-ure should, at minimum, tie back to the weekly or monthly data that shouldbe at their disposal and will serve as a useful proxy to daily P/L, whereversuch information is otherwise unavailable.
Weekly.If daily P/L observation information is unavailable for what-ever  reason,  weekly  data  is  the  next  best  proxy,  again  for  reasons  ofgranularity  and  statistical  significance.  Note  that  for  some  portfolios,under  some  conditions,  the  analysis  tied  to  weekly  P/L  streams  mayprovide a more accurate illustration of performance dynamics than dailydata will. Examples of this include international traders/markets, whoseday-to-day correlations may span multiple time zones and, therefore, notlend themselves to accurate daily analysis; and portfolios where pricingdynamics are not best fit into single-day increments (e.g., those with alarge  component  of  interest  rate  carry,  such  as  repo-financed  bondtransactions).
Monthly. This  is  probably  the  largest  acceptable  minimum  time  unitthat  can  be  applied  to  our  analytical  tool  kit.  Stated  another  way,  ifyou can’t  at  least  get  monthly  data  on  your  performance,  very  littleuse can be made of any of the statistics. Moreover, I would have to seri-ously question the ability of traders to perform the type of risk manage-ment  necessary  to  achieve  rational  financial  goals  typically  associatedwith  trading  and  investing  if  information  is  not  available  on,  at  mini-mum,  a  monthly  basis.  However,  this  is  almost  never  a  problem,as monthly  data  should  be  available  for  virtually  every  type  of  tradingprogram out there.
Monthly data have drawbacks in terms of both granularity and statis-tical  significance,  but  they  can  be  useful  nevertheless  from  a  number  ofperspectives. Over extended periods of time, they will provide insights intolonger-term performance patterns that are difficult to discern with daily orweekly information. This is particularly true for complex portfolios, whereit  may  not  be  practical  to  synchronize  performance  data  on  a  more  fre-quent  basis.  Moreover,  because  many  investment  portfolios  (particularlyhedge funds and Commodity Trading Advisors) report results on a monthlybasis, monthly data can be a useful means of benchmarking your perform-ance against other professional traders.
I  would  suggest  that  even  if  you  are  able  to  put  together  daily  orweekly  performance  results,  you  should  create  and  analyze  yourmonthly time series as well. In doing so, you are likely to find differentand  interesting  patterns  in  this  “higher  aggregation  level  data”  thatare potentially  important  to  the  full  understanding  of  your  portfolio
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management dynamics. For example, you might find your monthly per-formance highly correlated to the monthly returns of a benchmark suchas  the  S&P  500  but  much  less  correlated  or  not  at  all  with  respect  todaily data. If you take the further step of asking yourself what this mightmean—what  combination  of  external  conditions  and  internal  decisionmaking might generate such a pattern—you might come up with a num-ber of plausible explanations. Perhaps, as was the case for most of thepast  two  decades,  the  market  is  simply  rallying  while  you  are  makingyour money on the short side of the market. This would suggest that thedaily, low-correlation numbers were probably telling the more accuratestory. By examining these types of hypotheses (as well as any number ofequally plausible explanations you might find), you stand to learn some-thing about your trading that you didn’t already know, and that fact canonly be beneficial.
Quarterly. As we move down the scale of broader time units, we con-tinue to face issues of granularity and statistical significance. However,I submit that it is important to aggregate your data into quarterly resultsso as to identify seasonal patterns, those tied to equity earnings cycles,and so on.
Annual. No  matter  what  the  smallest  time  unit  is  that  you  are  able  toaccumulate,  it  is  important  to  aggregate  this  information  into  an  annualreturn  profile.  In  some  respects,  this  will  be  your  most  critical  time  unitbenchmark,  representing  among  other  things  the  time  interval  acrosswhich you expect to get paid, the best time unit against which to compareyour performance against external benchmarks, and so on.
Intraday. As indicated previously, it may in some cases be possible totrack your P/L performance on an intraday basis. Absent issues tied to theaccuracy of associated data, this type of analysis can be useful in helpingtraders  identify  the  manner  in  which  their  trading  activity  generates  P/Lacross the daily market cycle. However, I caution against allocating signif-icant resources to the task of logging your intraday performance, as, for allbut the most liquid markets, it is likely to be difficult to create a precisepicture of what you have made or lost at various points within a given day.For  this  reason  and  others,  I  recommend  undertaking  such  an  exerciseonly for traders with extremely advanced pricing systems and operating inthe most liquid, actively traded markets.
