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Bernie Madoff, the Wizard of Lies: Inside the Infamous $65 Billion Swindle by Diana B. Henriques
accounting loophole / creative accounting, airport security, Albert Einstein, banking crisis, Bernie Madoff, break the buck, British Empire, centralized clearinghouse, collapse of Lehman Brothers, computerized trading, corporate raider, diversified portfolio, Donald Trump, dumpster diving, Edward Thorp, financial deregulation, financial thriller, fixed income, forensic accounting, Gordon Gekko, index fund, locking in a profit, mail merge, merger arbitrage, money market fund, Plutocrats, plutocrats, Ponzi scheme, Potemkin village, random walk, Renaissance Technologies, riskless arbitrage, Ronald Reagan, short selling, Small Order Execution System, source of truth, sovereign wealth fund, too big to fail, transaction costs, traveling salesman
In his prison interviews and in subsequent letters, Madoff claimed that he was generating those solid, consistent profits for his father-in-law’s partnership accounts through an investment strategy that he said was his small firm’s specialty in the 1970s. It was called riskless arbitrage, and it was widely understood and accepted among the professionals on Wall Street in that era. Riskless arbitrage is an age-old strategy for exploiting momentary price differences for the same product in different markets. It could be as simple as ordering cartons of cigarettes by telephone from a vendor in a low-cost state and simultaneously selling them over the phone at a higher price in states where they are more expensive, thereby locking in a profit. Or it could be as complex as using computer software to instantly detect a tiny price differential for a stock trading in two different currencies and execute the trades without human intervention—again, locking in the profit. What distinguished riskless arbitrage from the more familiar “merger arbitrage” of the 1980s—which involved speculating in the securities of stocks involved in possible takeovers—was that a profit could be captured the moment it was perceived, if the trade could be executed quickly enough.
By simultaneously buying in Boston and selling in San Francisco, an alert investor could lock in that $0.75 difference as a riskless arbitrage profit. At a more sophisticated level, a level Madoff was known to exploit, riskless arbitrage involved corporate bonds or preferred stock that could be converted into common stock. A bond that could be converted into ten shares of stock should usually trade for at least ten times the price of the stock—but it didn’t always do so. If a bond that could be converted into ten shares of a $15 stock could be bought for less than $150—for $130 per bond, let’s say—that was an opportunity for arbitrage. An investor could buy that bond for $130, simultaneously sell ten shares of the underlying common stock at $15 a share, and lock in a “riskless” arbitrage profit of $20—the difference between the $130 price he paid for the bond and the $150 he received for the ten shares he got when he converted the bond into stock.
Market makers were traders who consistently and publicly maintained a ready market in specific securities, buying from other traders who wanted to sell and selling to traders who wanted to buy. Continually offering to buy and sell the arcane securities involved in riskless arbitrage strategies—convertible bonds, preferred stock, common stock units with warrants—and trading those securities for his own account and those of his clients became Madoff’s increasingly profitable market niche, he said. According to Madoff, none of the big Wall Street firms were willing to do riskless arbitrage in small pieces for retail investors. But he was, and some of the biggest names on the Street would send him small arbitrage orders to execute for their customers, he said. “They liked to send me the business,” he recalled. “They thought I was a nice Jewish boy.”
Derivatives Markets by David Goldenberg
Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial innovation, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, law of one price, locking in a profit, London Interbank Offered Rate, Louis Bachelier, margin call, market microstructure, martingale, Myron Scholes, Norbert Wiener, Paul Samuelson, price mechanism, random walk, reserve currency, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, Y2K, yield curve, zero-coupon bond, zero-sum game
One of the most important deﬁnitions in derivatives is that of an arbitrage opportunity. We give three deﬁnitions. The ﬁrst two are of a risk-free arbitrage opportunity and the third is of a risky arbitrage. DEFINITION 1 (RISKLESS ARBITRAGE) A risk-free arbitrage opportunity is one with the following properties: 1. It generates a positive profit (inﬂow) at time T, subsequent to today, represented by time t. 2. The profit generated at time T is riskless. That is, it is certain. 3. The cost today of generating that risk-free, positive proﬁt at time T is zero. DEFINITION 2 (RISKLESS ARBITRAGE) A risk-free arbitrage opportunity is one with the following properties: 1. It generates a positive profit (inﬂow) today, time t. 2. The proﬁt generated today is riskless. 3. There are no subsequent outflows (costs).
