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TradingRisk
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Founded in 1807, John Wiley & Sons is the oldest independent publishingcompany  in  the  United  States.  With  offices  in  North  America,  Europe,Australia, and Asia, Wiley is globally committed to developing and marketingprint  and  electronic  products  and  services  for  our  customers’  professionaland personal knowledge and understanding.
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TradingRisk
Enhanced Profitabilitythrough Risk Control
KENNETH L. GRANT
John Wiley & Sons, Inc.
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To Nina, for how could I possibly name anyone else?
Copyright © 2004 by Kenneth L. Grant. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.
Chapter 2 opening lyrics from Shawn Phillips, “Spaceman,” COLLABORATION, © 1971, DickJames  Music,  Inc.,  &  BMI.  Reprinted  by  permission  of  Shawn  Phillips  and  http://www.shawnphillips.com.
Chapter  6  opening  lyrics  from  Paul  Heaton  and  David  Rotheray,  Beautiful  South,    “LIAR’SBAR,” from BLUE IS THE COLOR, © October 1996, Universal Music. Reprinted by permissionof Universal Music Publishing Group.
No part of this publication may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, recording, scanning, orotherwise, except as permitted under Section 107 or 108 of the 1976 United States CopyrightAct,  without  either  the  prior  written  permission  of  the  Publisher,  or  authorization  throughpayment  of  the  appropriate  per-copy  fee  to  the  Copyright  Clearance  Center,  Inc.,  222Rosewood  Drive,  Danvers,  MA  01923,  978-750-8400,  fax  978-646-8600,  or  on  the  web  atwww.copyright.com. Requests to the Publisher for permission should be addressed to thePermissions  Department,  John  Wiley  &  Sons,  Inc.,  111  River  Street,  Hoboken,  NJ  07030,201-748-6011, fax 201-748-6008.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their bestefforts in preparing this book, they make no representations or warranties with respect to theaccuracy or completeness of the contents of this book and specifically disclaim any impliedwarranties of merchantability or fitness for a particular purpose. No warranty may be createdor extended by sales representatives or written sales materials. The advice and strategies con-tained herein may not be suitable for your situation. You should consult with a professionalwhere appropriate. Neither the publisher nor author shall be liable for any loss of profit or anyother commercial damages, including but not limited to special, incidental, consequential, orother damages.
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ISBN 0-471-65091-9
Printed in the United States of America.
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Contents
PREFACE
ACKNOWLEDGMENTS
CHAPTER 1 The Risk Management Investment
CHAPTER 2 Setting Performance Objectives
Optimal Target Return Nominal Target Return Stop-Out Level The Beach 
CHAPTER 3 Understanding the Profit/Loss 
Patterns over Time
And Now to Statistics, but First a Word
(or More) about Time Series Construction Time Units Time Spans 
Graphical Representation of Daily P/L 
Histogram of P/L Observations 
Statistics 
A Tribute to Sir Isaac Newton Average P/L Standard Deviation 
Sharpe Ratio 
Median P/L 
Percentage of Winning Days 
Performance Ratio, Average P/L, Winning Days 
versus Losing Days 
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CONTENTS
Drawdown 
Correlations 
Putting It All Together 
CHAPTER 4  The Risk Components of an 
Individual Portfolio
Historical Volatility Options Implied Volatility Correlation Value at Risk (VaR) 
Justification for VaR Calculations 
Types of VaR Calculations 
Testing VaR Accuracy 
Setting VaR Parameters 
Use of VaR Calculation in Portfolio Management 
Scenario Analysis Technical Analysis 
CHAPTER 5 Setting Appropriate Exposure Levels 
(Rule 1)
Determining the Appropriate Ranges 
of Exposure Method 1: Inverted Sharpe Ratio 
Method 2: Managing Volatility as a Percentage of Trading Capital  
Drawdowns and Netting Risk Asymmetric Payoff Function 
CHAPTER 6 Adjusting Portfolio Exposure 
(Rule 2)
Size of Individual Positions Directional Bias Position Level Volatility Time Horizon Diversification Leverage Optionality 
Nonlinear Pricing Dynamics
Relationship between Strike Price and 
Underlying Price (Moneyness)
70
7379
81
8486909192
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99
102104106
109
110111
114129130
