacts the number of participants in a contract; and to assess the growth rate of the five-year Treasury Note contracts benchmarked against relevant instruments along the yield curve. The program was designed to monitor a straight First In First Out (FIFO) algorithm, which matches trades on a strict time and price priority, versus a pro rata algorithm, which matches trades based on a distributed proportionate approach. The exchange will continue to change in contract volume, participation levels, and order management behavior.7 6.8 Conclusion Algorithms are designed to balance a juggling act.

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The common answer to the above is that markets were so overly manipulated that equity prices reflected their being the only game in town for investors who wanted some semblance of return. But to believe this, one would have to believe that central bankers suddenly figured out how to engineer bull markets. The problem with such an assertion, particularly one that says low rates push investors into stocks, is that the latter has been policy from the Bank of Japan since the 1990s. Low interest rates across the yield curve have long been the norm for Japan’s central bank, as has quantitative easing (Japan’s economy has suffered 10 doses of QE from the Bank of Japan10). Yet, the Nikkei 225 is still half of what it was in the late 1980s. Moving to China, its stock markets started to buckle in August 2015. Worried about stocks falling further, the Chinese government spent tens of billions of yuan trying to prop the market up.11 It failed.

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The Social Life of Money by Nigel Dodd

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Eurozone member states were able to borrow at lower interest rates because creditors (mostly bondholders) were treating them as part of a homogeneous financial space. That is to say, the introduction of the euro appeared to coincide with the unification of government bond yields across the Eurozone. Member states were borrowing at similar rates, reflecting that their debt carried a similar underlying degree of risk. It was as if a single yield curve had been established for the bonds issued by all Eurozone member states (Aglietta and Scialom 2003: 52). The effect of those lower borrowing costs on Greece was especially striking: starting with a yield of more than 11 percent in the beginning of 1998, Greek borrowing costs declined constantly to about 6 percent in mid-2000 and even further to a low at 3.3 percent in September 2005.36 Similar examples can be seen among more recent entrants to Euroland, Slovenia and Slovakia.

The effect of those lower borrowing costs on Greece was especially striking: starting with a yield of more than 11 percent in the beginning of 1998, Greek borrowing costs declined constantly to about 6 percent in mid-2000 and even further to a low at 3.3 percent in September 2005.36 Similar examples can be seen among more recent entrants to Euroland, Slovenia and Slovakia. On joining the euro, both experienced a rapid lowering of bond rates. Indeed, almost all newly joining countries have experienced a boom upon joining the Eurozone. If the Eurozone resembled a monetary and financial union during its first few years, it turned out to be an illusion. That single yield curve for sovereign bonds splintered midway through 2008, and spreads have been widening ever since. So why have rates diverged? One simple answer is that debt has been used in a different way since the global crisis. De Grauwe, for example, points to the “flight to safety” of investors dumping private debt and turning to low-risk sovereign debt. Crucially, this statement means that those Eurozone governments with a stronger reputation have enjoyed a lowering of rates, whereas those countries considered weaker could not draw the same benefit.

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13 Bankers: The Wall Street Takeover and the Next Financial Meltdown by Simon Johnson, James Kwak

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We did not realize they were already more like us than we cared to admit. * The Tenth Amendment, part of the Bill of Rights, was technically not yet in force, but by the end of 1790 it had been ratified by nine states out of the ten necessary. * A trust was a form of legal organization used to combine multiple companies into a single business entity. * Lowering short-term interest rates can also help banks by “steepening the yield curve.” Since banks typically borrow for short periods of time and lend for long periods of time, if short-term rates fall while long-term rates remain unchanged, their profit margin—the spread between long- and short-term rates—increases. * An alternative explanation, advanced by Barry Eichengreen and Peter Temin, is that the Federal Reserve was constrained by its adherence to the international gold standard; expanding the money supply would have caused a severe devaluation of the dollar.93 2 OTHER PEOPLE’S OLIGARCHS Financial institutions have priced risks poorly and have been willing to finance an excessively large portion of investment plans of the corporate sector, resulting in high leveraging.

