/23/04  4:53 PM  Page 160 Sudhir 27A:GK040:Chapter:Chapter-07:
160
TRADING RISK
in greater detail later) such as win/loss ratio, average trade size, and a num-ber of others will be obscured by viewing each execution separately.
For these reasons, it is my view that the former method of grouping allexecutions  tied  to  the  initiation  and  liquidation  of  a  position  in  a  singlename, on a single side of the market, is the preferred one. However, it mayvery  well  be  worthwhile  to  engage  in  some  experimentation  with  bothapproaches in order to obtain the broadest possible understanding of thestatistical  characteristics  of  your  trading.  Ultimately,  you  are  by  far  thebest judge of what constitutes a transaction within your trading universe.As always, the discovery process itself justifies the effort. 
Position Snapshot Statistics
In addition to tracking what happens at the individual transaction level, it isimportant to apply statistical measures to snapshots of your portfolio as theyexist over time. Think of your individual transactions as being brushstrokeson the dynamic canvas that represents your portfolio. From one perspective,its  content  is  best  described  by  the  brushstrokes  themselves;  but  fromanother, the best way to look at it is in terms of what is visible on the canvasat any time. The logical way to review the content of your portfolio is to cap-ture and analyze the individual positions that comprise it on a periodic basis.The ideal frequency for subsequent statistical analysis is daily, as this offersthe most precise set of meaningful datapoints; however, even if you do noth-ing  more  than  analyze  your  month-end  statements,  you  will  find  yourselfgaining unique and useful insights into the drivers of your success.
The  key  statistics  you  will  want  to  retain  from  routine  snapshots  ofyour  portfolio  are  relatively  few  and  entirely  intuitive  (comprising  whatyou will recognize as a standard position blotter); yet from them, as youwill see, emerge myriad interesting analytical opportunities. They include:
• Ticker or instrument name.• Entry price.• Current price.• Entry cost (can be derived).• Current market value (can be derived).• Unrealized P/L.
The retention of this information in a database will allow you to create thefollowing time series for subsequent analysis:
• Dollar  Investment  in  Individual  Securities. Most  of  us  trade  thesame instruments on a recurring basis. Every day the dollar amount ofthese investments will change by virtue of price fluctuation alone. The
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 161 Sudhir 27A:GK040:Chapter:Chapter-07:
The Risk Components of an Individual Trade
161
process of trading, of course, adds to the fluctuations. It will be usefulto  maintain  a  running  total  of  these  position  sizes  in  order  to  deter-mine subsequently their impact on your return profile.
• Total Long/Short Capital Utilized. This figure is simply the amountof dollars invested on the long side of the market across all positionsand the total dollars invested on the short side on the same basis. Thiswill also be a useful statistic to maintain in time series form for subse-quent analytical purposes.
• Gross Market Value. This is defined as the sum of the dollar valuesof your longs and shorts. Remember to reverse the sign of the shortpositions  so  that  they  are  added  to  your  longs,  as  opposed  tosubtracted.
• Net Market Value. While Gross Market Value is the sum of all posi-tions,  long  and  short,  Net  Market  Value  is  derived  as  the  differencebetween  longs  and  shorts.  In  time  series  form,  this  will  give  you  anidea of your tendency to trade with a directional bias as well as of theextent  to  which  this  bias  shifts  over  time  and  across  market  condi-tions. In addition to being a useful metric for subsequent analysis, theresults you uncover may surprise you.
• Number of Positions. This statistic can be measured in terms of longpositions or short positions or in aggregate across the portfolio. Thenumber of positions on your sheets is a crude but useful measure ofthe level of diversification in your portfolio; and by comparing this tothe profitability in your account, you stand to learn a great deal abouthow well this diversification program is working.
As  you  may  very  well  surmise,  it  is  in  your  power  to  combine  thesecore  data  sets  with  other  position  attributes  in  order  to  obtain  an  evenclearer and deeper understanding of portfolio dynamics. For example, youmay wish to see how each of the listed metrics operates at the sector levelor asset group level (e.g., grains versus meats) for commodities. Similarly,you may wish to beta adjust the totals in order to obtain some idea of howvolatility  and  market  correlation  factors  play  into  your  investment  deci-sion-making process. I highly encourage these types of second-order analy-ses and believe that they can only expand your knowledge base in waysthat are conducive to the objective of increased portfolio efficiency.