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Contents
Implied Volatility
Asymmetric Payoff Functions
Leverage Characteristics
Summary 
CHAPTER 7 The Risk Components of an Individual Trade
Your Transaction Performance 
Key Components of a Transactions-Level Database 
Defining a Transaction
Position Snapshot Statistics 
Core Transactions-Level Statistics 
Trade Level P/L 
Holding Period 
Average P/L 
P/L per Dollar Invested (Weighted Average P/L) 
Average Holding Period 
P/L by Security (P/L Attribution) 
Long Side P/L versus Short Side P/L 
Correlation Analysis 
Number of Daily Transactions 
Capital Invested 
Net Market Value (Raw) 
Net Market Value (Absolute Value) 
Number of Positions 
Holding Periods Volatility/VaR 
Other Correlations 
Final Word on Correlation 
Performance Success Metrics Methods for Improving Performance Ratios 
Performance Ratio Components 
Maximizing Your P/L 
Profitability Concentration (90/10) Ratio 
Putting It All Together 
CHAPTER 8 Bringin’ It on Home
Make a Plan and Stick to It If the Plan’s Not Working, Change the Plan Seek to Trade with an “Edge” 
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CONTENTS
Structural Inefficiencies 
Methodological Inefficiencies 
Play Your P/L Avoid Surprises—Especially to Yourself Seek to Maximize Your Performance 
at the Margin 
Seek Nonmonetary Benefits Apply Liberal Doses of Humility and Humor Be Healthy/Cultivate Other Interests 
APPENDIX 
Optimal f and Risk of Ruin
Optimal f Risk of Ruin 
INDEX
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PrefaceContents
Make voyages. Attempt them. There’snothing else.
—Tennessee Williams
Camino Real
You are interested in making money in the markets, or you would not
have  selected  this  book  from  the  millions  of  other  choices—from,say, Thomas Wolfe to Tom Wolfe. If you’re going to forsake the sub-lime in favor of the pedestrian, then certainly you expect to be paid for thesacrifice. And who am I to blame you? The truth is, I’d like to get paid, too.I’m  here  to  tell  you  that  our  common  objective  demands  more  of  usthan simply making the right trades. Every single successful trader I knowemploys effective risk management as a part of his or her working pro-gram. Of course, I am biased on this subject because risk management ismy  career—a  profession  that  has  rendered  me  neither  fabulouslywealthy nor immensely popular with my colleagues, but at least perpetu-ally employed. 
Not that I set out with any direct intention to become a risk manager.In  fact,  it  would  be  more  accurate  to  say  that  I  simply  stumbled  into  it.Prior to this watershed event, I would have best described myself as some-one  loitering  at  the  intersection  between  the  financial  and  the  academicworlds, looking for something to at least partially cover, if not justify, thefinancial toll visited on my parents as the result of their willingness to sub-sidize my two master’s degrees. Then, perhaps by fate, the futures marketsbeckoned.  My  uncle  and  his  partners  were  looking  for  quantitativemethodologies to estimate what they might lose if things went awry amongthe team of traders whose Chicago Board of Trade bond pit activity theywere  staking.  This  was  back  in  the  mid-1980s,  when  no  one  spent  muchtime thinking about risk management and, therefore, no one I spoke to hadmuch of a clue as to how I should begin this task. 
I  managed  to  muddle  through,  however,  and  did  it  well  enough  toconvince the Chicago Mercantile Exchange (the Merc) to entrust me withthe responsibility of building a risk management practice within the bow-els of its clearinghouse: the central risk-processing unit for that vast and
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complex  market  mechanism.  By  this  time,  the  field  of  risk  managementhad evolved to the point that when I told people that this was what I didfor a living, the comment was occasionally received with something otherthan a blank stare. We spent a good amount of time and resources think-ing, talking, and engaging in much hand wringing on risk management—and ultimately to good effect, I think. What is more, the stakes were high.Given the impact of the 1987 crash on the Merc’s financial system, it waspretty clear that in the future it would have to have a pretty good handleon who was risking what in its markets, and with what resources behindthem. Still, I won’t lie: There was much trial and error and many mistakesmade before we ever began to get it right.
