that  we  breathe,remains ubiquitous, necessary, and (oftentimes) unnoticed in the world ofportfolio management affairs. Our mission, whether or not we choose toaccept it, will be to manage this risk. If we do this job well, it’s a fair bet wewill be rewarded; if not, we are highly likely to suffer a penalty. Daily I hearfrom the traders I manage, “Don’t worry, Ken, of course we will manage therisk. After all, we’re professionals.” Fine. Good. Perfect. Only there’s oneproblem: Risk management costs money (or were you under the impres-sion that I do this for my health?). Risk management verily hovers over theportfolio management process, reminding you of its presence and makingdemands  at  the  most  inopportune  times.  During  periods  of  healthy  per-formance, its unrelenting protocols nag at you in a very bothersome man-ner. When performance suffers, the steps you neglect to take in its nameoften fall under the heading of “too little too late.”
Like highly personal physical exams my fellow baby boomers have thehonor  of  receiving  on  an  annual  basis,  risk  management  is  a  costly,  oftenunpleasant (not only for the recipient, but also, I assure you, for the practi-tioner) exercise that, if performed regularly, can help prevent nefarious out-comes. My doctor, who is nothing if not a salesman, encourages me to viewthese procedures as an “investment” (or did he say “intervention”?). That theexercise costs me (in addition to a modest loss of dignity) nothing more thana  nominal  co-payment  is  an  indication  that  my  insurance  company  agreeswith  this  characterization.  Lying  on  the  examiner’s  slab  last  year,  eagerlyanticipating our annual bonding ritual, the parallels between what lay in storefor me and the services I perform on a professional basis really hit home.
And so it is partly as a tribute to my doctor that I call this chapter withwhich we’ll begin “The Risk Management Investment.” Risk management isan investment; and the more you think of it in these terms, the better off you’llbe. As with any investment, it requires the allocation of scarce resources, forwhich it is reasonable to expect a return. I’m biased, but I believe that a well-conceived  and  efficiently  executed  investment  in  a  risk  management  pro-gram ought to generate as healthy and steady a return as anything that’s likelyto make its way into your portfolio. And I heartily recommend that the nexttime  the  invisible  hand  of  risk  management  finds  its  way  into  your  netherregions, just do like I do: Close your eyes, repeat over and over again “It’s aninvestment,” and wait for the returns to come rolling in.
The Risk Management Investment will insinuate itself into your other-wise tranquil portfolio management existence in myriad ways. For exam-ple, you’re almost certainly going to have to map your returns through aseries of risk metrics that offer perspectives that differ materially from theways in which you might otherwise view your overall performance. If youare a professional money manager, this measurement system is likely to bedesigned by others and will invariably, from time to time, yield results thatseem  counterintuitive.  Indeed,  as  we  will  discuss  later,  your  employing
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institution may have viewpoints on how to best measure and control riskthat  may  differ  from  yours  and  may  impose  constraints  on  you  thatactually interfere with your ability to efficiently manage portfolio exposureas you see it—even when you are operating with the purest of risk man-agement intentions.
The mapping of your portfolio into risk estimation mechanisms is alsolikely to require some computing power, data inputs, and other resourcesfor which the providers tend to charge a fee. Either you or someone youpay is going to have to understand this output, at least at its most superfi-cial level. If this person does happen to be you, the time and energy thatyou  apply  to  these  activities  will  come  at  the  expense  of  other  uses  youmight have in mind for these most precious of your resources. 
However,  all  of  these  commitments  are  minor  when  compared  tothis  most  important,  capital-intensive  element  of  the  risk  managementinvestment process: its impact on your portfolio management decisionmaking. Specifically, your success from a risk management perspectivewill  be  determined  by  your  willingness  and  ability  to  effectivelyadjust  your  portfolio  in  ways  that  serve  the  objective  of  risk  controland  capital  preservation  and  that  will,  at  times,  run  counter  to  theactions you would take if you were not constrained by a finite capac-ity  to  sustain  losses.  These  adjustments,  to  be  sure,  will  occasionallycost  you  money,  but  I’m  confident  that  not  making  them  will  cost  youmuch, much more.
