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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Explore the deadly elegance of finance's hidden powerhouse The Money Formula takes you inside the engine room of the global economy to explore the little-understood world of quantitative finance, and show how the future of our economy rests on the backs of this all-but-impenetrable industry. Written not from a post-crisis perspective - but from a preventative point of view - this book traces the development of financial derivatives from bonds to credit default swaps, and shows how mathematical formulas went beyond pricing to expand their use to the point where they dwarfed the real economy. You'll learn how the deadly allure of their ice-cold beauty has misled generations of economists and investors, and how continued reliance on these formulas can either assist future economic development, or send the global economy into the financial equivalent of a cardiac arrest. Rather than rehash tales of post-crisis fallout, this book focuses on preventing the next one. By exploring the heart of the shadow economy, you'll be better prepared to ride the rough waves of finance into the turbulent future. * Delve into one of the world's least-understood but highest-impact industries * Understand the key principles of quantitative finance and the evolution of the field * Learn what quantitative finance has become, and how it affects us all * Discover how the industry's next steps dictate the economy's future How do you create a quadrillion dollars out of nothing, blow it away and leave a hole so large that even years of "quantitative easing" can't fill it - and then go back to doing the same thing? Even amidst global recovery, the financial system still has the potential to seize up at any moment. The Money Formula explores the how and why of financial disaster, what must happen to prevent the next one.
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The Money Formula
DODGY FINANCE, PSEUDO SCIENCE, AND HOW MATHEMATICIANS TOOK OVER THE MARKETS
Paul Wilmott
David Orrell
This edition first published 2017© 2017 Paul Wilmott and David Orrell
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Library of Congress Cataloging-in-Publication Data
Names: Wilmott, Paul, author. | Orrell, David, author.Title: The money formula : dodgy finance, pseudo science, and how mathematicians took over the markets / Paul Wilmott, David Orrell.Description: Hoboken : Wiley, 2017. | Includes bibliographical references and index.Identifiers: LCCN 2016053256| ISBN 9781119358619 (paperback) | ISBN 9781119358664 (Adobe PDF) | ISBN 9781119358688 (ePub)Subjects: LCSH: Finance Mathematical models. | BISAC: BUSINESS & ECONOMICS / Finance.Classification: LCC HG106 .W555 2017 | DDC 332.64–dc23LC record available at https://lccn.loc.gov/2016053256
A catalogue record for this book is available from the British Library.
ISBN 978-1-119-35861-9 (paperback) ISBN 978-1-119-35866-4 (ebk)ISBN 978-1-119-35868-8 (ebk) ISBN 978-1-119-35872-5 (ebk)
Cover design concept: Beatriz Leon
To Oscar, Zachary, Genevieve, and Horatio
—Paul Wilmott
To Wendy and Katherine
—David Orrell
CONTENTS
Acknowledgements
About the Authors
Introduction
Notes
Chapter 1 Early Models
Monetary Alchemy
Gold Standard
The Systems of Nature
Rational Mechanics
Finding Equilibrium
Intrinsic Value
Notes
Chapter 2 Going Random
Theory of Speculation
Efficient Markets
Irrational Markets
Not Normal
Mental Virus
Notes
Chapter 3 Risk Management
Fundamentals
Beauty Contest
Technical Analysis
Quant Analysis
Correlation
Well…
Efficiency Squared
Value at Risk
The Edge of Chaos
Notes
Chapter 4 Market Makers
Options
What are Options for?
Bachelier's Return
The Ultimate Machine
Beat the Market
Hedging your Bets
Mathematical Dynamite
No Risk
Positive Feedback
Notes
Chapter 5 Deriving Derivatives
Time to Exercise
Decision Cost
New Flavors
You can't Always Delta Hedge
Market Price of Risk Again
Getting Carried Away
From the Sublime to the Ridiculous
Hold it Together
Model Abuse
Pass the Parcel
Money Crunch
Notes
Chapter 6 What Quants Do
What do Quants Make – and are They Adequately Paid?
Quants vs. Regulators
Writer-nomics
Blinding us with Science
Bots
Global Brain
Creative Finance
Notes
Chapter 7 The Rewrite
Blowing Smoke
Calibrating the Crystal Ball
Sources of Confusion
Model Risk
Flying Blind
Notes
Chapter 8 No Laws, Only Toys
A Clue
Back to Basics
A Model for Interest Rates?