Now let’s review how we can examine information from these P/L time
units across larger time spans.
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Time Spans
As  you  may  surmise,  the  availability  and  decisions  you  make  regardingtime units will drive your selection of time spans:
Weekly. First, at the risk of stating the obvious, we can only begin toexamine weekly time spans using daily data, which gives us at most fiveobservatzions—well below the threshold needed to perform meaningfulstatistical evaluation. Nevertheless, I am all in favor of traders lookingat weekly patterns of P/L data because they may provide many insightsinto  the  qualitative  aspects  patterns  of  their  performance.  Specifically,using this data, we can begin to question such matters as whether trad-ing programs are more successful on certain days of the week than oth-ers. Beyond this, if we start comparing weekly groups of daily perform-ance statistics against one another, we can begin to see patterns of whatsuccessful  trading  cycles  look  like,  as  compared  to  more  problematicones.  Are  gains  concentrated  in  one  or  two  days,  while  losses  tend  toextend out across larger time periods? Is the opposite true? What mightall of this mean for improving the success of your trading performance?A qualitative weekly analysis might begin to provide just these types ofinsights.
Second, because certain market events tend to play themselves outacross a period roughly spanning a given week, the analysis of a P/L pat-tern over this time frame might provide significant insight into the rela-tive success a trader is achieving in capturing market volatility opportu-nities. Examples of this type of dynamic abound, including weeks of busyearnings  releases  for  equities  and  multiday  treasury  auctions  for  fixedincome. In each case that may be relevant to your trading, I suggest thatyou  maintain  detailed  records  of  the  economic  events  that  will  impactyour portfolio and track your performance across the relevant multidayperiod.  Then  compare  and  contrast  similar  economic  intervals  withrespect  to  performance.  Does  your  portfolio  perform  better  when  neweconomic information is moving the markets, or worse? Why might thisbe the case?
The same approach may be applied to market-moving events that arenot  tied  to  planned  economic  releases.  You  could  compare  and  contrastyour performance on, say, the week that WorldCom defaulted on its debtto your P/L in the October crashes. Have you done well during periods ofunanticipated  market  volatility,  or  poorly?  What  could  you  have  legiti-mately  done  differently  to  improve  your  result?  These  types  of  analysescan  best  be  conducted  by  tracking  weekly  performance  against  a  cross-referenced list of economic activity.
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Monthly. The 20 observations of daily trading P/L that comprise a typi-cal  month  begin  to  form  a  data  set  across  which  we  can  perform  somemeaningful statistical analysis, including mean, volatility, and correlationstatistics, which will be discussed in the next chapter. In addition, a quali-tative  review  of  monthly  performance  data  will  provide  further  insightsregarding  your  relative  level  of  success  with  respect  to  capitalizing  onspecific  market  inefficiencies.  Of  course,  the  market  cycle  of  economicinformation that comprises a month differs from the weekly cycle we justreviewed and will include, among other things, an entire round of govern-ment  data  releases.  As  was  the  case  with  weekly  analysis,  one  possibleapproach  would  be  to  generally  catalogue  some  key  economic  statisticsthat characterize a given month and to start to compare and contrast yourperformance across months that have similar types of economic activity.Do they represent a pattern?
Finally,  monthly  data  is  probably  the  smallest  time  span  againstwhich  you  should  compare  your  performance  relative  to  the  goalsyou have  established  for  yourself,  which  will  be  discussed  in  greaterdetail later. However, to give you some foreshadowing of how monthlydata can help you manage your performance against targets, you shouldkeep  in  mind  that  there  are  only  12  monthly  chances  to  meet  annualgoals. So while one observation below the target is certainly acceptableand  in  most  cases  unavoidable,  a  sequence  of,  say,  three  or  four  suchoutcomes  should  cause  you  to  reevaluate  both  your  performance  andyour  objectives  in  ways  that  I  will  describe  in  further  detail  in  laterchapters.
Quarterly. By  the  time  you  have  gathered  a  quarter’s  worth  of  dailyinformation,  you  will  be  in  an  excellent  position  to  perform  statisticalanalysis with confidence that the numbers you generate will be both stableand statistically significant. Moreover, a quarter’s worth of economic activ-ity begins to offer meaningful information of overall anticipated perform-ance across the spans for which professional traders are typically paid fortheir performance (i.e., one year). It therefore is not too early here, in addi-tion to the standard volatility information I will discuss later in this chap-ter, to begin to benchmark your returns against those of relevant marketindexes,  against  the  returns  of  professional  portfolio  managers  whomyou’d like to emulate, and, again, against the targets you have establishedfor yourself.