Since that time, I have more or less made a career out of convincingothers that if risk management was their objective, I was their guy.  My firstsuch “patient” was Société Générale, the venerable French bank, where Igained the enormous advantage of applying the discipline to a multiprod-uct,  multicurrency  environment.  This  was  certainly  interesting  and  chal-lenging, for a while; but cursed wanderlust eventually overtook me again.Only this time, I really fixed things for myself, landing in what can only bedescribed as the Dodge City of risk management jurisdictions—the hedgefund  industry.  Here,  as  elsewhere,  when  I  arrived,  there  were  nearly  norules; so I had to make up my own. Now the place is a bit more civilized;but what is perhaps even more surprising is that the topic of hedge fundrisk management has held my attention for the better part of a decade. Partof the reason for this is that I’ve had the honor to manage risk for some ofthe  world’s  finest  traders,  including  Steve  Cohen  and  Paul  Tudor  Jones,and  have  managed  to  survive  such  wide-ranging  crises  as  the  emergingmarkets meltdown of 1997, the collapse of Long-Term Capital Management(everyone’s favorite hedge fund till the winds blew ill there), the Septem-ber 11 attacks, the fraud-related collapse of Enron and WorldCom, and ahost of others too pedestrian to name in this space.
Along the way, it is good that I’ve learned what I think are some valu-able lessons. And what’s even better (at least from an expository perspec-tive) is that these lessons are remarkably consistent with one another anddraw from a surprisingly small set of themes — themes that will form theframework  for  the  core  arguments  I  will  put  forward  in  this  book.  Andwhile it would be silly to reveal all of them in the preface, I can at leastbegin to make the case as to why I believe so strongly in these materials.As alluded to earlier, wherever I’ve gone in the world of risk manage-ment, from trading pits to hedge funds to banks, I have noted that the besttraders and investors (and I’ve worked with both the best and the worst) areall, first and foremost, great managers of portfolio risk. I believe that this ismore  than  mere  coincidence,  that,  in  fact,  there  is  a  positively  Darwinian
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dynamic  at  play  here.  Making  money  in  the  markets  is  very  difficult.  Noone does it all the time. Because great traders are seldom out of the mar-ket for extended periods, it follows that when they are not making money,they are actually losing it. Success, therefore, demands that they controltheir downside during periods of suboptimal performance. 
I hope to convince you that my experience is not an isolated phenom-enon  and  that  risk  management  is  not  only  useful  but,  in  fact,  essential.Even if you have the market insights and instincts of George Soros or War-ren Buffett, your fate as an investor may very well ride on your ability andwillingness  to  practice  sound  risk  management.  To  be  successful  in  themarkets means having a clear understanding of the risks that are inherentin trading/investing profiles so as not to be surprised when bad things hap-pen  (and  they  will).  Armed  with  this  understanding,  as  I’ve  been  tellingpeople for years, it becomes possible to actually control these exposures—at least most of the time, which, in my estimation, is a whole lot better thannever. 
The hard fact is that most people underestimate the control they wieldover  their  exposure  profiles,  and  this,  sadly,  applies  pretty  uniformlyamong  amateurs  and  professionals.  I  can’t  tell  you  how  many  times  I’veheard seasoned professionals express surprise at having lost $X in the mar-kets, even though the likelihood of their losing $X was entirely foreseeable.Then they’ll go out and lose $X again (or $2X, or $nX, or even $Xn) and besurprised  yet  again,  until  the  entire  cycle  degenerates  into  madness  andinsolvency.
Whether you are an individual trader or an investor who lost a bundleon the tech bust or a professional who bought the debt of one of the high-profile companies (e.g., Enron or WorldCom) that went belly-up as a resultof  the  fraudulent  activities  of  corporate  insiders,  it  is  entirely  likely  thatyou believe your misfortune was due to an ill wind—a virtual hurricane, aperfect storm—over which you had no control and couldn’t possibly haveseen coming. In my experience, this is seldom an accurate characterizationof matters. More often than not, when looking back on a difficult period inthe markets, you will see that (1) there was a wealth of information avail-able to estimate potential loss, and (2) this information could have beenused to size exposures in a way that would have rendered even the worst-case scenarios entirely manageable.