Unfortunately, we know that the payoff can be positive or negative at expiration so there is no guarantee of a positive proﬁt in any state of the world. Therefore, such positions are clearly not riskless arbitrage opportunities (see parts 1. and 2. of Deﬁnition 1). Neither are they risky arbitrage opportunities even though they have a chance of a positive proﬁt at expiration (see Deﬁnition 3, part 3., section 4.6.1). The reason is that part 2. of Deﬁnition 3 is violated, negative proﬁts (costs) could arise at expiration. b. An unexpired lottery ticket that someone lost and that you found is not a riskless arbitrage because winning is not a certainty. However, it is a risky arbitrage because there is a state of the world in which there is a (large) positive payoff, that in which you have the winning number.
So people would be as happy owning A as they were by owning B. We would be happy too, because we got it cheap relative to B. Our strategy would yield an immediate riskless arbitrage proﬁt of PB,t–PA,t>0, and no subsequent cash ﬂow implications because we have unwound all positions. The short sale of B has been closed out by covering the short sale. The long position we acquired in A has been liquidated by using A to cover the short sale, after which we own no position in A nor in B. Further, if we short sell B and purchase A fast enough, the immediate cash ﬂow will be almost riskless. Now, recall deﬁnition 2 of (riskless) arbitrage given in Chapter 4, section 4.6.1. Risk-Free Arbitrage Definition 2 A risk-free arbitrage opportunity is one with the following properties: 1. It generates a positive profit (inﬂow) today, time t. 2.
Albert Einstein, Asian financial crisis, Augustin-Louis Cauchy, Black-Scholes formula, British Empire, Brownian motion, capital asset pricing model, Cepheid variable, creative destruction, crony capitalism, diversified portfolio, Douglas Hofstadter, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Henri Poincaré, I will remember that I didn’t make the world, and it doesn’t satisfy my equations, Isaac Newton, law of one price, Mikhail Gorbachev, Myron Scholes, quantitative trading / quantitative ﬁnance, random walk, Richard Feynman, Richard Feynman, riskless arbitrage, savings glut, Schrödinger's Cat, Sharpe ratio, stochastic volatility, the scientific method, washing machines reduced drudgery, yield curve
The only principle you can rely on in finance (and it’s not always reliable) is the Law of One Price: If you want to know the value of one financial security, your best bet is to use the known price of another security that’s as similar to it as possible. When we compare it with almost everything else in economics, the wonderful thing about this law of valuation by analogy is that it dispenses with utility functions, the undiscoverable hidden variables whose ghostly presence permeates economic theory. Financial economists like to recast the Law of One Price as the more pedantically named Principle of No Riskless Arbitrage: Any two securities with identical future payoffs, no matter how the future turns out, should have identical current prices. This Law of One Price embodies the common sense that the author of “the fundamental theorem of finance” was trying so hard to convey but expressed so unclearly. In the imaginary world of the Efficient Market Model, a stock’s price movements are completely characterized by its expected return μ and its volatility a.