CORE TRANSACTIONS-LEVEL STATISTICS
Now  that  you  have  set  up  your  transactions-level  database,  you  will  findthat there is a virtually unlimited set of statistical analyses that are availableto you. I don’t intend to cover all such analytics in this book. I will focus
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 162 Sudhir 27A:GK040:Chapter:Chapter-07:
162
TRADING RISK
very directly on a few key themes in order to provide the broadest possibleidea of how this data can be processed and interpreted with an eye towardimproving performance. We will start with some basic calculations that inand of themselves may not be particularly fascinating but that will serve asthe basis for evaluating performance in a manner that cannot be simulatedabsent this information set. With these basics in place, we will then movetoward more complex concepts that hone in on specific aspects of tradingperformance that might lend themselves to efficiency improvement.
Let’s  begin  at  the  beginning  then,  shall  we?  The  first  set  of  statisticsyou need to gather will not give you great insight on its own, but rather willserve as the basis for subsequent analysis on a more detailed level:
Trade Level P/L
Although we’ve discussed the P/L time series concept in great detail, wenow want to turn to the equally valid methodology of evaluating your rela-tive profitability across individual transactions. The idea here is simply tocalculate  the  profitability  of  the  individual  trade,  which  can  be  done  byeither matching up buys and sells of equal quantity or calculating averageentry/liquidation prices. This will be a key unit of account for your overalltransactions-level analysis.
Holding Period
Also for reasons of subsequent analysis (which will become more appar-ent later in this chapter), it is important to calculate the time duration ofyour transactions. This figure can be derived in several different ways, butto  me  the  most  accurate  approach  is  one  that  mirrors  our  approach  todefining an individual transaction, where the holding period is defined asthe time interval between the beginning of the initiation of a trade and suchtime as you have fully liquidated it or reversed its direction from long toshort or short to long. The ideal unit of account for this statistic is the num-ber  of  days;  however,  for  day  traders  it  may  be  possible  to  express  theholding period in terms of hours or even minutes. This level of specificityis  in  most  cases  inefficient,  though,  as  it  becomes  very  difficult  to  accu-rately report the precise length of time that a given position is held intra-day  in  your  account;  the  associated  statistics  are  often  skewed  by  suchfactors as the interval between the time the trade is executed and when itis reported back to you, and even the lags that may exist in terms of record-ing the transaction in your books and records. For these reasons, I suggestthat you express holding periods for your intraday trading in daily units,using either 0 or 1, as appropriate.
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 163 Sudhir 27A:GK040:Chapter:Chapter-07:
The Risk Components of an Individual Trade
163
These “derived” statistics, along with the transactions attributes that Iasked you to collect at the beginning of this chapter, place you on a pathtoward  improved  understanding  of  the  trade-level  characteristics  of  theportfolio. The first such bits of information that I recommend you analyzeare the following:
Average P/L
This statistic is your total P/L divided by your total number of transactions.While admittedly limited in scope, average P/L can actually have somewhatimportant implications for understanding overall success levels. First of all,at the risk of stating the obvious, this number can only be positive if youroverall  P/L  is  positive;  so  in  this  sense,  average  P/L  becomes  an  absoluteindicator  of  your  overall  performance.  However,  beyond  this,  the  evalua-tion/comparison  of  your  average  profitability  across  different  periods  ofanalysis enables you to explore the finer points of your performance moredeeply than was possible with tools previously discussed in this book.
Significantly,  when  comparing  results  across  two  periods,  you  canlook independently at both the numerator (total P/L) and the denominator(number of trades) of the equation. Are they moving in a consistent fash-ion? Does it appear that you are more profitable when you execute moreindividual trades or fewer trades? If you are more profitable, why? If not,why not? These issues will become increasingly interesting when we addmore components to the transactions-level tool kit. However, there is noreason not to look at this data in isolation because it begins to enable youto understand the power of information available to you at the level of theindividual trade.