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The Bogleheads' Guide to Investing by Taylor Larimore, Michael Leboeuf, Mel Lindauer

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Turnover rate: An indication of the manager's trading activity during the past year. Unrealized capital gain/loss: A gain or loss that would be realized if the fund's securities were sold. Wash sale: An IRS rule that disallows the loss from the sale of a fund if the investor invests in a "substantially identical" fund within 31 days. Yield: Income received from an investment expressed as a percentage of its current price. Yield curve: A line on a graph that depicts the yields of bonds of varying maturities. APPENDIX II Books We Recommend BOOKS FOR NOVICE INVESTORS The Coffeehouse Investor by Bill Shultheis (Kirkland, WA: Palouse Press, 2005). A little book with a big message: How to invest simply and successfully. The Millionaire in You by Michael LeBoeuf (New York: Crown Business, 2002). A primer on how to invest money and time intelligently to achieve financial freedom.

pages: 350 words: 103,270

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Just how heavily traded these contracts became can be gauged from the total “notional” amount of debt that was supposed to be transformed by the swaps (which is not the same as their value): by June 2008, a staggering \$356 trillion of interest rate swaps had been written, according to the Bank for International Settlements.2 As with forward contracts on currencies and commodities, the rates quoted on these swaps are considered to be a more informative way of comparing different borrowing timescales (the so-called yield curve) than the underlying government bonds or deposit rates themselves. Derivatives—at least the simplest, most popular forms of them—functioned best by being completely neutral in purpose. The contracts don’t say how you feel about the derivative and its underlying quantity. They don’t specify that you are a hate-to-lose-money corporate treasurer looking to reduce uncertainty in foreign exchange or commodities.

pages: 311 words: 99,699

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Since 2004, the Fed had been steadily raising interest rates, along with the Bank of England, in a deliberate effort to prick the bubble. The European Central Bank had belatedly followed suit. Yet these moves hadn’t worked. Instead of rising, the cost of borrowing had stubbornly continued to fall in many corners of the market. In the US government bond sphere, yields on 10-year Treasuries even tumbled below short-term bond yields, creating a bizarre pattern known as an “inverted yield curve.” Alan Greenspan dubbed the situation a “conundrum.” There were other puzzles, too. In previous decades, the price of assets had been volatile when surprises hit the markets, be they an oil price shock, a rate rise, or a swing in the housing market. However, as Basel’s BIS noted at the time, the “striking feature of financial market behavior” in the twenty-first century was “the low level of price volatility over a wide range of financial assets and markets.”

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Atrocity Archives by Stross, Charles

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What yield have you set it to?" I ask. Howe raises an eyebrow. "Tell him," says Alan. "It's a selective yield gadget," says Howe. "We can set it to anything from fifteen kilotons to a quarter of a megaton--it's a mechanical process, screw jacks adjust the gap between the fusion sparkplug and the initiator charge so that we get more or less fusion output. Right now it's at the upper end of the yield curve, dialled all the way up to city-buster size. What's this got to do with anything?" "Well." I lick my lips; it's really cold in here now and my breath is steaming. "To open a gate big enough to bring through a large creature like whatever ate this universe takes a whole lot of entropy. The Ahnenerbe did it in this universe by ritually murdering roughly ten million people: information destruction increases entropy.

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The Power of Passive Investing: More Wealth With Less Work by Richard A. Ferri

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unrealized capital gain/loss An increase (or decrease) in the value of a security that is not yet realized because the security has not been sold. volatility The degree of fluctuation in the value of a security, mutual fund, or index. Volatility is often expressed as a mathematical measure, such as a standard deviation or beta. The greater a fund’s volatility, the wider the fluctuations between highs and lows. yield curve A line plotted on a graph that depicts the yields of bonds of varying maturities, from short-term to long-term. The line, or curve, shows the relationship between short- and long-term interest rates. yield-to-maturity The rate of return an investor would receive if the securities held in his or her portfolio were held until their maturity dates. Notes Preface 1. John C. Bogle, “The Chief Cornerstone,” (speech, Superbowl of Indexing conference, Phoenix, Arizona, December 7, 2005). 2.