See also Black-Scholes Model metaphor(s): as analogies definition/nature of models and electromagnetic theory as facts confused with feelings as financial models as God and hierarchy of linguistic and irreducible nonmetaphor language as tower of limitations of mysteries of world and physical basis of positron and purposes of of Schopenhauer symbols and theories and method: Goethe’s view about content and mind: body relationship with composition of world and domino computer and idea and invention/ discovery as synthesis of world and laws of materialism and Spinoza’s emotions theory and will and Minsky, Marvin miscegenation mnemonics Modeh (children’s prayer) Model T Modelers’ Hippocratic Oath models: accuracy of analogies and assumptions and benefits of as caricature as collection of parallel thought universes definition of explanations required for as fetish as gedankenexperiments good and bad ideal language and laws and limitations/inadequacies of and making the unconscious conscious as metaphor mysteries of world and nature of purposes of for risk rules for using as saving mental labor as simplifications theorems and theories compared with time and types of unreliability of validity of verification of vulgarity of as way of understanding world See also failed models; specific model or topic money See also currency/cash monocular diplopia Montagu, South Africa: Derman visit to morals: markets and mortgages Moses: burning bush and Mossin, Jan moth in refrigerator example motion, laws of Mottelson, Ben mudita, Nabokov, Vladimir National Union of South African Students (Nusas) Nationalist Party, Afrikaner nature: inner relationships of negative energy Newton, Isaac: as a bird calculus and CAPM and and Derman’s question about laws and explanations discoveries about matter of electromagnetic theory and Keynes’s views about laws of laws of the universe and mechanics theory of and perfection via intuition and right way to use models theories of observation Oersted, Hans Christian “On the Suffering of the World” (Schopenhauer) options: benefits of financial models and Black-Scholes Model and Merton and as objects of interest to financial models Spinoza’s theory of emotions and valuing of vulgarity of financial models and pain: definition of money and Spinoza’s emotions theory and Palestine parity violation passions perfection: definition of electromagnetic theory and God as intuition and knowledge and levels of nonexistence of reality and Spinoza’s definition of Spinoza’s emotions theory and of theories phenomena: electromagnetic theory and importance of physics: abstractions and analytic continuation in birds and frogs in collective model in nuclear Derman’s interest in studying equilibrium in failed models in financial models and function of fundamental theorem of God and good and bad models and theories in laws of and making the unconscious conscious mathematics and Maxwell’s impact on nature of models and negative energy and purpose of models in and right way to use models theory as distinguished from models and uncertainty and values of fundamental constants in world as focus of See also specific scientist, model, or theory “A Piece of Chalk” (Chesterton) The Pirates of Penzance (Gilbert and Sullivan) Planck, Max pleasure: definition of as derivative of love expected financial models and generalized intuition and localized money and perfection and Spinoza’s emotions theory and pleasure premium Poalei Zion (Workers of Zion) Poincaré, Henri points politics: failed models in financial models and human affairs and Population Registration Act (1950) portfolios, investment Portnoy’s Complaint (Roth) positrons postulates Powers, Melvin pragmamorphism “The Precision of Pain and the Blurriness of Joy” (Amichai) preconceptions prediction: financial models and purpose of models in physics and presence: absence as price: definition of drift in financial models and fluctuation in futility of using financial models and history of implied opaque prediction of future purpose of finance models and risk model and value and volatility of See also Law of One Price; specific financial model or theory primes primitives See also specific primitive Principle of No Riskless Arbitrage. See Law of One Price principles: definition of theories and Euclid’s geometry and in finance privatization probability Prohibition of Mixed Marriages Act (1949) proxies: artists’ models as psyche, Freud’s theory of psychoanalysis psychology Pygmalion model Pythagoras’s theorem QED. See quantum electrodynamics quanta quantum electrodynamics (QED): accuracy of atomic physicists and as best theory in world complexity of as genuine theory history of light and as metaphor quantum dreams and renormalization and quantum field theory quantum mechanics quarks race: in South Africa radioactive beta decay, theory of Rainwater, James Rand, Ayn random walk randomness: EMM and risk and theory of real estate: financial models and See also apartments reality reason regulation relativity, theory of renormalization research: principles of return: average Black-Scholes Model and CAPM and EMM and excess expected financial models and return (cont.)