From  a  qualitative  perspective,  one  quarter  of  economic  activitybegins to tell the story of an entire year (which, of course, is one reasonwhy it is the unit of time over which investors most thoroughly analyze theearnings  performance  of  corporations).  In  evaluating  your  performance
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over  this  time  span,  you  will  want  to  ask  yourself  generally  whethermarket conditions were poor or favorable and to critically evaluate yourperformance against this backdrop.
Annual. Perhaps it is not surprising that I would argue that the annualtime  span  is  probably  the  most  important  window  for  analysis,  offeringample data to ensure statistical significance along with an entire cycle ofeconomic  activity  against  which  to  evaluate  your  relative  performance.Moreover, most professional traders are paid on some sort of annual cycle,so  it  is  imperative  to  view  performance  in  annualized  terms.  Here,  aselsewhere, there is a large opportunity to view things through both a qual-itative and a quantitative filter. With regard to the former, the more ques-tions you ask yourself the better. Was it a good year or a bad year for yourmarkets?  How  would  you  evaluate  your  overall  compensation  in  light  ofthese conditions? How did you perform as compared to your peers? Whatwas your best decision over the course of the trading year? What was yourworst decision? What were the associated impacts of these? Where do yougo from here?
A thorough and objective qualitative evaluation of your performanceon an annualized time span is a critical component of your planning forthe next year. Here, the process needs to start a bit before year-end, asyou  move  from  asking  and  answering  the  hard  questions  into  a  modewhere you begin to carefully and honestly examine the manner in whichyou  plan  to  attack  the  markets  over  the  next  12  months.  If  things  aregoing extremely well, this process might center on fixing the appropriateset of objectives for the next annual cycle. However, for the majority oftraders, a great deal more should be involved. In particular, I recommendthat even the most successful traders take the time to evaluate such crit-ical  but  often  deemphasized  elements  of  trading  as  cost  structures  andcapital  investments,  technology  platforms,  and  execution  and  clearingrelationships.
Whether you are pleased or (to whatever degree) disappointed withyour performance the preceding year, you should focus this analysis onsetting  your  objectives  going  forward,  and  I  will  discuss  this  at  greaterlength in the coming chapters. As a general guideline, if your evaluationleads you to objectively conclude that your performance was satisfactoryor  better  (and  you  have  reason  to  believe  that  favorable  conditions  inyour markets will persist), it might be time to focus on the scalability ofyour portfolio. The good times won’t last forever (they never do), so it’simportant to try to make as much as possible when you’re getting thingsright.  Conversely,  if  you  have  fallen  short  of  expectations,  you  mustexamine your overall business strategy and infrastructure so as to ensure
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that there is nothing inrooted in these basics that is at the source of yourproblems.
For professional traders working for financial institutions, the processof  evaluating  your  infrastructure  will  often  be  imposed  on  you  formallythrough  that  organization’s  budgetary/performance  review  cycle.  Aspainful  as  it  may  be,  it  is  a  good  thing,  and  I  strongly  recommend  thattraders  take  the  opportunity  to  use  this  exercise  as  an  opportunity  toundertake the more personalized evaluation of the administrative sides ofyour portfolio as described earlier.
Finally, as I will discuss later, there will come a point in many traders’career  cycles  where  they  must  reevaluate  their  entire  approach  to  themarkets,  including,  perhaps,  what  they  are  trading  and  who  is  fundingthem.  The  best  time  to  undertake  such  an  analysis  is  at  the  end  of  anannual trading interval. This is true most notably because it coincides withmany  of  the  most  important  structural  elements  of  the  trading  calendar,including those associated with compensation, budgets, and the setting ofobjectives. It is obviously easier both to address these issues at year-endand to effect any changes that are needed at that time than it is at midyear,where there may not be sufficient data to make such a determination andwhen embedded financial/contractual issues may render them more diffi-cult to resolve.
The point here is to ensure that no matter what the circumstances areunder which you participate in the markets, you should establish routineintervals for evaluation of your performance. While there may be signifi-cant benefit to undertaking a multifaceted approach to this task and per-forming the evaluation across multiple time spans, it is essential to committo  some  program  of  this  kind.  For  most  traders,  the  ideal  program  mayinvolve a review of daily data, over both an annual and a monthly/quarterlytime span.