Once you are able to calculate average P/L across the entire portfolio,it may be useful to subdivide the individual observations into various cat-egory  classifications  in  order  to  determine  whether  there  are  wide  dis-crepancies  across  them.  It  could  be  extremely  edifying,  for  example,  tocalculate your average P/L on trades initiated on the long side versus thoseon  the  short  side  in  order  to  determine  whether  you  have  a  more  finelytuned  edge  based  on  a  specific  market  direction.  You  may  also  want  toundertake  this  exercise  across  market  sectors  (e.g.,  technology  versusfinancials),  specific  instruments  (soy  beans  versus  live  cattle),  counterparties, modes of execution, and so on. Indeed, there are as many ways ofcomparing  average  P/Ls  as  there  are  of  characterizing  individual  trades;and later in this chapter, I will introduce the comparison I feel to be the oneof single greatest importance: P/L on winning versus losing trades. In themeantime, please take some time out to think about the various ways youmight want to parse out the average P/L statistic, as this alone will get youthinking about the subcomponents of your portfolio management process
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 164 Sudhir 27A:GK040:Chapter:Chapter-07:
164
TRADING RISK
for which greater mastery can often lead to increased portfolio efficiencyand, in turn, to greater profits.
Finally, it is important to note that you can calculate average P/L bothgross  and  net  of  commissions;  and  by  comparing  these  two  results,  youbegin to determine how much commission costs are cutting into your over-all profitability. 
P/L per Dollar Invested (Weighted Average P/L)
This  is  simply  the  calculation  described  prior  with  the  denominatorweighted by the dollars invested in each transaction. For example, if yourtransactions  history  contains  nothing  more  than  two  transactions—a$50,000 investment in Security A and a $100,000 investment in Security B—your weighted average P/L would differ from your average P/L in that thelatter  would  equally  weight  the  two  transactions,  whereas  the  formerwould assign twice the weight to the trade in Security B.
By  calculating  a  weighted  average,  we  obtain  a  sense  of  the  relativereturn  on  investment  associated  with  the  portfolio  at  the  transactionslevel.  This  offers  a  slightly  different  perspective  than  the  simple  averageP/L calculation. For example, if you make $10,000 on both Securities A andB,  your  average  P/L  would  be  $10,000,  but  your  weighted  average  P/Lwould only be two-thirds of this amount—a reflection of the fact that a dol-lar invested in Security B only generated half the returns associated withyour Security A investment. It’s important to compare and contrast thesefigures. If, for instance, the weighted average is lower than the simple aver-age, it may be an indication of inefficient sizing of positions. Needless tosay, you can also play around as much as you want with these statistics bygrouping  your  transactions  data  into  subcategories  and  comparing  andcontrasting weighted and simple averages across these narrower informa-tion sets and by other similar tactics.
Average Holding Period
Just  as  you  can  translate  P/L  figures  on  individual  trades  into  portfolio-wide averages, so too can you apply the same concept to holding periods.Here,  however,  weighting  each  observation  by  transaction  size  takes  onadded  importance.  Also  similar  to  average  P/L,  it  is  very  instructive  tobreak  down  your  portfolio  into  various  categories  in  order  to  determinewhether  there  is  a  broad  disparity  in  your  approach  as  defined  in  theseterms.
An equity trader may find, for example, that his or her holding periodsare significantly longer for short positions than for longs; and in my opin-ion,  such  a  discovery  might  very  well  be  worth  further  evaluation  and
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 165 Sudhir 27A:GK040:Chapter:Chapter-07:
The Risk Components of an Individual Trade
165
analysis. You may learn, by way of further illustration, that this is attribut-able to the fact that most of the short positions in the portfolio are hedges,having  a  more  generic  quality,  and  are  used  specifically  to  guard  againstthe event risk of an abrupt, marketwide downturn. These may not be tiedto specific catalysts and, in fact, may remain on a more consistent basis inyour portfolio thereby creating a condition of extended holding periods onthe short side. Or it may be that the short positions in a given portfolio sim-ply  tend  to  carry  hypotheses  that  require  longer  time  intervals  to  playthemselves out. Finally, the pattern could indicate an entirely unintendedbias. In any case, it is worthwhile to understand these things with an eyetoward ensuring that you are actively managing all controllable elementsof  the  investment  process  and  making  adjustments  whenever  they  aremost likely to add efficiency to the entire mechanism.