My guess is that just about everyone who has read this far agrees withthis general premise. However, we will be seeking more than moral victo-ries  from  here  on.  Specifically,  now  that  we’ve  agreed  that  a  solid,  com-prehensive, and consistently applied risk management program is a goodidea,  we  will  devote  the  balance  of  our  time  together  developing  such  aprogram, the objective of which will be to provide you with the means to 
• Establish rational and effective risk parameters for your account.• Measure your exposures against these parameters.• Identify  the  various  alternatives  in  the  marketplace  to  adjust  your
exposures, should you deem it advisable to do so.
• Pinpoint the specific situations that call for such adjustment, as wellas the psychological and market-based obstacles that might interferewith your ability and/or willingness to make such adjustments—evenwhen they are critical to your financial well-being.
As part of this process, we will develop a statistical tool kit, which willprovide  a  simple,  quantitative  framework  for  both  risk  management  andperformance  assessment.  Certainly,  this  tool  kit  will  not  make  us  omni-scient: We won’t be able to predict with precision exactly what will happento a portfolio every single time it is subject to market events—any more
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than a heart surgeon can forecast the precise sequence of events that takeplace  each  time  he  or  she  opens  up  someone’s  chest.  In  both  situations,there is an ability to estimate a range of outcomes, along with associatedprobabilities, given a careful reading of internal and external conditions.Moreover, in either case, while the outcome of any single intervention (intothe portfolio or the chest) cannot be engineered with certainty, it’s a fairbet that practitioners who use available empirical information as the basisfor  decision  making  will  achieve  favorable  outcomes  more  often  thanthose who don’t. Over time and across situations, more heart patients sur-vive and, in a similar fashion, more market portfolios are rendered muchhealthier—each  by  using  techniques  of  simple  statistical  estimation  thatare based on inputs derived from empirical data. 
However, while no one dares to describe the field of medicine (or anyother biological discipline) as falling outside of the realm of science justbecause outcomes can’t be predicted with certainty, people often wrinkletheir noses at the suggestion that trading and risk management be giventhe same designation. In my estimation, both are life sciences, driven byfactors  that  lend  themselves  to  prediction that  falls  short  of  certainty.Moreover, if we don’t accept that we can learn a great deal from certainpatterns that tend to repeat themselves, in trading and risk management asin  medicine  and  biology,  then  I  would  argue  that  we  have  no  businesswhatsoever  risking  capital  in  the  markets.  From  this  perspective  alone,unless you are committed to the use of available information inputs as thebasis for a scientifically driven approach to portfolio management, there’snot much point in wasting your time with these materials. On the one hand,if you don’t see the opportunity—in fact, the need—to establish as clinicala trading environment as nature will allow, then your time will be wastedhere. On the other hand, if you do choose to seek a statistical advantagethrough a sustained commitment to a rational and dynamic evaluation ofboth  the  market  environment  and  the  behavioral  characteristics  of  yourportfolio,  then  I’d  say  there’s  cause  for  heady  optimism.  Your  powers  ofintervention  through  observation-based  decision  making,  should  you  beshrewd enough to use them, can open windows of profitability that are notonly sustainable but also scalable.
The keys to success in the effort are, in my view: 
1. Identification of a rational set of return objectives, combined with anunfettered  commitment  to  adhere  to  the  essential  constraints  thatapply to your investment program.
2. Ability to estimate portfolio exposures, for the most part on the basis
of simple, historical statistics.
3. Understanding of the tools available to adjust these exposures.
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4. Capacity  for  identifying  situations  where  exposure  adjustments  arenecessary (i.e., when risk profiles don’t jibe with the aforementionedobjectives and constraints).
5. Commitment to make such adjustments consistently and irrespective
of the temptations that invariably exist to the contrary. 
As  we  will  see,  risk  management  is  much  less  about  estimating  andmuch  more  about  doing—a  subtle  distinction  that,  sadly,  is  often  over-looked by professional risk practitioners, as well as by those whose port-folios they impact.