Thus,  we  are  not  typically  the  victims  of  “Mother  Nature”  or  otherunseen forces; rather, we are often our own greatest oppressors. My busi-ness is to study market patterns to measure their attendant impact on port-folio exposures. And I can tell you for sure that, regardless of your place inthe market pecking order, if you spend five minutes a week looking at sim-ple statistics available online from any e-broker or professional data service
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(such  as  Bloomberg),  you  afford  yourself  the  opportunity  to  gain  a  veryclear understanding of the type of losses you are likely to incur when themarkets take a turn against you. It is then in your power to adjust the riskdownward if you don’t like the digits that such a review produces.
Of course, adopting this sort of approach isn’t necessarily conduciveto the maximization of returns during periods of peak market opportunity.Quite  to  the  contrary;  it  is  designed  to  reign  investors  in  at  points  whentheir enthusiasm might otherwise reach an apex. It may even cause you tocurse your fates when it seems as though everyone else is riding a gravytrain that left you at the station. But if you make capital preservation oneof  your  main  objectives  and  institute  a  simple  program  to  achieve  thisoutcome, not only will you not lose in the (not even very) long run, but youwill  see  sustained  and  consistent  enhancement  of  your  overall  financialwell-being.  Capital  preservation  during  difficult  periods  pays  off  in  theform of having the ability to put more capital at risk when trends becomemore favorable. Risk management is not just about not losing money; it isabout preserving your capital in a way that will increase profits over thecourse of your investment career. 
This book, then, will show you how to implement a risk managementprogram and how to stick to it. I promise that you won’t regret it. The ideawill  be  to  create  a  system  that  will  protect  your  capital  and  grow  yourreturns. We will not be focusing on what markets you should trade or whichspecific financial instruments you should use or what trades you should puton once you have made these decisions for yourself. In these areas, you’repretty much on your own. Our work together will largely be confined to cre-ating a tool kit that will help you understand the statistical characteristicsof your portfolio and to defining ways to use these statistics to effect port-folio decision making that is consistent with your financial objectives andassociated constraints.
You can think of this book as a practical guide to the art and scienceof risk management. I hope that once we’re through, you’ll agree with methat  this  is  a  unique  perspective  on  this  topic,  primarily  because  of  itsdirect  focus  on  how  to  actually  devise  and  execute a  risk  managementstrategy for your portfolio. It’s not that we will ignore entirely the conceptof risk estimation, which, near as I can tell, is the all-encompassing obses-sion  of  the  risk  management  literature  published  thus  far.  No,  we  won’tforsake these mysteries; rather, we will reduce them to the simplest math-ematical  forms  possible,  such  that  they  are  both  understandable  andapplicable to the practical situations you will face as a portfolio manager.Perhaps more important, we will use risk estimation merely as the start-ing  point  for  our  risk  management  program,  rather  than  as  an  end  initself. We will focus most of our time on discussing how to use these and
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other  tools  to  deal  effectively  with  such  real-life  portfolio  managementproblems as
• Determining  the  levels  of  exposure  most  consistent  with  our  objec-
tives, in light of our constraints.
• Identifying  alternatives  for  risk  adjustment  whenever  exposures  fall
outside of these ranges.
• Anticipating and correcting for internal and external factors that createincentives  for  portfolio  managers  to  take  action  that  works  againsttheir  interest  from  a  risk  management  and  capital  preservation  per-spective.
Trust me, brothers and sisters, your success in risk management (and,I would argue, in portfolio management as a whole) turns much more onthese matters than it does on selecting the right betas for your stock port-folio or the appropriate model for pricing your options. I have learned thisthe hard way, in extraordinarily aggressive risk-taking environments, acrossas diverse a set of market conditions as anyone could reasonably expect toexperience  over  an  entire  career.  I  feel  that  these  experiences  are  bothunique and instructive and that they have given me insights worth sharing. So I’m excited about the prospects for success in this little joint ven-ture of ours, and I hope you are, too. If it works, you’ll come away from theexperience with a handful of simple guidelines that will save you a fortunein times of duress and, as a result (so I would argue), make you a fortuneover the course of your investing career. Along the way, I’ll share some ofmy  goofier  experiences  and  give  you  some  insight  into  rock  and  roll—atopic on which I have even more to say than I do about risk management.But rest assured that throughout, we’ll keep our eyes on the prize: estab-lishing  a  simple,  workable  risk  management  program  that  is  consistentwith your objectives and that allocates your scarce, risk-taking resourcesefficiently  across  the  full  range  of  triumphant  and  tragic  conditions  youwill experience as an investor.