YOU’VE GOT A FRIEND
You’ve  got  a  friend,  and  I’ll  call  him  Keith.  He’s  a  bit  of  a  renaissance  man,careerwise, having undertaken roles as varied as burger flipper, pig raiser, andworld-class  money  manager.  He  gets  paid  a  percentage  of  the  profits  in  thislatest (most lucrative) gig each December 31. This means that he doesn’t getpaid in April and he doesn’t get paid in June. If he hasn’t covered his nut (andthen some, I daresay), he still doesn’t get paid come December 31 if his returnsfor the year come to zero. His mission? Have as much greenery as possible onhis  books  at  precisely  eight  hours  before  the  ball  drops  and  the  corks  startpopping.  He  knows  it  and  acts  accordingly.  To  him,  good  months  and  goodquarters are only valuable if they add up to good years.
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I  also have  a  friend  (unlikely  as  that  may  seem).  Call  him  Mo.  Someday,he’s going to be a big Hollywood producer. He already has a half dozen (some-what misunderstood) alternative films to his credit. One of these days, any oneof  his  projects  could  launch  him  into  the  bright  lights.  In  the  meantime,  tomeet his expenses, he straps himself each morning into a workstation at thelocal  ISCALP  electronic  trading  complex  in  a  major  East  Coast  city.  Mo,  as  itturns out, is a very good trader; some might even say he’s a better trader thanproducer. However, for those who know and love him (and I feel fortunate tocount myself among this number), he has the soul of an artist.
ISCALP puts up the capital and pays 50% of the profits on a monthly basis.This works out well for Mo because, as I mentioned, he has bills to pay; andtypically the big ones (rent, car payment, health club membership) come dueon a monthly basis as well. Mo focuses his attention on maximizing his prof-its  each  month.  This  helps  him  manage  his  risk,  keep  creditors  at  bay,  andmaintain the schedule flexibility he needs to be able to drop everything whenhe receives word (and the phone call is expected at any time) that Dreamworkshas decided to provide funding for his bold but underdeveloped concept for amusical adaptation of Adam Smith’s The Wealth of Nations, featuring his self-penned (soon to be) smash hit, “I Wanna Hold Your (Invisible) Hand.”
In addition, I have a relative in this game, who I also consider a friend. Hername is Barbara. She’s raised a whole passel of kids and grandkids and is thechief financial officer of the family business. We don’t see eye-to-eye on everyissue,  but  she  has  a  better  outlook  on  life  than  just  about  anybody  I  know.Improbably,  she  is  also  a  very  good  trader.  She  has  bought  and  sold  stock,profitably, for several decades, across all types of market conditions; and it hasprovided a steady source of supplemental income for her and her brood. Shetrades  part-time  and  tends  to  evaluate  her  performance  not  across  units  oftime, but rather across results thresholds. For example, she might try to tradeher way to a couple of thousand dollars profit to finance a trip to Europe thatshe is planning this summer.
She knows that I don’t think people should set return targets on the basisof personal financial need (in fact, it’s a perfect example of the type of thingwe  differ  on);  but  she  is  very  disciplined  about  identifying  her  targets,  theamount she is willing to risk, and the time horizon that is most consistent withthe  realization  of  her  objectives.  She  has  demonstrated  an  uncanny  marketfeel. Her market-based successes are a marvel to me and serve as a constantreminder that a disciplined adherence to a methodology of any kind is betterthan no methodology at all. There are many, many days when I feel tempted togive her all my money to manage.
All  three  of  these  friends  have  successfully  incorporated  the  concept  oftime  into  their  trading  and  investing  framework—albeit  in  widely  divergentways. Ultimately, this will be your challenge as well.
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Now that we have discussed the various alternatives, let’s take anotherlook at the time unit/time span matrix, to see what inferences we can drawas to what works best:
Weekly
Monthly
Quarterly
Annual
Time SSpan
TimeUnitT
Daily
Weekly
Monthly
Quarterly
Annual
Key:
Important
Interesting
Marginal
Not Usable
I reckon that’s about all I have to say about time series construction,and no doubt we’re all glad to get it out of the way. Now let’s start seeinghow it can be applied to some useful analytical purposes.
Graphical Representation of Daily P/L
The first type of data analysis I recommend is a graph of daily performanceacross the relevant time span. Ideally, the graph will feature a continuousline,  representing  your  cumulative  P/L,  and  a  series  of  individual  bars,reflecting individual daily performance, as is indicated in Figures 3.1 and3.2. However, these graphs can be broken out separately if this is easier forthe user to create or evaluate.
