of complexity that isinvolved  in  the  portfolio  management  process,  any  change  you  make  toyour program designed to address an anomaly uncovered by these types ofstatistical analyses may very well have implications for other elements ofyour  methodologies  that  could  offset  the  potential  benefits  you  seekthrough  the  change.  For  example,  if  you  attempt  to  reduce  your  holdingperiods to address a negative correlation with P/L, this reduction may end
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up  impacting  your  win/loss  ratio,  your  capital  usage,  and  any  number  ofother  factors.  The  end  result  may  be  that  the  very  steps  you  take  toimprove efficiency in one aspect of your trading may have undeterminableimplications for the rest of your routine; and for this reason, you need tobe extremely careful in interpreting too literally the outcome of the statis-tics tools provided in this section.
TANK MANEUVERS
There are guys out there, very smart ones mostly, who know they need disci-pline in their trading and don’t entirely trust themselves to adhere to what’sgood for them. A guy who falls into this category (call him John) once describedto me a system he built, called The Tank, that was designed to save him from,well, himself.
The Tank was a very complicated computer program that performed a lotof functions, but none of them all that efficiently. To borrow further from themilitary  analogy  implied  in  the  nomenclature,  this  Tank  was  more  like  aSherman than a Tiger. One problem with the system was that it was written inits  own  programming  language,  which,  in  turn,  was  created  for  the  sole  andexpress  purpose  of  running  the  Tank.  To  be  sure,  the  system  was  well-documented, with volumes of operating manuals available for anyone who hadthe time or inclination to pore through them; but while some in the firm hadnothing but time, inclination was in very short supply.
The  primary  job  of  the  Tank  was  to  identify  patterns  in  markets  and  intrading activities that had acute P/L implications. It featured a healthy compo-nent  of  the  type  of  correlation  analysis  described  in  this  chapter.  One  veryinteresting  analytical  measurement  that  John  undertook  was  a  correlationbetween  profitability  and  the  ratio  of  orders  he  executed  with  stops  in  hisaccount. He had an excellent theory that the more he adhered to the disciplineof using stops, the more money he would make; and that the more orders with-out stops, the more money he was likely to lose. As it happens, he was correct.Correlation statistics showed that he almost always did better when he reliedon stops and worse when he went without them.
John  then  did  something  unconventional,  arguably  dramatic.  He  pro-grammed the Tank to shut down his trading capabilities any time the ratio oforders without stops went about 40%. The system tracked this ratio on a real-timebasis,  but  it  did  not  issue  warnings  when  the  threshold  was  in  jeopardy  ofbeing violated. What is more, John didn’t watch it particularly closely. Once hehit the 40% figure, the Tank simply sent a message with the following generallanguage:
Orders without stops exceed 40%. System not accepting new trades.
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The Tank would continue to fill all orders that had been placed before thethreshold was violated, but it would not accept new transactions requests untileither  (1)  the  European  markets  opened  the  next  day  or  (2)  John  had  addedenough  stops  to  bring  him  back  into  compliance.  Although  John  could  haveoverridden the rules of the Tank by simply picking up the phone and calling abroker  or  changing  the  programming  logic,  to  the  best  of  my  knowledge  henever did. Instead, he’d accept the portfolio profile that he was left with whenthe system shut down and work diligently to create the appropriate balance inhis order structure, when his trading privileges were restored.
John, who was a Brit, was a disciplined trader; and because of this, he onlytripped the boundary condition once or twice a year. However, as you may haveguessed,  this  tended  to  happen  during  very  volatile  market  conditions  whenhis portfolio exposure was at the high end of the range. His colleagues weresure that his stubborn adherence to what was certainly a rather arbitrary (andentirely self-imposed) restriction cost him millions of dollars a year in tradingrevenues.  They  often  called  him  to  the  carpet  on  this;  and  every  time  theystarted in on him, he’d just grin and say, “I know the damned thing costs mea lot of money, but not nearly as much as it would to shut it down.” His part-ners would just walk away frustrated.