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The End of Doom: Environmental Renewal in the Twenty-First Century by Ronald Bailey

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“if during the next”: Paul Waggoner, “How Much Land Can Ten Billion Spare for Nature?” Jesse H. Ausubel and H. Dale Langford, eds., Technological Trajectories and the Human Environment, National Academy of Engineering, 1997, 56–73. www.nap.edu/openbook.php?record_id=4767&page=56. India produces 31 bushels: Ronald Phillips, “Mobilizing Science to Break Yield Barriers.” Background paper to the CGIAR 2009 Science Forum workshop: “Beyond the Yield Curve: Exerting the Power of Genetics, Genomics and Synthetic Biology,” “2009, 17. www.scienceforum2009.nl/Portals/11/BGWS4.pdf. that past population growth: Julio A. Gonzalo, Félix-Fernando Muñoz, David J. Santos, “Using a Rate Equations Approach to Model World Population Trends.” Simulation: Transactions of the Society for Modeling and Simulation International 89 (February 2013): 192–198. “Overpopulation was a spectre”: “A Model Predicts That the World’s Populations Will Stop Growing in 2050.”

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Liar's Poker by Michael Lewis

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Says Ranieri: "I stopped trying to argue with customers about prepayments and finally started talking price. At what price were they attractive? There had to be some price where the customers would buy. A hundred basis points over treasuries [meaning one percentage point yield greater than U.S. treasury bonds]? Two hundred basis points? I mean, these things were three hundred and fifty basis points off the [U.S. treasury yield] curve!" All American homeowners had a feel for the value of the right to repay their mortgage at any time. They knew if they borrowed money when interest rates were high that they could pay it back once rates fell and reborrow at the lower rates. They liked having that option. Presumably they would be willing to pay for the option. But no one even on Wall Street could put a price on the homeowners' option (and people still can't, though they're getting closer).

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The Man Who Knew: The Life and Times of Alan Greenspan by Sebastian Mallaby

They make us more vulnerable to the buildup of distortions in financial markets that can only be unwound with some drama.” “Bankers are willing to take on more risk than I have heard them admit to in recent years,” added Governor Mark Olson, who was himself a former banker. Vice Chairman Roger Ferguson pushed the argument further, linking the financial exuberance with the Fed’s forward guidance about future interest rates. “Perhaps we are anchoring the yield curve more than we’d like,” he suggested. “The fixed-income markets in particular are not in fact doing the appropriate job of pricing risks.” He was suggesting that the Fed’s forward guidance had made life too predictable, lulling speculators into complacency. “We need in some sense to remove the anchor that we have placed on those markets,” he concluded. Greenspan also sounded worried. “It sounds as though we’re back in the late ’90s or perhaps early 2000,” he said, recalling the extremes of the tech bubble.

If house prices did turn out to constitute a bubble, they could always clean up afterward. The danger of a snapback had to be weighed against more certain and immediate goals: to allow as much growth and employment as possible, consistent with a stable consumer-price index.45 • • • For the next few months, the Fed continued to guide investors about its future policy, oblivious to Roger Ferguson’s warning that this might “anchor” the yield curve and lull investors into complacency. In March 2004 the FOMC repeated its promise to be patient about raising interest rates; in May it declared it would tighten “at a pace that is likely to be measured.” It was only in June, after fully twelve months with a 1 percent federal funds rate, that the FOMC ventured a quarter-point hike. By this point, house prices had risen by 20 percent in a year.46 It was the same amount that they had gained during the entire decade of the 1990s.

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The Quants by Scott Patterson

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In January 1992, he received a call from Pimco, the West Coast bond manager run by Bill Gross. A billionaire former blackjack card counter (in college he’d devoured Beat the Dealer and Beat the Market), Gross religiously applied his gambling acumen to his investment decisions on a daily basis. Pimco had gotten hold of Asness’s first published research, “OAS Models, Expected Returns, and a Steep Yield Curve,” and was interested in recruiting him. Over the course of the year, Asness had several interviews with Pimco. In 1993, the company offered him a job building quantitative models and tools. It was an ideal position, Asness thought, combining the research side of academia with the applied rigor of Wall Street. Goldman, upon learning about the offer, offered him a similar job at GSAM. Asness took it, reasoning that Goldman was closer to home in Roslyn Heights.