These graphs allow sharp-eyed observers to quickly obtain numeroususeful  insights  into  portfolio  performance  over  the  period  in  question.First, as with any chart, we hope that the general trend is upward. Second,
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Daily P/L
150,000
100,000
50,000
0
(50,000)
(100,000)
Cumulative P/L
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
0
(150,000)
1 1/1 4/2 0 0 21 0/3 1/2 0 0 21 2/1 3/2 0 0 29/5/2 0 0 29/1 9/2 0 0 26/1 1/2 0 0 21 0/1 7/2 0 0 21 1/2 9/2 0 0 23/1 5/2 0 0 24/1 5/2 0 0 21/2/2 0 0 21 0/3/2 0 0 25/1 3/2 0 0 23/1/2 0 0 28/7/2 0 0 25/2 8/2 0 0 21/3 1/2 0 0 21 2/3 0/2 0 0 28/2 1/2 0 0 21/1 6/2 0 0 27/1 0/2 0 0 22/1 4/2 0 0 26/2 5/2 0 0 27/2 4/2 0 0 24/2 9/2 0 0 24/1/2 0 0 2
Daily P/L
Cumulative P/L
FIGURE 3.1 Prototype volatility for successful account. Note that in acombined graph such as this one, it is necessary to establish two different verticalscales: one for the daily P/L observations and another (presumably higher) for thecumulative performance. This is easily done in either Microsoft Excel or otherspreadsheet programs.
we can immediately identify any periods of difficulty, assess their magni-tude  relative  to  overall  performance,  and  use  this  as  the  basis  for  addi-tional analysis. We can also tell a great deal about how the individuals inquestion  manage  risk,  whether  they  respond  to  periods  of  adversity  bypreserving capital or whether their reactions show undue impatience, asmanifested  in  spiraling  increases  in  volatility  patterns.  Third,  we  canassess whether the overall pattern is reflective of the smooth upward archthat  represents  the  ideal  in  this  business  or  whether  the  P/L  path  is  onewith many peaks and valleys, which indicates that the portfolio, whateverits overall performance, was one with material levels of market risk.
Take  a  good  look  at  these  graphs—they  speak  volumes  about  thetrade-offs  between  risk  and  return.  Pay  particularly  close  attention  to
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Daily P/L
200,000
150,000
100,000
50,000
0
(50,000)
(100,000)
(150,000)
(200,000)
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Cumulative P/L
800,000
600,000
400,000
200,000
0
(200,000)
(400,000)
(600,000)
(800,000)
(1,000,000)
(250,000)
1 0/3 1/2 0 0 21 0/1 7/2 0 0 21 2/3 0/2 0 0 28/7/2 0 0 29/5/2 0 0 23/1/2 0 0 24/1/2 0 0 21/2/2 0 0 26/1 1/2 0 0 27/1 0/2 0 0 25/1 3/2 0 0 29/1 9/2 0 0 21 0/3/2 0 0 24/2 9/2 0 0 27/2 4/2 0 0 28/2 1/2 0 0 23/1 5/2 0 0 24/1 5/2 0 0 26/2 5/2 0 0 25/2 8/2 0 0 21/3 1/2 0 0 21/1 6/2 0 0 22/1 4/2 0 0 21 1/2 9/2 0 0 21 2/1 3/2 0 0 21 1/1 4/2 0 0 2
Daily P/L
Cumulative P/L
FIGURE 3.2 Prototype volatility for troubled account.
“drawdowns.”  Mark  the  dates,  and  try  to  reverse  engineer  what  wentwrong. Were market conditions atrocious? Was your specific performancebelow  expectations?  Perhaps  some  combination  of  the  two?  Conversely(and as we will discuss later), it may be that your drawdown occurred aspart  of  a  process  of  scaling  into  your  most  profitable  positions,  at  suchtime as these positions were moving against you. If so, my guess is that youcan feel pretty good about things, as you most likely made a fortune.
It is also quite instructive, I find, to compare the time periods associ-ated with a given drawdown with the corresponding recovery period (i.e.,the time period that is involved in recouping all of your drawdown-relatedlosses). Note that duration of these periods may exceed the time periodsassociated with the corresponding downdrafts (which are unavoidable formost  mere  mortals)  by  significant  amounts  (i.e.,  twice  as  long  or  more);and this is why it is important to exert as much control over their magni-tude as is humanly possible. 
Figures 3.1 and 3.2 are simplified illustrations of these phenomena atwork. In Figure 3.1, the account in question demonstrates a healthy volatil-ity  pattern,  under  which  the  drawdowns  that  do  take  place  occur  at  theends of intervals of strong performance and are of magnitudes that reducebut  do  not  exhaust  the  P/L