For what it’s worth, year in and year out, he was the most profitable trader
in the firm.
This doesn’t mean that there are no appropriate responses to patternsuncovered through correlation analysis. It is useful to compare these typesof correlations across periods of relative success to see if the differencesin your returns correspond to material changes in the subcomponents ofyour  trading  activity.  It  may  very  well  be  the  case  that  during  periods  ofunderperformance certain of your core disciplines have deteriorated andthat the path to improvement lies not through large scale modification ofyour methodologies but rather through enhanced enforcement of some ofthe guidelines to which you had committed, but without rigorous, perpet-ual  follow-through.  Correlation  analysis  can  help  uncover  shortcomingsthat  can  be  eradicated  with  tweaks  to  your  methodology.  If  you  believethat  deeper  strategic  changes  are  merited,  I  urge  you  to  road  test  thesemodifications using specified amounts of financial and risk capital and toapply the statistical tool kit to measure the success of the outcomes, witha willingness to abandon your campaign if you lose an amount equal to thisrisk-capital  threshold.  This  type  of  approach  will  enable  you  to  take  therisks associated with attempting new strategies with the confidence thatthese  attempts  can  be  framed  as  controlled  experiments  with  limited,predetermined downside.
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FAMILLE HEUREUSE
As  we  move  toward  the  denouement  of  the  morality  tale  that  this  book  hasbecome, it’s time to wrap up some unfinished business. We can’t possibly takeour leave without bidding a fond adieu et bon chance to our friends and col-leagues across the ocean, whose financial, military, and moral support were socrucial in our efforts to win our independence. I want to say again that I had agreat experience working in French banking, met some fantastic people there,and both witnessed and participated in some enormously successful projects.Moreover, Société Générale (Soc Gen), where I worked, was enormously prof-itable  year  in  and  year  out  (at  least  when  I  was  there)  and  seldom  failed  toachieve any business objective to which it truly committed itself.
I also wish to formally distance myself from any animosity expressed bymy government and countrymen over that minor difference of opinion duringGulf War II. “Vive la différence,” they are proud of saying, and let me echo thosesentiments.
Call me a Francophile, and I will plead guilty as charged. I have one smallexperience  to  share  with  you,  a  souvenir  from  my  younger  days,  before  wemake our final return transatlantic voyage—at least for now. I dedicate it to theonly French rock-and-roll band that I have ever been able to stand, Les NegressVertes  (LNV).  They  were  a  loose  confederation  of  marginal  musicians  thatformed  a  hybrid  sound:  part  folk,  part  punk,  part,  well,  African.  The  overalleffect  was  a  little  bit  frightening;  and  this,  as  anyone  who  has  ever  had  toendure the banal claptrap that passes for rock and roll in France can attest, isa  major  accomplishment.  Although,  as  becomes  such  an  eclectic  enterprise,LNV’s eccentric lead singer died in 1993 (yup, heroin overdose); I’m pretty surethe  band  is  still  kicking  around  somewhere.  I  hope  they  come  to  New  Yorksome time; I’d really like to catch their act.
In my work at Soc Gen, I had an opportunity to interact pretty extensivelywith many of its principal financial engineers; and I want to tell you the storyof my dealings with one such individual, a small, wiry, chain-smoking politech-nician whose exact name I can’t recall, so I’ll simply refer to him as Petit. Oneof my missions in the bank was to negotiate with Petit and his entourage, toentreat, beseech, and otherwise plead with him to temper Justice with Mercy inthe setting of certain risk parameters for a pet project of my boss’s, the detailsof which escape me in the fog of the years that have since passed. 