A Role Model
Reasons to be Mathematical
Quantum Finance
Order and Chaos
Notes
Chapter 9 How to Abuse the System
Exercise 1: The Newbie Trader
Exercise 2: The Hedge Fund Manager
Exercise 3: The Risk Manager
Triple-A
Defeat Device
Notes
Chapter 10 Systemic Threat
Foresight
The MacGuffin
But High-Speed Trading Provides Liquidity!
A Million Billion Dollars
The Bionic Hand
The System (John Law feat. Isaac Newton)
Notes
Epilogue: Keep it Simple
Quants: The Math Sweet Spot
Regulators: Go Full Iceland
Economists: Wake Up
Banks: Learn to Fail
Traders: Why Does My Bonus Have a Minus Sign in Front?
Journalists: Watch Out for Saboteurs
Educators: Quantity and Quality
Politicians: Create an FAA for the Financial System
I Solemnly Swear…
The Nuclear Option
Notes
Bibliography
Index
EULA
List of Tables
Chapter 9
Table 9.1
Table 9.2
List of Illustrations
Chapter 2
Figure 2.1
Coin toss results
Figure 2.2
A histogram showing the final distribution after 14 iterations
Figure 2.3
100-Step random walk
Figure 2.4
Density plot for the Dow Jones Industrial Index, which dates back to Oct 1, 1928
Figure 2.5
Histogram of the price changes after 100 days for each segment of the Dow Jones data
Chapter 3
Figure 3.1
P/E ratios by industry
Figure 3.2
General Motors
Figure 3.3
Random
Figure 3.4
Example risk/return chart
Figure 3.5
A selection of stocks plotted according to their risk and expected return, and a portfolio
Figure 3.6
Lines representing the efficient frontier and, when the risk-free investment is included, the capital market line and market portfolio
Chapter 4
Figure 4.1
Plot of theoretical option vs. stock price curves, for a call price of $100
Figure 4.2
Diagram of option prices for the coin-tossing game, for different times and scores
Figure 4.3
Plot of option price vs. score at time 2 (dashed line) and time 4 (solid line) for the coin-tossing game
Chapter 5
Figure 5.1
Market price of risk
Chapter 9
Figure 9.1
Two extreme strategies: (A) successful for both investor and manager in the long run; (B) successful for the manager, but ultimately catastrophic for the investor
Guide
Cover
Table of Contents
Introduction
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Acknowledgements
The authors would like to thank publisher Thomas Hyrkiel, project editor Jeremy Chia, production editor Samantha Hartley, and the rest of the Wiley team. Thanks also to Seth Ditchik, Ed Howker, Julia Kingsford, Robert Lecker, Beatriz Leon, Robert Matthews, Myles Thompson, and Andrea Wilmott.
About the Authors
Paul Wilmott is a mathematician and serial entrepreneur. His textbooks and educational programs provide the definitive training for quants; his website wilmott.com is the center of the quant community; his eponymous bi-monthly – and according to Esquire the world's most expensive – magazine is a quant must-have. As a practitioner he has been a consultant to leading financial institutions and managed his own hedge fund. As a commentator he has appeared on many TV and radio programs and written OpEds for the New York Times. Nassim Nicholas Taleb calls him the smartest quant in the world: “He's the only one who truly understands what's going on… the only quant who uses his own head and has any sense of ethics.” Paul divides his time between London, the Cotswolds, and New York.
David Orrell is an applied mathematician and writer. Founder of the scientific consultancy Systems Forecasting, his scientific work has encompassed diverse areas such as particle accelerator design, weather prediction, cancer biology, and economics. His books on subjects including prediction, economics, and science have been national bestsellers and have been translated into over ten languages. A revised and expanded version of his book Economyths: 10 11 Ways That Economics Gets it Wrong is also published this year. He lives in Toronto.
Introduction
“How about the scandalous stories of thousands of families with small and medium investments who have been ruined because of the greed of financial institutions in the United States and Europe. Look at the evictions, ruined families, and suicide attempts caused by the financial crisis of those who have failed to control the capital markets or the prices of raw materials. ¡Vaya mierda!”1
—Response to the survey question: “Do you have any outrageous or hilarious stories that you think ought to be in Paul and David's new book? Share some details, please!” at wilmott.com
“The truth about their motivation in writing.”