What do you say? Let’s get started.
KENNETH L. GRANT
New York, New YorkJuly 2004
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Acknowledgments
This book, nearly five years in the making, draws both directly and indi-
rectly on my experiences in risk management over the past couple ofdecades.  As  such,  I  want  to  express  my  heartfelt  appreciation  toeveryone I worked with over this time period, for all of their instruction andfor a million smiles (and a few tears).  I am particularly indebted to severalof my bosses and closest colleagues, among them my uncle Ron Manaster(who  gave  me  my  start  in  the  business);  John  Davidson,  Kate  Meyer,  andPhupinder  Gill  (my  bosses  and  colleagues  at  the  Chicago  MercantileExchange, who gave me my first big break); Pierre Schroeder (my supervi-sor at Société Générale, and one of the most outstanding professionals I everencountered); Dr. Ari Kiev (who planted the writing seed in my brain); JohnMacfarlane (my manager at Tudor, who helped me really frame much of thephilosophy embedded in this book); and, of course, the illustrious chairmenand senior management of SAC Capital and Tudor Investments.   In addition,I gratefully acknowledge specific assistance on this project from individualsincluding John Higgins, David Hwang, Chris Meier, and others, who knowwho they are but whom, for various reasons, I won’t name specifically.  Eachlent  a  significant  hand  to  the  process  at  critical  stages;  and,  had  they  notbeen there to provide a helping hand, I believe it would not be an exaggera-tion to say that the book might not have been completed.  I’d also like tothank my editor, Pamela van Giessen, who hung in there over the past halfdecade through many fits and starts and whose patience and guidance werea driving force in bringing these materials into publication.
Finally, and at the risk of descending beyond the point of utter senti-mentality, I want to thank my wife, Deanna, and my children, Brianna andAlex, for making the journey a joyous and worthwhile one and for forcingme from time to time to be at my best, whether I wanted to be or not.
Sincere apologies (and thanks) to anyone I’ve forgotten.  My memory
is not what it used to be.
K. L. G.
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CHAPTER  1
The RiskThe RiskManagementManagementInvestmentInvestment
Once a jolly swagman camped by a billabong,under the shade of a coolibah tree, and he sang ashe watched and waited ’til his billy boiled, you’llcome a-waltzing Matilda with me.
Waltzing Matilda, waltzing Matilda, you’ll come awaltzing Matilda with me. And he sang as hewatched and waited ‘til his billy boiled, you’llcome a-waltzing Matilda with me.
—“Banjo” (A.B.) Paterson
“Waltzing Matilda”
In  the  words  of  a  famous  and  well-compensated  but  (perhaps  under-
standably) anonymous economist, “market prices tend to fluctuate.” Iknow  this  to  be  the  case,  for  I  have  witnessed  such  fluctuation firsthand. Perhaps you have, too. Furthermore, I think we can agree thatthis,  on  balance,  is  a  good  thing.  It’s  certainly  beneficial  to  my  business,and I believe it is to yours, as well. However, I don’t pretend that this littlebit  of  philosophy  will  offer  much  comfort  to  you  when  said  price  move-ment adversely affects your portfolio—particularly if, as often is the case,the movement is significant and abrupt and occurs without warning. Still,I encourage you to bear in mind the big picture the next time your favoritestock  preannounces  bad  earnings.  And  also,  come  to  think  of  it,  do  thesame thing when your other favorite stock preannounces a good number,because you are much more likely to attribute this to your own shrewd-ness than you are to a lucky roll of the dice.
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The  truth  is  that  market  risk,  like  the  very  oxygen 