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Crash of the Titans: Greed, Hubris, the Fall of Merrill Lynch, and the Near-Collapse of Bank of America by Greg Farrell

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The idea was simple enough, to package mortgages of various durations and interest rates into tranches, then securitize those tranches and sell them like bonds, where buyers could look forward to receiving annual payments, or “coupons,” on their investment. Thain immersed himself in the business, learning the arcane details of mortgage trading, from the payment cycles and coupon rates to the special considerations of prepayment pools and the “negative convexity”—an inversion of the standard price/yield curve—that creeps into the valuations of mortgage portfolios. Mortgage trading fell within Goldman’s fixed-income trading division, and the leader of that business, Jon Corzine—who would eventually be elected U.S. senator from New Jersey and governor of the Garden State—took a special interest in Thain, a fellow native of Illinois. At Goldman Sachs, which employed only the best and brightest financial minds trained at the top business schools, everyone is smart, so a partner’s rise in the organization comes from how much revenue he generates for the firm and whether one of the firm’s top partners takes an interest in him.

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Planet Ponzi by Mitch Feierstein

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You’d want to cover your manipulation in plenty of complicated talk about statistics, but the talk wouldn’t signify a string bean. The second thing you’d want to do is to start churning out new dollar bills. You’d print like crazy. You wouldn’t talk about trashing the currency, of course; you’d talk about price stability, about quantitative easing, about Operation Twist and bringing down the long end of the yield curve. Ideally, too, you’d have someone in charge who really believed in the value of what he was doing, someone who didn’t really live in the real world. Maybe a professor of something. A guy who had studied a period of history from eighty years ago and who’s been yearning all his life to save the world using techniques which might or might not have worked back then, but which certainly don’t make sense in the present day.

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Wealth and Poverty: A New Edition for the Twenty-First Century by George Gilder

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PROLOGUE THE SECRET OF ENTERPRISE THIRTY YEARS AFTER THE publication of Wealth & Poverty, shaken by a global financial fiasco, I find myself buckling down to engage once again these central themes of human life and economics. Back during the tempestuous late years of the 1970s, with President Jimmy Carter waving limp white flags of national malaise, with hostages still held in Tehran, petroleum and gold prices shrilling doom-laden alarms, U.S. banks gasping for capital down a ferociously inverted yield curve (borrowing dear in short-term markets and lending low in long-term bonds and mortgages), with the Soviet Union battening rich on oil wealth, and John Kenneth Galbraith joining the CIA in acclaiming the robustness and fast growth of the “astonishing” Soviet economy, I declared that socialism was dead. This fact, I acknowledged, remained unrequited by a comparable triumph of capitalism. Even Irving Kristol, then the most eloquent and sophisticated defender of enterprise, could only muster Two Cheers for Capitalism.

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Unconventional Success: A Fundamental Approach to Personal Investment by David F. Swensen

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If tax rates change, the value of the tax exemption for municipal bonds changes too. A reduction in tax rates reduces the value of the tax exemption and vice versa. If Congress limits or eliminates the tax exemption, the values of municipal bonds would decline. Legislative uncertainty contributes to higher-than-expected long-term tax-exempt yields. Proving that generalizations invite exceptions, sometimes market forces fail to work on the short end of the yield curve. Consider yields for Vanguard’s money-market offerings. In September 2004, the tax-exempt money fund yield matched the taxable fund yield. A top-marginal-bracket taxpayer benefited to the tune of 0.4 percent on an after-tax basis by choosing the tax-exempt fund. The early-September yields represented more than a passing opportunity. For the year prior to August 31, 2004, Vanguard’s tax-exempt fund produced a yield of 0.9 percent, materially higher than the taxable fund’s yield of 0.8 percent.