I didn’t come at Petit all gangbusters, because this way never works withthe  French,  particularly  if  you  are  an  American,  for  there’s  nothing  aboutAmericans  that  the  French  despise  so  much  as  our  lack  of—how  can  I  putthis?—finesse. Instead, I just sort of hung around him the summer he spent inNew  York  working  with  us,  taking  him  to  ballgames,  feeding  his  nicotinefrenzy, swapping risk management fish stories (yes, they do exist), and all thewhile gaining his confidence, in the hopes that he would let his guard down.
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As Larry Holmes once said of an opponent (I think it was Marvis Frazier, Joe’sson), I was getting him drunk before I mugged him.
Late  one  night  (after  he  trusted  me  enough  to  drop  trou,  so  to  speak),  Ifinally got what I was looking for: Petit entrusted me with a peek at the sourceof his risk calculations. He kept them in a 9.5-by-6-inch spiral notebook, filledfront to back with dog-eared, tobacco-stained pages. As you might expect, I did-n’t  get  to  examine  this  precious  document  very  closely,  but  I  saw  enough  toreceive  a  frightening  glimpse  into  the  depths  to  which  a  man’s  mathematicaldepravity can take him. Know that Petit’s mathematical rational featured no lessthan  seventh-order  integration.  In  other  words,  Petit  was  calculating  the  anti-derivative of the antiderivative of the antiderivative, and so on, seven times over.
On paper, these monstrous equations looked something like this:
(cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:10)
ex dx
There is almost nothing that I’m aware of in the known universe that lendsitself to this level of mathematical complexity. The solving of Fermat’s last the-orem did not require it, nor, to the best of my knowledge, did the smashing ofthe atom. Newton himself, were he alive today (and from this perspective I’mglad he’s not), would no doubt be aghast to see his precious calculus so osten-tatiously abused. I cannot imagine anything in the realm of human perceptionthat  requires  anyone  to  ever  use  an  equation  remotely  like  Petit’s—nothing,that is, except the formulas generated by Petit and his team to calculate risklimits for the bank’s proprietary traders.
Astonishing as all of this was to me, our friend Petit had one more trick uphis  sleeve,  and  this  one  left  me  absolutely  gobsmacked.  As  I  was  flippingthrough his little book of equations, my curiosity naturally drifted toward thelast page, and I held my breath in deep anticipation as to the nature of the finalfruits of his efforts. And as I turned the page, there, on the other side, in themiddle of the other side, away from everything else on the other side, read thefollowing:
(cid:3) 5%
5%!!!!!!!!!!?  Mon  Dieu  et  Sacre  Bleu!!!! What  has  become  of  you,  Petit?Wherefore  hast  thou  been  led  astray?  Methinks  that  even  the  politechnicianswould  feel  themselves  violated  by  such  travesty,  committed  by  one  of  theirown. One hundred godforsaken pages of the most mind-numbing calculus everimagined, and you end up with a lame number like 5%? Couldn’t we be a littleglib here and make it, say, 5.14954534%? Our traders, I think, would’ve gladlylived with this larger number in the name of human decency and good taste.
What happened next is not very clear in my mind. I may very well have fol-lowed my first inclination, grabbed Petit by his scruffy, Frenchified collar and
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demanded that he either add at least 8 decimal places or immediately destroyat least 80 pages of his spiral notebook—all before pitching him right out ofthe window no matter what his response. Again, I just don’t know, as my lastmemory of the encounter involved falling off a barstool, into a pool of my ownsick, at a grimy place on Seventh Avenue, not far from the bank’s offices.
I never again laid eyes on my good friend Petit, nor did I ever hear anythingfurther as to his fate. I suspect, though, that he continues to thrive—at leastprofessionally, because guys like Petit always do. The risk management indus-try grinds them out like link sausages, and firms ranging from banks to brokerdealers to institutional money managers gobble them up insatiably. Somehow,I managed to escape to the hedge fund industry, which of course has moralitytales of its own. Here, at least, I am confident in stating that we use our calcu-lus  with  more  discretion—a  factor  that  I  hope  adds  a  measure  of  comfort  toNewton’s slumbers on the banks of the Thames.
