Financial Hacking

Evaluate Risks, Price Derivatives, Structure Trades, and Build Your Intuition Quickly and Easily

Philip Maymin

• Publisher: WSPC
• Year: 2012
• Print ISBN: 9789814322553
• eBook ISBN: 9789814440660
• Topic: Business
• Subtopic: Finance
• Index: Business

This book teaches financial engineering in an innovative way: by providing tools and a point of view to quickly and easily solve real front-office problems. Projects and simulations are not just exercises in this book, but its heart and soul. You will not only learn how to do state-of-the-art simulations and build exotic derivatives valuation models, you will also learn how to quickly make reasonable inferences based on incomplete information. This book will give you the expertise to make significant progress in understanding brand new derivatives given only a preliminary term sheet, thus making you extraordinarily valuable to banks, brokerage houses, trading floors, and hedge funds.

Financial Hacking is not about long, detailed mathematical proofs or brief summaries of conventional financial theories; it is about engineering specific, useable answers to imprecise but important questions. It is an essential book both for students and for practitioners of financial engineering.

MBAs in finance learn case-method and standard finance mainly by talking. Mathematical finance students learn the elegance and beauty of formulas mainly by manipulating symbols. But financial engineers need to learn how to build useful tools, and the best way to do that is to actually build them in a test environment, with only hypothetical profits or losses at stake. That's what this book does. It is like a trading desk sandbox that prepares graduate students or others looking to move closer to trading operations.

Foreword
Foreword (309 KB)

Sample Chapter(s)
Chapter 6: Puzzles and Bugs (269 KB)
Chapter 9: The Best Trade in the World? (93 KB)

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Contents:

• Vanilla World:
  • Risk
  • Arbitrage
  • Trading Puzzles
• Vanilla Derivatives:
  • Black-Scholes
  • Simulation
  • Puzzles and Bugs
• Exotic Derivatives:
  • Single-Asset Exotic Options
  • Multi-Asset Exotic Options
• Exotic Worlds:
  • The Best Trade in the World?
  • Variance Swaps
  • Esoteric Worlds and Derivatives

Readership: Graduate and research students, finance practitioners and anyone passionate about the field of financial engineering.

Part 1

Vanilla World

Chapter 1

Risk

Risk is the “why?” behind finance. Without risk, there is no reason for finance or insurance or derivatives to exist at all. Of course there is risk in the real world. But it can be hard to understand when wrapped in all the complexities of reality. We can gain a lot of intuition about it by exploring it in the context of a plain vanilla world.

1.1 What is Risk?

There is no single perfect definition of risk. But you think you have one. If you have studied some finance or risk management before, you may think that risk is the probability and impact of a loss. That's a reasonable sounding definition, right? I've used it myself many times. But it's wrong. Let's see why.

Suppose you are my broker and I wish to invest my life earnings of $100 in IBM. I ask you a simple question: “What is my risk?”

What is the risk of putting $100 in IBM?

To go with the standard definition above, you might say that you need to calculate the answer based on a complicated formula involving the historical returns of IBM and perhaps even other securities, forecasts about the future, information about my preferences and income streams, and so forth. Suppose for specificity that after all your calculations the numbers that come out are like this: I would have a 20 percent chance of losing $30. Is that my risk?

If that's really my full risk, you should be willing to stand behind your claim. You should be willing to make me whole on losses beyond $30, or you should at least be willing to give me 4:1 odds that I won't experience a loss at all. Not quite ready to do that? Then maybe you haven't fully defined risk.

“Alright,” you say, “I get it. You're just trying to separate quantifiable risk from raw uncertainty, like the difference between tossing a coin and predicting the stock market.”

Am I?

True, there is a difference between the two concepts, but that distinction is more a pedagogical or a philosophical one. As traders and as financial hackers, we are just as comfortable assigning probabilities to uncertain outcomes as we are taking objective probabilities as given. After all, in the nitty-gritty world of actual life, there are no infinite samples or true probabilities, only a measure of how much we are willing to gamble and at what odds.

Instead, what I am arguing is that risk itself is hard to define.