—Response to the survey question: “What topics should definitely feature in the book?” at wilmott.com
The global financial crisis that peaked in late 2008, and whose aftershocks have yet to fully dissipate, was the culmination of many years of dubious financial practices. If carried out alone they might have caused only localized harm, but they became aligned in the way that only the most dramatic of astrologers can dream of: a quadrillion dollars in complex financial products that no one understands; risk-management techniques that hide risk rather than decrease it; moral hazard and dangerous incentives; lack of diversification; regulators that are oblivious; mathematicians acting as psychological enablers. It was a story where the naïve, the negligent, and the downright nasty all pulled together in seizing as much as possible for themselves while almost destroying the financial foundations of the planet.
Of course, things have moved on since then. The banking system has become even more concentrated. Global debt – the engine fuel of finance – has grown to unprecedented levels. Markets, in which activity is increasingly dominated by high-frequency-trading robots, experience constant “flash” events where prices suddenly go wild before returning to more normal levels. The world financial system is once again rattling at its cage, ready to blow. And quantitative finance – the use of mathematical models to assist or dictate investment decisions – has become more powerful and influential than ever.
The story, in other words, isn't over – not by a long shot. Indeed, the stakes have never been higher, which is why previously arcane topics such as hedge funds, high-frequency trading, and too-big-to-fail banks have become a major topic of often-confusing debate for everyone from TV pundits to politicians. And why the confusion is often deliberate.
It has been estimated that in 2010 the notional value of all the financial derivatives in existence was $1.2 quadrillion.2 That's $1,200,000,000,000,000. For comparison, it's about 17 times the market capitalization of all the world's stock markets, or 150 times the value of the above-ground gold supply, or $170,000 for every living human on the planet. Actually, it's larger than the entire global economy. We'll explain this number, and how it could be interpreted, later. For the moment, let's just say that whatever it means in terms of risk, it seems like a dangerously big number for what is, let's be honest, just a service industry.
This book is not about the fallout from the crisis – plenty of books and column inches have been written about that – but about helping to prevent the next one (which won't look like the last one). To do that, it is necessary to go into the engine room of this massive shadow economy and understand how quantitative analysis works. How do you create a quadrillion dollars out of nothing, blow it away, and leave a hole so large that even years of the deliberately misnamed “quantitative easing” can't fill it – and then go back to doing the same thing, only faster? Part of a quant's job, as we'll see, is science, and another part (the one where mathematics is used to obfuscate reality) is the opposite of science. We will discuss both, starting with the science.
The book is divided into two main parts. The first five chapters dip into the history of quantitative finance and explain its key principles, such as risk analysis, bond pricing, portfolio insurance – all those gold-standard techniques, in short, which completely failed during the crisis, but have yet to be properly reinvented. We explore the elegant equations used in financial mathematics, and show how the deadly allure of their ice-cold beauty has misled generations of economists and investors. We trace the development of financial derivatives from bonds to credit default swaps, and show how mathematical formulas helped not just to price them, but also to greatly expand their use to the point where they dwarfed the real economy. And we show how risk-management and insurance schemes have led to more risk and less insurance than arguably at any time in history.
The second part is about the quantitative finance industry today, and how it is evolving. We will show what quants do, the techniques they use, and how they continue to put the financial system at peril. Part of the problem, we'll see, is that quants treat the economy as if it obeys mechanistic Newtonian laws, and – by nature and by training – have no feel for the chaos, irrationality, and violent disequilibrium to which markets often seem prone. The same can also be said of the regulators watching the system. We'll lower ourselves into the hidden caves of finance, with their “dark pools” navigated by swarms of high-frequency traders, and show how new ideas from areas such as complexity science and machine learning are providing analytic tools for visualizing and understanding the turbulent eddies of financial flows. Along the way, we will grapple with some of the philosophical and practical difficulties in modeling the financial system – and show how models are often used less for predicting the future than for telling a story about the present.
The authors are both Oxford-trained applied mathematicians, who have worked in a variety of industries but otherwise come to this project from different angles. Paul is a quintessential insider – named “arguably the most influential quant today” by Newsweek – but he is also (as visitors to quant forum wilmott.com will know) a longstanding critic of standard practices. David works primarily in the areas of mathematical forecasting and computational biology (he invented a program called “Virtual Tumour,” which gives you an idea). He has argued in a number of books that economics needs to take a similarly biological approach – and that our out-of-control financial sector is in serious need of a health check.
The Money Formula provides new insights into one of the largest, best-paid, but least-understood industries in the world – and the one with the most capacity to either help our future economic development or give it the financial equivalent of a cardiac arrest.
We begin by turning to the early 18th century, when France was seeking financial advice from a mathematician.