PERFORMANCE SUCCESS METRICS
We now turn to a set of statistics that critically defines the success or fail-ure of any portfolio, no matter what its orientation: the percentage of timesyour transactions generate a profit and the ratio of gains extracted on prof-itable trades to losses remitted on unprofitable transactions. Indisputably,it  is  necessary  to  perform  well  in  terms  of  at  least  one  of  these  factorsbecause, to operate profitably, it is mathematically impossible to (1) havea  majority  of  your  trades  generate  losses  and  (2)  on  average,  lose  morewhen  you  are  wrong  than  you  make  when  you  are  right.  In  light  of  thisinevitability, I have often used these statistics as a first-order diagnostic todetermine what is going wrong with a portfolio that is performing subop-timally. The simplicity and the elegance of this exercise will become clearonce we have set down the following definitions:
Accuracy  Ratio  (Win/Loss  Ratio). This  statistic  simply  measuresthe  percent  of  transactions  that  liquidate  profitably  as  measured  againstthe total number of transactions for the period. Note that there are severalways to calculate this percentage, including those based on raw number oftrades and the amount of dollars invested. It is also possible, and indeedcan  be  very  useful,  to  calculate  your  win/loss  ratio  across  various  sub-components of your portfolio, including counterparty, industry/sector, andinstrument class.
If  you  are  like  most  portfolio  managers,  your  percentages  will  varyover time across these subcomponents. I strongly encourage you to iden-tify and analyze these trends, as you can harness them in a number of ways
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to  bring  about  significant  improvements  in  the  overall  portfolio  manage-ment process. High accuracy percentages indicate a strong fundamental ortechnical  edge,  and  it  behooves  the  portfolio  manager  to  understand  asmuch as possible about this market advantage. A number of specific ques-tions come to mind, including: Does the advantage tend to cycle out acrosstime? If so, it certainly would be interesting to compare and contrast theup  cycles  with  the  down  cycles.  And  if  you  can  pinpoint  these  with  anydegree of consistent accuracy, the path to higher profits may involve noth-ing more than being aggressive when you suspect your selection accuracyperformance is likely to be at its peak and trading more modestly when theopposite condition prevails. Similarly, it may be possible to isolate areas ofsystemic over- and underperformance in various subcomponents of yourportfolio. For example, a futures trader may be very prescient in grains butsimply  terrible  at  predicting  price  trends  in  meats.  If  the  data  pointtoward  one  of  these  patterns,  then  adjustments  needed  to  bring  aboutimproved performance may be entirely intuitive.
The win/loss ratio is important because it is impossible to trade prof-itably without being right more often than you are wrong or making moremoney on profitable trades than you give back on losing transactions, orsome combination of the two. However, this is not to say that it is neces-sary to have a win/loss ratio in excess of 50% in order to have a very suc-cessful program. Quite the contrary. I know of many portfolios that are soeffective  in  their  actual  trading/execution  and  risk-control  practices  thatthey make large sums of money in a consistent, risk-adjusted manner withwin/loss percentages in the low forties or below. The trick, of course, is tomake sure that your winners pay off at higher multiples than those of yourlosers.  In  the  meantime,  as  a  final  note  on  selection  percentage,  thewin/loss ratio is obviously a variable that you should make every effort tomaximize, and my experience indicates that nothing can help you so muchin  this  regard  as  simply  doing  your  homework.  You  should  try  to  under-stand as much fundamental information about the markets you are tradingas is feasible—given whatever constraints you face. This includes financialinformation, industry dynamics, pricing patterns, flow of funds intricacies,and  the  like.  Don’t  be  afraid  to  explore  your  key  markets  from  new  per-spectives. For example, if you are a market technician, it can’t hurt you totake a look at a financial statement or to talk to high-quality analysts. Bythe  same  token,  if  your  approach  is  fundamental  in  nature,  fear  not  theprospect of looking at a chart once in awhile. It won’t bite.