Nevertheless, you may be asked at an interview to define risk. This is a weak, early-round question usually asked by younger interviewers who don't really know how to best conduct an interview. They are only looking for one answer: “Risk is uncertainty about the future.”

This is a silly answer. For one thing, if your electricity fails, and you do not see market data, then you also have exposure to market movements occurring in the past, not just the future. Just because you don't know what has already happened doesn't make it riskless.

Minsky then shut his eyes.

“Why do you close your eyes?” Sussman asked his teacher.

“So that the room will be empty.”

At that moment, Sussman was enlightened.

The ending to a famous hacker koan

I don't think there is a good definition of risk. Some people see less risk in skydiving than others. Some people can hedge risks that others cannot. Ultimately risk is just the set of your unhedged exposures, including ones you don't know about.

How should you respond when you are asked this question? It depends; if you are asked in a social setting, or after you already have the job, go ahead and opine freely. But if you are asked at an interview, start first with what they want to hear; then you can discuss the more intricate details.

This holds as a life lesson too: when people ask you questions expecting to hear a particular answer, they won't listen to what you are saying until you first speak the magic words their brains are tuned in to. Can you imagine being asked, “Does this make me look fat?” and responding with a treatise on nutrition and fashion and lighting and culture? The person asking will be fidgeting nervously, not processing a word you say, growing increasingly angry and hurt, until you at last mercifully let out a sharp and firm “No!” And then they'll ask you why it took so long.

Historically, risk was more of a nautical term referring to uncharted waters. When you discover new lands and new civilizations, when you boldly go where no one has gone before, you may die, or you may find riches. Today, risk only refers to bad outcomes. There is no “risk” to winning the lottery, but there is a very high risk of losing. This is merely a semantic difference and should not bother you too much. After all, in the financial world, someone's downside risk is someone else's upside potential.

So risk may not have a perfect definition. Does that mean finance is doomed? A sham? A false pursuit?

Not at all.

So what if risk isn't easily defined? Many fields cannot define the basics of what they study.

Biology is the study of life; life does not have a perfect definition. Physics is the study of matter; matter does not have a perfect definition.

1.2 What is Finance?

Finance is the study of risk, even though risk does not have a perfect definition.

You may have thought finance was also the study of money and savings and budgets and loans. There is some of that, but risk is central.

The origin of the word apparently traces back to the word “fine,” which related to the completion of a debt or the fulfilling of an obligation. It has the same meaning as one of the oldest words for freedom, the Sumerian “amargi,” which was literally an order to release to their mothers the children that had been held as slaves and collateral on the debt. Finance is thus a very libertarian concept.

How is it pronounced? Is it fin-ANCE or FINE-ance?

(a) It is pronounced FINE-ance when it is a verb, as in, “I want to finance this vehicle,” but fin-ANCE when it is a noun, as in, “I work in finance.”

(b) The exact opposite is true.

(c) Neither of the above is true.

The answer seems to be (a) in the U.S.A. and (b) in the U.K., so globally the answer must be (c). I don't think anybody knows. Pronounce it however you like, in any context.

If you ask people what finance means today, the answer will be some variation of “money.” It could be personal finance dealing with personal money, corporate finance dealing with corporate money, and so on. Yet we don't call what financial hackers do monetary engineering, but rather financial engineering. So there is some difference between money and finance.

Indeed, one view of finance is that it is about the slicing and dicing of money, and, of course, risk. Through securities, derivatives, and contracts, finance reallocates risk in exchange for money.

1.3 Value-at-Risk Puzzles

Philosophy aside, we need to manage risk in the real world. If we don't do it, someone else will, and they may not do as good a job.

The most common systematic approach to evaluating the risk of an arbitrary portfolio or position is to ask what is its value-at-risk or VaR. Note that the middle letter is lowercase to help distinguish it from VAR or Var, which may refer to variance.

The idea behind the VaR is reasonable enough. It asks what is the worst case loss that can result from the given position, assuming we would be unable to liquidate it for a given period of time.

Actually, what it asks is slightly different. It asks what is the almost worst case loss. If it were asking about the true worst case loss, for a long-only unleveraged portfolio, that answer would be 100 percent, regardless of the time period. That's not a very useful answer for the real world, even though it is technically correct, because it doesn't help compare and contrast across different possibilities.