Endless Money: The Moral Hazards of Socialism by William Baker, Addison Wiggin
Andy Kessler, asset allocation, backtesting, bank run, banking crisis, Berlin Wall, Bernie Madoff, Black Swan, Branko Milanovic, break the buck, Bretton Woods, BRICs, business climate, capital asset pricing model, commoditize, corporate governance, correlation does not imply causation, credit crunch, Credit Default Swap, crony capitalism, cuban missile crisis, currency manipulation / currency intervention, debt deflation, Elliott wave, en.wikipedia.org, Fall of the Berlin Wall, feminist movement, fiat currency, fixed income, floating exchange rates, Fractional reserve banking, full employment, German hyperinflation, housing crisis, income inequality, index fund, inflation targeting, Joseph Schumpeter, laissez-faire capitalism, land reform, liquidity trap, Long Term Capital Management, McMansion, mega-rich, money market fund, moral hazard, mortgage tax deduction, naked short selling, negative equity, offshore financial centre, Ponzi scheme, price stability, pushing on a string, quantitative easing, RAND corporation, rent control, reserve currency, riskless arbitrage, Ronald Reagan, school vouchers, seigniorage, short selling, Silicon Valley, six sigma, statistical arbitrage, statistical model, Steve Jobs, The Great Moderation, the scientific method, time value of money, too big to fail, upwardly mobile, War on Poverty, Yogi Berra, young professional
One in particular, Harry Marcopolos, took it upon himself to pen a 19-page examination of Madoff complete with a recitation of no less than 29 “red flags,” which he presented seemingly on a silver platter to SEC officials titled, The World’s Largest Hedge Fund is a Fraud.12 Marcopolos is a derivatives expert, having traded portfolios in the billions of dollars in various options strategies for hedge funds and institutional clients. The general thesis Marcopolos advances is that for Madoff to have outdone the returns the market permits for riskless arbitrage, he would have had to deviate from it and consistently made bets that were winners for nearly 200 months, consecutively. (Madoff had seven months in which he claimed losses of less than 1 percent.) Zeroing in on periods of time when the market was pricing options such that riskless arbitrage was essentially inoperable, such as the Asian currency crisis, he concluded the likelihood of Madoff not having suffered more than a few skin lacerations is statistically almost impossible. (It could also be said it was strange he never hit the cover off the ball if he had needed to deviate from riskless posturing during such unusual market conditions.)
While selection of and access to funds with high returns is a key determinant of the success of funds of funds, an equally large selling point for them is usually their procedures for due diligence (how well they kick the tires). The most amazing part of the Madoff affair is that experienced hands in the industry which practiced the investment strategy Mr. Madoff Wings of Wax 25 professed to employ, an options trading technique long known as “riskless arbitrage,” loudly proclaimed that it was impossible to produce a track record with it akin to what Madoff reported to his investors. When practiced in its purest form, it involves buying and selling calls, puts, and an underlying equity such that risk of price movement is hedged away. Under these circumstances the market has long offered essentially Treasury bill type returns, because arbitrage has narrowed spreads since at least the 1970s.
Mathematics for Economics and Finance by Michael Harrison, Patrick Waldron
Brownian motion, buy low sell high, capital asset pricing model, compound rate of return, discrete time, incomplete markets, law of one price, market clearing, Myron Scholes, Pareto efficiency, risk tolerance, riskless arbitrage, short selling, stochastic process
To avoid degeneracies, we require: 1. that not every portfolio has the same expected return, i.e. e 6= E[r̃1 ]1, (6.4.5) and in particular that N > 1. 2. that the variance-covariance matrix, V, is (strictly) positive definite. We already know from (1.12.4) that V must be positive semi-definite, but we require this slightly stronger condition. To see why, suppose ∃w 6= 0N s.t. w> Vw = 0 (6.4.6) Then ∃ a portfolio whose return w> r̃ = r̃w has zero variance. This implies that r̃w = r0 (say) w.p.1 or, essentially, that this portfolio is riskless. Arbitrage will force the returns on all riskless assets to be equal in equilibrium, so this situation is equivalent economically to the introduction of a riskless asset later. In the portfolio problem, the place of the matrix A in the canonical quadratic programming problem is taken by the (symmetric) negative definite matrix, −V, which is just the negative of the variance-covariance matrix of asset returns; g1 = 1> and α1 = W0 ; and g2 = e> and α2 = W1 . (6.4.5) guarantees that the 2 × N matrix G is of full rank 2.