If you do trade on the basis of technical indicators, you should makeevery effort to hone whatever edge you have developed in technical analy-sis as finely as possible. Here, win/loss statistics and other analytical toolscan be of unique and specific assistance. It is possible, for instance, for youto  track  your  win/loss  percentages  on  the  basis  of  different  technical
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factors  simply  by  isolating  the  specific  indicators  that  have  driven  yourdecision-making process. For example, you may choose to initiate a longposition  in  a  security  when  a  short-term  moving  average  price  (say,  the50-day) has crossed a longer-term average (for example, the 200-day). Atother times, you may rely on such technical tools as Relative Strength Indi-cators  (RSI)  or  Volume-Weighted  Average  Price  (VWAP)  signals.  Simplestatistical  analysis  will  indicate  which  of  these  methodologies  producesthe most consistent stream of profits. That methodology may differ acrossindustry/sector, instrument type, and so on. All of these trends are entirelydiscoverable,  and  all  offer  opportunity  for  potential  improvement.  In  myexperience, most of the difficulties you will face in this regard stem fromthe  psychological  obstacles  that  often  accompany  any  process  underwhich the inefficiencies of natural habits and patterns of behavior are chal-lenged  with  hard  data.  However,  I  strongly  urge  you  to  rise  above  theseentirely human constraints. When it comes to the trading markets, remem-ber that knowledge and information are your friends and that ignorance isanything but blissful.
Impact Ratio (Average P/L:Winning Trades/Losers). This statis-tic, in my estimation, is perhaps the single most important metric in ourentire  statistical  tool  kit  because  the  performance  measure  that  mostclosely  correlates  with  profitability,  in  both  a  raw  and  a  risk-adjustedsense, is the extent to which trades that liquidate profitably produce, on aunit basis, a P/L that is larger than the associated losses on unprofitabletransactions. If you can maintain this ratio above 1.0 (and the higher theratio the better), you are more than likely doing a number of things cor-rectly; and, perhaps most important, you are successfully selecting trans-actions under the critical criteria that the likely payoff is greater than theassociated exposures. 
In  addition,  the  impact  ratio  indicates  efficient  risk  management,including a propensity to liquidate losing trades at levels below which theycan cause material damage to overall returns, as well as a willingness totake profits on winners at appropriate times. Finally, it is consistent with avery active and diligent approach to trade execution, which is also a cor-nerstone of successful portfolio management. For active traders in partic-ular, it is my experience that the difference between profitability and losscan  often  be  measured  in  small  fractions,  and  it  is  with  respect  to  theseportfolios in particular that the impact ratio best measures the quality ofthe executions process.
Before carrying forward with a broader discussion of the applications ofthe impact ratio, let’s try to define the statistic with some level of precision.There a number of ways to effect this calculation, the simplest of which is toutilize the definition of trade provided earlier in this chapter (namely, that a
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trade is defined as the group of transactions in a single financial instrumentthat takes the portfolio from zero exposure back to zero exposure as yourbase unit). From here we would undertake the following steps:
1. Separate trades into a group of winners and a group of losers.
2. Calculate both the number of trades and the total P/L for each group.
3. For each group, divide total P/L by number of trades.
4. Specify the results as the average P/L of winners and the average P/L
of losers.
5. Divide the former by the latter. 
The resulting figure is your raw impact ratio, and it expresses in sim-ple  terms  the  magnitude  of  your  winners  and  losers  in  relation  to  oneanother. Note that you can also calculate the impact ratio on a unit basisby utilizing “dollar values” instead of “number of trades” in Step 2. Whilethe  resulting  unit  impact  ratio offers  a  slightly  different  set  of  insightsfrom the raw figures, I caution against assuming that the unit calculationis superior to the raw figures. Both are useful, and each provides uniqueand complimentary insights. In particular, because the unit calculation willoffer a clearer picture of your performance success on a dollars-investedbasis,  it  arguably  provides  a  better  means  of  discerning  success  acrossyour entire portfolio. Conversely, the raw score, which makes no such dol-lar-invested adjustment, will supply a better measure of the level at whichyou are sizing your trades according to what represents, ex-post, your bestset of market opportunities. Apply both methods across multiple time hori-zons in order to gain the broadest possible perspective on the subject.