Notes
1
We're translating from the Spanish. We think that “
¡Vaya mierda!
” is slang for “Have a great day!” but we're not sure.
2
This was estimated by the economist Tim Harford and Paul for the BBC Radio 4 program
More or Less
based on data from the website of the Bank for International Settlements. This “headline” figure, which is open to interpretation, includes both the contracts traded through an exchange and the over-the-counter market in which two parties trade directly. It is also what is called the “notional” value. If a contract specifies that it will pay you 1% of $1 million in a year's time then that would be recorded as a notional of $1 million, whereas it's really just worth about $10,000. So it's tricky to say what amount really is at risk in that $1.2 quadrillion.
CHAPTER 2Going Random
“We are floating in a medium of vast extent, always drifting uncertainly, blown to and fro; whenever we think we have a fixed point to which we can cling and make fast, it shifts and leaves us behind; if we follow it, it eludes our grasp, slips away, and flees eternally before us. Nothing stands still for us. This is our natural state and yet the state most contrary to our inclinations. We burn with desire to find a firm footing, an ultimate, lasting base on which to build a tower rising up to infinity, but our whole foundation cracks and the earth opens into the depth of the abyss.”
—Blaise Pascal, Pensées
“Random; a dark field where dark cats are chased with laser guns; better than sex; like gambling; a little bit of math, some finance, lot of hypotheses, a lot of assumptions, more art than science; an attempt to predict or explain financial markets using mathematical theory; the art of collecting rent from the real economy; mathematical rationalisation for the injustices of capitalism; much like math, physics, and statistics helped meteorologists in building technology to predict weather, we quants do the same for markets; well, I could tell you but you don't have the necessary brain power to understand it *Stands up and leaves*.”
—Responses to the survey question: “How would you describe quantitative finance at a dinner party?” at wilmott.com
Quantitative finance is about using mathematics to understand the evolution of markets. One approach to prediction is to build deterministic Newtonian models of the system. Alternatively, one can make probabilistic models based on statistics. In practice, scientists usually use a combination of these approaches. For example, weather predictions are made using deterministic models, but because the predictions are prone to error, meteorologists use statistical techniques to make probabilistic forecasts (e.g., a 20% chance of rain). Quants do the same for the markets, but then bet large amounts of money on the outcome. This chapter looks at how probability theory is applied to forecast the financial weather.
In 1724, after the collapse of his French monetary experiment, John Law supported himself in Venice by gambling. He would sit at a table at the Ridotto casino with 10,000 gold pistole coins arranged in stacks like casino chips, and offer any challenger the chance to make a wager of a single pistole. If they rolled six dice and got all sixes, then they could keep the lot. Law knew the odds of this happening were only 1 in 46,656 (6 multiplied by itself 6 times). So people always lost, but would go away happy at having gambled with the notorious John Law.
A key concept from probability theory is the idea of expected value, which equals the payout multiplied by the probability. For Law's gamble, this was 10,000 multiplied by 1/46,656, or 0.21 gold pistoles. Since the stake was 1 pistole, Law had an edge (a fair payout would have been 46,656 coins instead of 10,000). It was his money, after all, so he wanted to make a profit. We'll see later that he could still have made money even if he had offered the punters better odds, odds giving them the positive expectation. The solution to this apparent paradox is that he would have to do his gambling via a financial vehicle, a hedge fund, and he'd have to be betting with other people's money.
The connection between basic probability theory and something like the stock market becomes clear when we consider the result of a sequence of coin tosses, as in Figure 2.1. Here the paths start at the left and branch out to the right with time. If the coin comes up heads, you win one point, but if it is tails, you lose a point. The heavy line shows one particular trajectory, known as a random walk, against the background of all possible trajectories. At each time step, the path takes a random step up or down. Most paths remain near the center. Figure 2.2 shows how the final distribution looks after 14 time steps. The mean or average displacement is zero, and over 20% of the paths end with no displacement. If this were a plot of price changes for a stock, and the horizontal axis represented time in days, we would say that the expected value of the stock after 14 days would be unchanged from its initial value.
Figure 2.1 Coin toss results
The black line shows one possible random walk, with a vertical step of plus 1 (up) or minus 1 (down) at each iteration. The light gray lines are an overlay of all possible paths through 14 iterations. The plot shows how the future becomes more uncertain as the possible paths multiply.
Figure 2.2 A histogram showing the final distribution after 14 iterations