Expected Returns: An Investor's Guide to Harvesting Market Rewards by Antti Ilmanen
Andrei Shleifer, asset allocation, asset-backed security, availability heuristic, backtesting, balance sheet recession, bank run, banking crisis, barriers to entry, Bernie Madoff, Black Swan, Bretton Woods, buy low sell high, capital asset pricing model, capital controls, Carmen Reinhart, central bank independence, collateralized debt obligation, commoditize, commodity trading advisor, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, debt deflation, deglobalization, delta neutral, demand response, discounted cash flows, disintermediation, diversification, diversified portfolio, dividend-yielding stocks, equity premium, Eugene Fama: efficient market hypothesis, fiat currency, financial deregulation, financial innovation, financial intermediation, fixed income, Flash crash, framing effect, frictionless, frictionless market, George Akerlof, global reserve currency, Google Earth, high net worth, hindsight bias, Hyman Minsky, implied volatility, income inequality, incomplete markets, index fund, inflation targeting, information asymmetry, interest rate swap, invisible hand, Kenneth Rogoff, laissez-faire capitalism, law of one price, Long Term Capital Management, loss aversion, margin call, market bubble, market clearing, market friction, market fundamentalism, market microstructure, mental accounting, merger arbitrage, mittelstand, moral hazard, Myron Scholes, negative equity, New Journalism, oil shock, p-value, passive investing, Paul Samuelson, performance metric, Ponzi scheme, prediction markets, price anchoring, price stability, principal–agent problem, private sector deleveraging, purchasing power parity, quantitative easing, quantitative trading / quantitative ﬁnance, random walk, reserve currency, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, riskless arbitrage, Robert Shiller, Robert Shiller, savings glut, selection bias, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, stochastic volatility, survivorship bias, systematic trading, The Great Moderation, The Myth of the Rational Market, too big to fail, transaction costs, tulip mania, value at risk, volatility arbitrage, volatility smile, working-age population, Y2K, yield curve, zero-coupon bond, zero-sum game
If any particular asset should offer a higher expected return due solely to the increase in the quantity outstanding, investors will soon arbitrage away such profit opportunities. Arbitrage is possible because assets are “not unique works of art” but have close counterparts in other assets or mixes of other assets (Scholes, 1972). If there are perfect substitutes and frictionless markets, buying a highexpected-return asset while selling a substitute with a lower expected return constitutes a riskless arbitrage. Subsequent empirical studies disputed the notion that perfect substitutes exist. Demand effects may play a key role in explaining time-varying risk premia, given the lack of substitutes for market risk exposures. Even the substitutability of single stocks can be challenged. A key example is the S&P 500 inclusion effect—the finding that new entries to the S&P 500 index experience a sudden and persistent price jump, presumably due to new buying pressure from index funds.
Frictions related to illiquidity, funding constraints, and trading costs, as well as counterparty risk, agency concerns, and other information problems can be first-order important, as the 2008 experience shows. Bearish expectations, elevated risk, and risk aversion do not alone explain the distressed price levels of securitized bonds and other assets. Many financial intermediaries and investors became forced sellers as market frictions prevented them and other investors from taking advantage of good deals or nearly riskless arbitrage opportunities. Opportunities that appeared compelling over the long horizon could not be taken due to the possibility that further de-levering and related mark-to-market volatility would make the investment positions unsustainable over the short run. A diverse literature on market frictions explains why asset prices might deviate from fair values or respond sluggishly to new information.