The  risk  management  investment  takes  several  forms:  These  willinclude time, effort, and maybe some outlays for systems if your portfoliois sufficiently complex as to require the application of mathematical mod-els to understand the pricing dynamics of instruments that you are trading.Most important, adherence to a sound risk management doctrine will rou-tinely compel you to make trades and to assume portfolio profiles otherthan those that would precisely apply if risk management were not a con-sideration.  Specifically,  if  you  act  as  you  ought,  you  will  oftentimes  findyourself unable to put as much capital at risk as you might like when greattrading/investment  opportunities  present  themselves.  Similarly  (thoughperhaps not as often), it may make sense to apply an excessive amount ofcapital  at  a  trade  about  which  you  are  less  than  thrilled—again,  in  thename of risk management.
The outlays imposed on those who choose to practice sound risk man-agement  therefore  take  the  form  of  direct  expenditures  and  opportunitycosts.  It  should  not  surprise  you  that  I  will  be  encouraging  you  to  viewthese “sacrifices” as investments rather than as expenses, for reasons thatare implied in the title of this chapter and that comprise the core premiseof this exercise.
Many of these concepts were well established long before that fate-ful day when I ventured into the field of risk management; but at leastfrom where I stand, the process of applying them cohesively to the prac-tice of portfolio management has been painfully slow to take hold. Mostof  my  work  over  the  years  has  thus  involved  the  application  of  simplestatistical  principals  to  a  practical  risk-taking  setting.  Throughout  theevolution of these efforts, I have attempted, at least nominally, to applythe  scientific  method  (OGHET—Observe,  Generalize,  Hypothesize,Experiment, Theorize—to those who remember their school days) andwould  summarize  the  conclusions  that  I  have  drawn  in  the  process  inthe following manner:
• There  is  a  bona  fide  science  that  underlies  the  activities  of  trading,
investment, and portfolio management.
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• The various components of this science can be isolated and evaluated
in terms of their impact on financial performance.
• Using an extremely simple set of statistical and arithmetic tools, it ispossible to evaluate which elements of a given portfolio managementprocess are working efficiently and which are not.
• In  turn,  by  making  these  quantitative  comparisons  across  periods  oftime and intervals of varying success, it is possible to gain insights intothe specific elements of the process that are underperforming in peri-ods  of  performance  difficulty  versus  those  that  are  working  whenthings are going right.
• Although it is not always possible to correct problems without gener-ating  other  inefficiencies  in  the  portfolio  management  process,  it  isextremely useful to understand these undercurrents, such that traderscan harness their strengths and minimize their weaknesses in the mosteffective manner available.
• The  methodology  is  also  very  useful  in  determining  which  types  ofmarket conditions work most directly in portfolio managers’ favor andwhich work against them. In turn, this knowledge offers the opportu-nity to more efficiently match resource allocation to associated oppor-tunity in the marketplace.
• When  and  where  a  portfolio  manager  finds  areas  for  potentialimprovement, the same simple set of statistical tools that is useful inidentifying problem areas can also be applied to attack the problemsin a controlled manner.
This book and the risk management strategy I will outline simply buildon these themes. We begin by discussing a process of identifying and liv-ing by a set of core objectives that will serve as the macrolevel measuringsticks of your success and/or failure. Here, you need to think very carefullyabout  your  options  because,  as  I  will  argue  when  we  get  to  it,  there  aremultiple  core  objectives  that  rational  investors  can  set  for  themselves,each  based  on  a  combination  of  market  and  personal  factors  and  eachimplying a slightly different approach to portfolio management.