P/L by Security (P/L Attribution)
Professional  and  part-time  traders  must  try  to  understand  where  theymade and lost money on an individual names basis. Typically, profession-als  will  receive  this  information  from  their  firms  on  a  routine  (e.g.,monthly) basis. Most brokerage firms supply this information to individualinvestors if not in the form of monthly brokerage statements then certainlyby request. I think it is important to scrutinize this information for insightsthat  it  may  provide  into  where  you  can  allocate  your  trading  capital  formaximum efficiency. For example, securities traders may find themselvestrading  a  certain  set  of  names  more  efficiently  than  others,  and  thesetrends will become apparent through a basic but comprehensive P/L attri-bution analysis. The same pattern may emerge for futures traders. Take aclose look at these figures. Does anything in particular jump out at you?Are  there  similarities  across  the  names  where  you  are  making  the  mostmoney? What about the big losers? The results may tell you a great dealabout which parts of the market offer better money-making opportunitiesthan others.
Equity  traders  often  operate  more  effectively  in  certain  sectors  thanothers.  Certainly,  when  we  review  the  big  technology  run-up  of  the  late1990s, it is common knowledge that most individual investors who weregenerating  great  returns  were  doing  so  in  technology  names  such  asYahoo!  and  Amazon.com  rather  than  in  more  earthbound  parts  of  themarket, such as auto manufacturers and real estate investment trusts. Sim-ilarly, futures traders may demonstrate a big edge in trading, say, interest-rate products such as bonds and eurodollars, while performing much lesseffectively  in  agricultural  products,  foreign  exchange  instruments,  orequity  indexes.  If  such  a  pattern  is  discernible  in  your  own  trading,  it  isuseful  to  examine  the  range  of  potential  underlying  causes.  Are  you
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 166 Sudhir 27A:GK040:Chapter:Chapter-07:
166
TRADING RISK
performing better or worse in markets that you understand better from afundamental perspective? In markets that are rallying or breaking badly?In markets experiencing certain volatility patterns (e.g., highly volatile ver-sus relatively stable)? Whenever you can form such hypotheses, it may beworth your while to test them by deploying additional incremental capitalwhere you are operating effectively, perhaps at the expense of areas of themarket where you are not. 
In  addition,  it  makes  sense  to  compare  your  P/L  attribution  acrossperiods of varying performance. Take a look at returns in individual namesduring periods of maximum success and compare them to your returns ona security-level basis during more difficult market intervals. Is your under-performance  concentrated  in  what  are  traditionally  your  most  profitablenames,  or  did  large  losses  in  other  tickers  reduce  your  profitability?  Bykeeping track of these patterns, you should be in a stronger position to effi-ciently allocate your capital, manage your exposures, and do all of thoseother things that I have argued are essential to maximizing profits.
Long Side P/L versus Short Side P/L
It is equally important, in my view, to examine your performance on trans-actions where you have bought into the market presumably expecting it togo up versus transactions where you have established a short position, pre-sumably  anticipating  the  market  to  go  down.  As  we  have  discussed,  Ibelieve that trading on both sides of the market is important, from both arisk-management and a market-opportunity perspective. 
There  are  multiple  methodologies  for  two-sided  trading;  and  factorssuch as the nature of the markets in which you are participating as well asyour own biases and orientations will determine the manner in which youattack this challenge. One common approach is to allow your directionalmarket bias to show itself unencumbered and to then use positions on theother side of the market to provide a hedge. This is often the way that par-ticipants in the equity market operate: hoping to make most of their moneyby identifying securities they expect to go up in value, and using the shortside of the market by and large as a means of hedging out their exposures.Other  methodologies,  including  the  so-called  relative  value  trading,involve identifying two similar market instruments that appear to be mis-priced in relation to one another and buying the one that is undervaluedwhile selling the one that is overvalued. Finally, there is a highly effectivemethodology that involves bona fide position selection on both sides of themarket  and  that  seeks  to  capture  revenues  not  on  a  relative  basis  butrather  on  an  absolute,  position-by-position  basis.  This  methodology  iscommon among hedge funds that seek to be uncorrelated to the underly-ing markets.