Next, I discuss the literature on value and momentum strategies which initially focused on the U.S. equity market. Cross-sectional trading strategies may be relatively value-oriented (buy low, sell high) or momentum-oriented (buy rising stocks, sell falling ones; essentially buy high, sell low)—and they may be applied within one market (say, equities) or across many asset markets. Micro-inefficiency refers to either the rare extreme case of riskless arbitrage opportunities or the more plausible case of risky trades and strategies with attractive reward-to-risk ratios. Cross-sectional opportunities are safer to exploit than market-directional opportunities—one can hedge away directional risk and diversify specific risk much more effectively. The value effect refers to the pattern that “value stocks”, those with low valuation ratios (low price/earnings, price/cash flow, price/sales, price/dividend, and price/book value ratios) tend to offer higher long-run average returns than “growth stocks” or “glamour stocks” with high valuation ratios.
Hedge Fund Market Wizards by Jack D. Schwager
asset-backed security, backtesting, banking crisis, barriers to entry, beat the dealer, Bernie Madoff, Black-Scholes formula, British Empire, Claude Shannon: information theory, cloud computing, collateralized debt obligation, commodity trading advisor, computerized trading, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, diversification, diversified portfolio, Edward Thorp, family office, financial independence, fixed income, Flash crash, hindsight bias, implied volatility, index fund, intangible asset, James Dyson, Long Term Capital Management, margin call, market bubble, market fundamentalism, merger arbitrage, money market fund, oil shock, pattern recognition, pets.com, Ponzi scheme, private sector deleveraging, quantitative easing, quantitative trading / quantitative ﬁnance, Right to Buy, risk tolerance, risk-adjusted returns, risk/return, riskless arbitrage, Rubik’s Cube, Sharpe ratio, short selling, statistical arbitrage, Steve Jobs, systematic trading, technology bubble, transaction costs, value at risk, yield curve
Since you had gotten off to such a good start with the fund, did you consider the possibility of building that into a career instead of getting a job? I thought I had more to learn. It was a good experience managing other people’s money and knowing what that felt like. What was your first investment based job? After my first and only year at law school, I took a summer job trading options at Bear Stearns. Did you know anything about options at that point? No, I ended up doing forward conversions, which are a riskless arbitrage.2 The idea was to put on these arbitrage trades and earn 18 to 19 percent annualized. The option market was that inefficient at the time? No, interest rates were that high at the time. I think the arbitrage added about 5 percent to 6 percent to the risk-free rate. Frankly, the trading was kind of mechanical. At the time, you didn’t have the option prices on the screen in front of you. I had to run to the other side of floor to get a printout of option prices to see what options were setting up attractively relative to the stock.
Albert Einstein, Andrew Wiles, asset allocation, availability heuristic, backtesting, Black Swan, capital asset pricing model, cognitive dissonance, compound rate of return, computerized trading, Daniel Kahneman / Amos Tversky, distributed generation, Elliott wave, en.wikipedia.org, feminist movement, hindsight bias, index fund, invention of the telescope, invisible hand, Long Term Capital Management, mental accounting, meta analysis, meta-analysis, p-value, pattern recognition, Paul Samuelson, Ponzi scheme, price anchoring, price stability, quantitative trading / quantitative ﬁnance, Ralph Nelson Elliott, random walk, retrograde motion, revision control, risk tolerance, risk-adjusted returns, riskless arbitrage, Robert Shiller, Robert Shiller, Sharpe ratio, short selling, source of truth, statistical model, systematic trading, the scientific method, transfer pricing, unbiased observer, yield curve, Yogi Berra
If this level is exceeded, the bettor faces greater risk without the beneﬁt of a faster growth of capital. If one were to employ a bet fraction of 0.58 it is likely all funds would be lost, despite the favorable expectation. This is what happens to an arbitrageur with good information who uses too much leverage. Another constraint on an arbitrage’s ability to enforce efﬁcient pricing is the lack of perfect substitute securities. An ideal (riskless) arbitrage transaction involves the simultaneous purchase and sale of a pair of securities with identical future cash ﬂows and identical risk characteristics. An arbitrage transaction based on securities that do not conform to this ideal necessarily involves risk. And it is risk that limits the degree to which arbitrage activity can force prices to efﬁcient levels. When a broad class of assets, such as all stocks, become overpriced, as they did in the spring of 2000, there is no substitute security to use as the long-side hedge to a short sale of the entire stock market.