Once  we  have  established  the  applicable  objectives  for  performanceanalysis,  we  begin  to  build  the  statistical  tool  kit,  which  is  designed  todescribe  your  trading  portfolio  from  a  quantitative  perspective.  The  firstelement of this is what is commonly referred to as profit/loss (P/L) timeseries  analysis,  through  which  we  will  put  your  profitability  patternsacross time under a microscope—much in the same way that you wouldlook at the technical patterns on the chart of your favorite security. Notethat in order to achieve a practical understanding of time series analysis, itis necessary to grasp a small number of bedrock statistical concepts, mostnotably mean, standard deviation, and correlation. Each, in my opinion,
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is conceptually simple and easy to calculate. Taken individually and as agroup, they can offer insights into everything from the way markets behaveto the relative merits of trading strategies that hope to capitalize on thismarket behavior.
It is likely that you will have encountered these concepts elsewhere,perhaps in your academic training; and I believe they are useful tools foranyone wishing to better understand portfolio management and its varioussubcomponents. I encourage you, if necessary, to review your understand-ing of them, as they are easy to master; and very little else in the bother-some area of statistics is needed to perform the type of targeted perform-ance measurement that is the centerpiece of this book.
Through  P / L  time  series  analysis,  we  will  discuss  ways  to  measureyour returns not just in terms of dollars invested, but also as a function ofthe amount of risk you are taking. We will also explore a methodology forsetting  your  exposures  to  levels  that  will  allow  you  to  reach  your  objec-tives, while at the same time enabling you to ensure that under most mar-ket conditions you do not lose more than the amount you have predeter-mined to be your maximum threshold for economic reversal. Separately, Iwill cover the topic of correlation analysis, focusing on ways to measureand  interpret  the  implications  of  similarities  between  your  performanceand external factors, such as the performance of the market as a whole, aswell as internal factors, such as how actively you are trading, how muchyou are investing, and so on.
With the P/L time series tool kit available to help you identify and eval-uate your performance in a much more scientific manner, I then describea range of alternatives at your disposal that allow you to modify some pat-tern  you  have  determined  is  counterproductive  to  your  overall  portfolioobjectives  (or  making  inefficient  use  of  scarce  portfolio  managementresources, such as risk capital). In addition, I discuss ways to use the sametool kit that identifies problem areas to evaluate the effectiveness of anycorrective action you choose to take. Again, these methodologies won’t beof any help in determining what trades to do when you are somehow oper-ating outside zones of effectiveness. Instead, they will give you the meansto identify and evaluate your alternatives in such a way that, I believe, bestsuits the very personal nature of the portfolio management process.
The final pieces of the statistical methodology I present are those thatcharacterize your performance not across time but on an individual trans-action  level.  By  simply  aggregating  information  that  you  have  stored  onindividual transactions, you can do everything from figuring out how oftenyou are right on a trade versus how often you are wrong, to determininghow long you are holding each position and how this impacts profitability.Beyond this, I cover such topics as identifying and analyzing performancein  individual  securities,  in  sectors  or  market  segments,  in  sides  of  the
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market (long versus short), and in amount of capital deployed in individ-ual trades.
Trust  me  on  this  one—there’s  a  treasure  trove  of  useful  informationhere. What is more (and you’ll find me annoyingly repetitive on this topic),by  frequently  performing  these  same  statistical  reviews—across  differenttime intervals and periods of varying performance—you stand to achieve amuch clearer understanding of the impact of external factors (e.g., the mar-ket environment) and internal considerations (e.g., the individual compo-nents of your decision making) on your prospects for achieving your goalsand living within your constraints. In turn, the routine performance of sta-tistical  analysis  across  periods  of  relative  success  will  allow  you,  shouldyou so choose (and I think you should), to match up your market activitywith the conditions and the modes of operation that are most conducive toyour success. This alone won’t ensure glory or even consistent profitability,but it will give you a heck of an edge over your peers and other market par-ticipants who don’t heed these metrics and, as a result, risk squandering atleast a portion of their scarce investment resources in ways that are almostcertainly counterproductive—given their goals and constraints.