Instead, VaR asks, ignoring the really bad outcomes, let's say the worst 1 percent, other than those, what is the most we can expect to lose over a given period of time?

Your first day on the job as a risk manager, or perhaps even during an interview, you may be asked to calculate the VaR. “Hey new kid, get me the VaR on IBM,” the boss might bark and start to walk away.

Before he is out of earshot, you need to ask him three questions, and possibly four.

First, what is the underlying? “IBM,” he says, looking at you like you are hard of hearing. Okay, if he has already told you, don't ask again.

Second, what is the percentage for the VaR? This is usually a number like 95 or 99 percent, and it represents the portion of the distribution you do not throw away. So a 95 percent VaR means, what is the worst case loss, except for the really worst case 5 percent? “99 percent,” he says.

Third, what is the holding period? This means how long you are expected to have to withstand the risk to the position. If you only have to hold the position one day against your will, that will have less VaR than if you have to hold a month. “10 days,” he says. That's the usual answer and it represents ten business days, or two weeks.

The possible fourth question is how far back to look in historical data. You could make this judgment call yourself, but it is an important consideration. The further back you look, the more data you'll have, but the distribution of IBM returns 50 years ago is probably not very relevant to their distribution tomorrow.

To give him some comfort that you know what you are doing, you can combine all these questions with the typical default assumptions into one quick shout: “99 percent, 10-day VaR on IBM, looking back five years?”

“Sure,” he says, and nods approvingly, and disappears.

“And poof. Just like that, he's gone.”

Verbal Kint (Kevin Spacey), “The Usual Suspects”

The best way to compute the VaR is if you have a distribution for the future that you believe. But you usually don't have that, so you use past data as an indication of what the future might look like. You don't believe the past will repeat verbatim, in the same order, but perhaps the distribution is the same, or at least similar enough.

“History doesn't repeat itself — at best it sometimes rhymes.”

Mark Twain

There are two primary ways to compute the VaR: parametric and non-parametric. Non-parametric is easier to understand. Take your historical data. Divide it into returns of the same length as your target time period. For example, slice it up into overlapping ten-day returns. Now you have a list of ten-day returns that happened in the past. Order those from most negative to most positive. Throw away the first 1 percent, if you are doing 99 percent VaR. The remaining number is your VaR. It means, if the future rhymes with the past, the worst case ten-day loss that can happen, ignoring the really worst 1 percent, is this number.

Now, with non-parametric, you sometimes have jumps between the returns. Your ninth-worst return and your tenth-worst return might be separated by a few percent. If you want a more continuous number that doesn't jump so much, you can interpolate between the two closest numbers. It doesn't matter for conceptual purposes.

Parametric is simpler to calculate but requires more assumptions. For parametric VaR, you have to assume what the future distribution will look like, and then calibrate the particular parameters based on the historical data.

Almost always, the parametric family is the normal distribution. So you would just calculate the historical average and standard deviation of returns and assume your future distribution will be the normal with those parameters. Then your 99 percent VaR is just 2.33 standard deviations below the mean, and your 95 percent VaR is 1.96 standard deviations below the mean.

Whether you do parametric or non-parametric, you should end up with a negative number, representing, as it does, a loss. When we speak the VaR, however, we omit the negative sign. So we might say the 99 percent 10-day VaR on a $100 million investment in IBM is $10 million, meaning that the most we will lose over a ten-day period, except f...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• dedication
• Foreword
• Contents
• Part 1
• Chapter 1 Risk
• Chapter 2 Arbitrage
• Chapter 3 Trading Puzzles
• Chapter 4 General Principles of Molecular Imaging Probe Design
• Chapter 4 Black-Scholes
• Chapter 5 Simulation
• Chapter 6 Puzzles and Bugs
• Part 3
• Chapter 7 Single-Asset Exotic Options
• Chapter 8 Multi-Asset Exotic Options
• Part 4
• Chapter 11 The Best Trade in the World?
• Chapter 10 Variance Swaps
• Chapter 11 Esoteric Worlds and Derivatives