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Why Stock Markets Crash: Critical Events in Complex Financial Systems by Didier Sornette

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GDP at 7% growth rate Asia up P/Sales new metric big jobs number NAV angst Bull market forever? Insults Back into cave 8 week bear market!? Disbelief Looking good! B2C Greenspan speaks Optimistic CNBC guest Pain Joe Ignore history Arggh! Larry Nothing matters Any gains lost in next day rally Ralph Bad breadth Wealth effect Abby Earnings slowdown Big volume Futures up Greenspan silent Rally!!! Bears bail Phew! MSFT breakup e-broker TV ads P/E’s of 2000 Weird yield curve Buy and hold forever “Bottom is in” Mergers Soros out Gold auctions Margin call W\$W elves 401k inflows 16 year olds beat market vets Flight to safety Hot market Dollar goes every which way Old Economy New Economy Oil up DOW 36,000 IPO billionaires 30yr bond extinct Fig. 4.1. Cartoon illustrating the many factors inﬂuencing traders, as well as the psychological and social nature of the investment universe (source: anonymous).

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The Death of Money: The Coming Collapse of the International Monetary System by James Rickards

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Corporations in the EU are predominantly taxed on a national basis, meaning tax is paid to a host country only based on profits made in that country, which contrasts favorably with the U.S. system of global taxation, in which a U.S. corporation pays tax on foreign as well as domestic profits. Both the EU and the United States have managed to maintain low inflation in recent years, but Europe has done so with significantly less money printing and yield-curve manipulation, which means its potential for future inflation based on changes in the turnover or velocity of money is reduced. In contrast, China has had a persistent problem with inflation due to Chinese efforts to absorb Federal Reserve money printing to maintain a peg between the yuan and the dollar. Of the three largest economic zones, the EU has the best track record on inflation both in terms of recent experience and prospects going forward.

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Fed Up: An Insider's Take on Why the Federal Reserve Is Bad for America by Danielle Dimartino Booth

The combination of Dodd-Frank, with its aim of limiting risk-taking, and Basel III, with its increased capital requirements, had proved to be a toxic combination. Was it any wonder that commercial bank officers were stumped? The stated aim of QE was to encourage banks to loan money. But other rules required they hold more capital against fresh loans if they did—to say nothing of the risk they assumed if yield curve normality ever made a comeback. Private equity kingpins had become the new overlords of the corporate bond market. They had also discovered the profitability of being landlords. Money was cheap for those who could access it. And investors were eager to buy into the next private equity fund in the hopes they could eke out positive returns. So private equity set its sights on the “sand states,” ground zero of the housing crisis.

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An Extraordinary Time: The End of the Postwar Boom and the Return of the Ordinary Economy by Marc Levinson

Although Carter was able to push Burns out in January 1978, by then inflation was climbing back toward the double digits. As the Fed began raising overnight interest rates aggressively to clamp down on inflation, interest rates on the Treasury’s short-term bonds rose close to those on its long-term bonds. On August 18, 1978, the lines crossed: investors earned more for lending to the government for two years than for ten. That unusual condition, known in the financial markets as an inverted yield curve, was an alarm bell, an unmistakable warning that a recession was likely in the second half of 1979. And then came the second oil crisis, driven by the revolution in Iran and a decision by Saudi Arabia to limit oil production. After holding steady since 1974, the average cost of a barrel of crude doubled over the course of 1979. A more relevant figure for American voters, the price of gasoline, went from seventy cents per gallon to \$1.11, and buying it often required a lengthy wait in line.

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Money and Power: How Goldman Sachs Came to Rule the World by William D. Cohan

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“This was a trial-by-fire, put-your-butt-in-a-seat, we-really-need-you-to-structure-stuff-right-now kind of thing,” he said. “There’s no orientation, there’s none of that crap. It was just a phenomenal experience for me to be able to do something real in a very hot area at the time.” Goldman asked him to return the following summer. Once again, he structured CMOs. “It was still a great time to do it in 1993,” he said. “There was a steep yield curve”—meaning the cost of debt was higher the longer someone could take to pay it back—“so intellectually it was an interesting thing.” He had straight As when he graduated from the Wharton undergraduate program in December 1993—a semester early—and because of that, and having Goldman Sachs on his résumé for two summers, he had any number of job offers to choose from. But he decided to return to Goldman, as do the vast majority of people who work there during the summers before they graduate.