We  don’t  want  to  overstate  the  case  here.  While  the  analyticalapproach I will recommend ought to be useful to just about everybody, itis wrong to think that it offers a precise road map for improved perform-ance.  In  my  experience,  there  are  very  few  unambiguous  diagnoses  andeven  fewer  unilaterally  beneficial  remedies  that  emanate  from  the  regi-mens prescribed in these pages. In fact (as we will discuss in detail later),there is a significant risk of taking too literal an interpretation of the ana-lytical output and reacting to it in ways that will actually impede your pathto  optimal  performance.  For  example,  the  numbers  may  indicate  veryclearly that the longer you hold on to individual positions, the better theresult.  However,  if  you  respond  to  this  input  by  simply  lengthening  yourholding periods on every trade you do, taking little or no heed as to howthis  adjustment  might  impact  other  elements  of  your  portfolio  decision-making  process,  it’s  a  fair  bet  not  only  that  will  you  not  experienceimprovement, but also that you will lose in terms of both money and aggra-vation. It pains me to offer this disclaimer, but in the name of public serv-ice, I believe I am obliged to do so. Put it this way: If I had discovered anyreliable  statistical  methodology  that  offered  simple,  unambiguous  reme-dies for the scourge of portfolio management underperformance, (1) I’d beeven more fabulously wealthy than I already am, and (2) I’d need to havemy  head  examined  if  I  even  considered  the  possibility  of  sharing  theseresults in written form for the royalty on the price of a book. 
Know instead that the secrets to deriving full benefit from this magiccan  be  found  in  the  subtler  shades  of  your  market  experience.  Thesesecrets take the form of putting your capital to work when its prospects for
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yielding  some  benefit  are  high;  of  avoiding  the  repetition  of  identifiablemistakes; and of relying on those formidable but elusive twin pillars of thetemple  of  gracious  living,  patience  and  discipline,  when  the  likely  short-term benefits for such reliance are neither comfortable nor gratifying.
“To thine own self be true,” said Polonius to Laertes, in Shakespeare’sHamlet; and even though both were ultimately dispatched by the capriciousblade of the Mad Dane, I think this advice was worthy of a loving father tohis son. Brutal internal honesty is about as adaptive a trait for market par-ticipants  as  I  can  think  of;  and,  for  reasons  that  should  be  clear  by  now,honesty will  be  a  major  theme  of  this  document.  With  this  in  mind,  andbefore we start with the gory but necessary details of portfolio analysis, I’dlike to share some high-level qualitative observations that I believe are per-fectly in keeping with the spirit of both what I’ve written thus far and whatthose steadfast enough to forge ahead will read in subsequent chapters:
Have a Plan and Stick to It. Prior to engaging in market activity, itis important to take a careful study of everything from your objectives, tothe resources you have at your disposal, to the market inefficiencies youare trying to exploit. Unfortunately, my experience in these matters is thateven  among  professional  money  managers,  this  type  of  planning  is  theexception rather than the norm.
Fight for Every Fraction of a Point in Trade Execution. Often-times, even the best portfolio managers are focused more on the quality oftheir trading ideas than on the execution of the strategies. This is a criticalmistake. Great ideas are easy to squander, and great follow-through alwayspays off. By carefully engineering your points of initiation and liquidation,you will experience significant positive differentiation of revenues, relativeto  a  strategy  that  doesn’t  feature  this  level  of  diligence—no  matter  howgreat or lousy your ideas are.
Don’t Do a Trade Unless It Is Tied to a Predetermined TargetPrice and Stop. As part of the process of both position selection andexecutions management, you should always adhere to a prespecified pricerange, on both the upside and the downside, that serves as a prerequisitefor  keeping  the  position  open.  This  means  that  if  the  market  you  aretrading  either  reaches  your  target  or  violates  your  stop / loss  level,  youmust liquidate the position. If you still feel you are correctly positioned inthis particular instrument, then get out and reinitiate the position with newtarget /stop parameters. If you do this, you are shaping your own destinyon every trade. If you don’t, then there’s no limit to how much money youcan theoretically lose on a given transaction. Sooner or later, some combi-nation of trades will blow you up.