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 167 Sudhir 27A:GK040:Chapter:Chapter-07:
The Risk Components of an Individual Trade
167
The  manner  in  which  you  interpret  your  long-side  versus  short-sideperformance statistics should, of course, depend entirely on the method-ologies you are using for dual-orientation trading. For example, if you arean equity trader who buys stocks and uses the short side purely for hedg-ing purposes, you would expect the overwhelming majority of your P/L toderive from the long side of the market. In fact, I would argue that if, usingthis  methodology,  you  saw  most  of  your  profitability  tied  to  short-sidepositions that are intended primarily to dampen exposures, it would pro-vide a strong indication that something in your model is not working cor-rectly. By contrast, if you are a relative-value trader or if your methodologyinvolves pure two-sided position selection for absolute return, you wouldhave reason to hope that your profitability would be balanced across bothsides of the market.
However, as with other elements of our statistical tool kit, the purposeof quantifying and comparing your long-side P/L with your short-side P/Lis not to determine how well you fit into some textbook template of port-folio strategies, but rather to offer yourself the ability to ask subsequentquestions that will enable you to better understand the workings of yourportfolio  management  system  as  a  whole.  Once  you  have  calculated  thebasic statistic, you may find it useful to delve more deeply into your analysis,perhaps grouping your results into the following two-by-two matrix:
Winners
Long-side
Short-side
Losers
Short-side
Long-side
Take a look at the individual names that fall into each of these boxes. Isthere a common, identifiable thread within each of them? Is there some-thing similar about winning/losing trades in general (long or short)? Howabout long/short trades (winners or losers)? Perhaps they fall into a spe-cific sector or asset class. Perhaps there is something common about theirmodes  of  execution,  holding  periods,  market  conditions  at  the  time  ofposition entry, or other factors. If so, you can then ask yourself a numberof  additional  questions,  including:  Are  these  patterns  consistent  withyour core portfolio management strategies (as you understand them)? Dothey highlight inefficiencies that you can perhaps improve in, say, the exe-cution or risk-control processes? Only when you begin to solve these mys-teries (and I am betting that even if they don’t lead to magnificent paradigmshifts  in  your  methodologies,  they  will  take  you  on  a  discovery  processthat is bound to be beneficial to your efforts as a whole) are you ready tounleash  the  full  power  of  diagnostic  portfolio  analysis  on  your  tradingprowess.
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 168 Sudhir 27A:GK040:Chapter:Chapter-07:
168
TRADING RISK
In addition, it may be very useful to mix and match this statistic withother elements of your statistical analysis for even deeper insight into port-folio dynamics. For example, you may want to look at your long/short P/Lby market sector, by length of holding periods, and by other transactionscomponents.  There  is  a  virtually  unlimited  number  of  combinations  youcan  examine  in  this  regard,  and  I  believe  you’ll  find  the  results  to  beinstructive.
Finally, as is the case with other statistical tools, it is useful to comparelong/short  performance  across  periods  of  relative  success.  Oftentimes,  Ihave found that these types of exercises help identify concentrated areasof underperformance within a portfolio. You may find that during difficultperiods any one of the four boxes in the matrix shown on page 167 mayrepresent a disproportionate percentage of the underperformance; and ineach case this would provide an opportunity to answer additional impor-tant questions regarding your results. You may wish to ask yourself whyyour long-side winners are not producing the gains that they once gener-ated. By the same token, you may discover that your short-side losses aredeeper than they were during periods of peak accuracy. Can you tie thesetrends back to conditions in the market; perhaps to some change in yourselection,  execution,  and  risk  management  methodologies;  perhaps  tosome combination of the foregoing?