As an alternative means of calculating this ratio (and particularly forthose who maybe be unable to execute the formula at the individual trans-actions level), you can capture much of its intent by calculating the ratioacross  individual  securities  (average  gain  on  a  winning  security  versusaverage loss on a losing one) or trading days (average gain on a profitableday versus average loss on an unprofitable one). While you may lose someprecision here, both of these alternative formulas convey the same sorts ofmessages  regarding  trade  selection,  risk  control,  and  the  like,  as  areimplicit in the pure-form impact ratio.
The impact ratio is a critical diagnostic of portfolio selection, executionmanagement, and risk control; and it is typically the first statistical measureto which I would turn in order to help isolate a problem within an account. Inorder to do this, it is necessary to track the statistic over multiple time peri-ods and to use the results as a filter through which to evaluate your tradingperformance.  If  you  are  in  the  midst  of  a  difficult  period,  chances  are  thatyour  impact  ratio  will  have  declined  contemporaneously.  When  this  is  the
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case, by evaluating the underlying components of the calculation, it is oftenpossible to pinpoint elements of your performance that are displaying mate-rial inefficiencies. Break up the numerator and the denominator, and com-pare the unit performance with respect to each to periods of greater success.Is the performance degradation concentrated in the numerator? It could be asign that the quality of your themes isn’t quite as strong as it was when youwere on a roll. Alternatively, it may be that you are simply being impatient andliquidating before your hypotheses are fully playing out.
By contrast, if the denominator in the calculation is edging up, it canbe an indication of several things. Most likely, it suggests that you are hold-ing on to positions longer than is optimal, a factor that can be the result ofseveral underlying inefficiencies in the decision-making process, includingsuch common themes of human nature as wishful thinking, stubbornness,and laziness. Beyond this, a larger-than-optimal average P/L on your losersmay suggest problems in the markets you are operating, including dimin-ished liquidity and poor performance on the part of counterparties and/orthose responsible for your executions.
Finally, your impact ratio can drop as the result of both a decrease inyour  average  positive  P/L  and  an  increase  in  your  average  P/L  on  losingtransactions. If you see this pattern emerge, it suggests that a number ofthings may be going wrong simultaneously, among them those that fall intothe combined categories of portfolio selection and risk management. If thepattern  sustains  itself,  it’s  probably  time  to  take  some  corrective  action;and later in this chapter, we will discuss some of the corrective method-ologies at your disposal. 
Performance Ratio. As it happens, it is possible to combine the accu-racy ratio with the impact ratio in a way that provides an overall index ofportfolio  management  efficiency.  This  index,  which  we  will  call  the  per-formance ratio, is derived by simply multiplying the two component ratiostogether.  For  example,  if  a  given  portfolio  manager  has  a  win/loss  per-centage  of  50%  and  books  $2  of  profits  for  every  $1  that  he  or  she  givesback on losing trades, the associated performance ratio would simply be theproduct of the two ratios: 0.5 (cid:11) 2.0 (cid:3) 1.0.
The performance ratio provides a most comprehensive single assess-ment of overall portfolio management effectiveness because (1) there is alower bound to the statistic below which it will be nearly impossible forany account to be profitable; and (2) at higher levels, you can be increas-ingly confident of your ability to generate sufficient risk-adjusted returnsto increase your exposures toward the maximum levels supportable by theworking capital you have at your disposal.
The performance ratio also synthesizes all portfolio management intotwo distinct yet complementary objectives: (1) to be right more than you
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