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Don’t  Operate  outside  Your  Limits  or  Other  Constraints.Whether you are trading for yourself or earning your keep managing otherpeople’s money, you should have a series of limits in place that govern yourportfolio  management  activities.  These  limits  will  invariably  prevent  youfrom  constructing  your  ideal  portfolio  from  time  to  time,  so  adhering  tothem  will  routinely  imply  trade-offs  between  what  you  feel  is  warrantedbased on market opportunity and what I argue is best for your long-termwell-being  as  a  portfolio  manager.  You  will  provide  your  own  counsel  inthese instances, but I urge you to allow risk-control considerations to carrythe day. Although you may be correct in your assessment of what’s goingto happen in the markets at any given time, your risk parameters are basedon more static considerations that are likely to be less influenced by wish-ful thinking (e.g., by personal financial constraints or by the risk-appetiteconstraints of external capital providers). 
If you live within these parameters (assuming they are set rationally),you may give up some upside in selected situations, but you gain the con-siderable  benefit  of  control.  By  contrast,  if  you  violate  them  routinely,someday  you  are  almost  certainly  going  to  be  wrong,  and  in  a  big  way (to  paraphrase  Blondie,  “One  way  or  another,  it’s  gonna  getcha  getchagetcha”). I have seen even the most highly regarded traders in the worldend their careers rather meekly because of this unfortunate reality. 
Compare and Contrast Periods of Relative Success. Among themost important methodologies for portfolio diagnosis that I will describein this book is that of comparing individual portfolio decision-making ele-ments in periods of strong success against those in intervals of frustration.For example, you may want to compare such factors as your correlationsto market benchmarks, or trading winning percentages across these inter-ludes of diverging fortune, in order to see if they are markedly different.As we  will  discuss  in  great  detail,  this  won’t  necessarily  give  you  ananswer key as to what will work in the future, but it will certainly offerinsights that may help you apply your capital and other scarce resourcesmore efficiently.
Try New Things. Markets, by their very nature, are in a constant stateof  flux.  One  reason  for  this  is  that  any  strategy  yielding  above-averagerisk-adjusted return (which we will define in painful detail later) is, by theunshakable laws of human nature, under a sustained threat by other mar-ket participants seeking to correct this “inefficiency.” Indeed, as any closeobserver  will  tell  you,  the  rate  of  change  is  increasing  at  an  increasingrate. This means that there is a limited shelf life for nearly any highly suc-cessful  market  approach.  Ultimately,  I  believe  that  almost  any  strategyeither will require significant tweaking or will be periodically subject to
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diminished returns over what constitutes a very real but little understoodbusiness cycle that exists for market participation of all kinds.
As a result, only those who are willing to perpetually adapt to changehave  the  opportunity  to  succeed  consistently  at  trading  and  investmentover a lifetime. In addition to encouraging you to be proactive in the adap-tation of your strategies, I will show you ways to use a statistical tool kitto establish a framework to ensure that your forays into uncharted watersare undertaken as controlled experiments, such that the likelihood of theirsuccess can be maximized, with minimal damage if things go wrong.
Take  More  Risk  When  You  Are  Up  and  Less  When  You  AreDown. The  Children  of  Israel  didn’t  receive  this  commandment  fromMoses on the mountaintop, but I’m pretty sure that it was in the first draftof  the  tablets.  Rumor  has  it  that  the  Almighty,  in  his  infinite  wisdom,removed it as part of the punishment for that idol-worshiping romp in thedesert (as led by Edward G. Robinson in the Cecil B. DeMille vehicle). Itthus falls upon mere mortals such as myself to lead the faithful out of thewilderness of setting risk levels that don’t include recent performance as akey decision factor. 
The practice of sizing your risk on the basis of recent P/ L performanceis perhaps the most important rule for success that I’ve encountered in themarkets. However, even if you buy into the concept, you will find it amongthe most difficult of conventions to follow (ranking, by some accounts, ona  par  with  that  one  about  thy  neighbor’s  wife).  This  is  particularly  truewhen  you  are  losing  money,  as  there  is  a  natural  urge  to  increase  expo-sures during difficult periods in