CORRELATION ANALYSIS
In preceding sections, I have described a data collection methodology thatwill enable users to analyze many aspects of their portfolio activity as it ismeasured in terms of both individual transactions and the investment pro-files that are created by these trades. We will now review some of thesestatistics in combination with the time series tools that we covered earlierto unleash a truly mind-blowing analytical cocktail that ties portfolio con-struction to performance efficiency.
While it is possible to apply complex statistical tools to this task, forour purposes we will focus on correlation analysis as a proxy for the typesof predictive modeling that can be accomplished with more complex sta-tistical  methodologies.  Recall  the  correlation  analysis  from  the  previouschapters in which we used it to compare profitability patterns with exter-nal  phenomena  such  as  the  returns  to  equity  benchmarks,  including  theS&P 500 and others. While that type of analysis is essential to an under-standing of portfolio dynamics, it is only broadly descriptive in nature. Forinstance,  you  can  always  try  to  adjust  your  correlation  patterns  to  theindicative benchmark indexes you have identified. However, you can onlyaccomplish  this  indirectly,  by  changing  the  decision-making  components
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 169 Sudhir 27A:GK040:Chapter:Chapter-07:
The Risk Components of an Individual Trade
169
of your portfolio management activities that you suspect are causing youto exhibit these patterns; and this is a path that is fraught with the poten-tial for error.
Let’s  look  at  an  illustration:  As  a  net  buyer  of  equity  securities,  youmight find that your correlation to the S&P 500 index is higher than youwould view as ideal and, in response, might try to dampen this correlationby running a more balanced portfolio, reducing the market sensitivity ofthe securities you are trading and other similar matters. This may reduceyour correlation to the broader equity markets (on the other hand, it maynot), but perhaps at the expense of a portion of your profitability.
By  contrast,  the  correlation  analysis  I  recommend  in  this  chapter  isone that compares your performance to the actual decisions you make inthe  portfolio  management  process.  Correcting  a  portfolio  managementcorrelation pattern that appears to be suboptimal will not necessarily leadto unilateral increases in success (more about this shortly). Targeted inter-vention based on the type of correlation analysis featured here, rather thanthat associated with standard portfolio correlation statistics such as betacalculations and the like, will in all probability give you a better chance forsuccess.
Because  the  concept  of  correlation  can  be  confusing,  it  is  importantboth to review its basic premise and to establish a useful framework foranalyzing  its  results.  Correlation is  a  measure  of  similarity  between  twovariables—across a series of independent data points. Typically in finan-cial analysis, these data points fall across points in time, and this will bethe  core  but  not  exclusive  focus  of  our  discussions  here.  Financial  vari-ables that display consistently similar patterns across time or other factorscan reasonably be thought of as being interrelated in some manner. Eitherone is a predictor of the other, or both are driven by a similar set of inde-pendent  dynamics.  However,  please  note  that  correlations  can  also  benegative, indicating that although the behaviors of the variables are inter-connected, the factors that drive them tend to have opposite impacts ontheir paths across time.
For  example,  one  might  expect  the  price  of  wheat  and  the  price  ofcorn  to  be  highly  correlated,  due  not  only  to  the  fact  that  both  are  con-sumable  grains  but  also  to  their  common  reliance  on  everything  fromweather conditions to the cost of farm raw materials to the global demandfor food products. In a similar sense, the correlation between gold pricesand the level of the Dow Jones Industrial Average has, over broad periodsof history, been strongly negative because investors have typically drivenup the price of gold as a safe haven for their capital when equity marketprices are declining or are expected to do so shortly. Finally, there are wideranges  of  financial  variables  that  are  wholly  uncorrelated,  suggesting  acomplete  absence  of  a  relationship  among  the  variables.  For  example,
GK040-1502G-C07[155-212].qxd   7/23/04  4:53 PM  Page 170 Sudhir 27A:GK040:Chapter:Chapter-07:
170
TRADING RISK
there’s  no  reason  to  believe  that  there  are  any  statistical  commonalitiesbetween, say, the Swedish rate of inflation and the price of silkworms inMalaysia; and over time we would expect a correlation between these twovariables to be roughly zero.
In  terms  of