ively on either longs or shorts. Moreover, in these circumstances, itwould be logical (and perhaps even in some cases desirable) that the aggre-gate P/L for the hedging side of the market would be negative. However, inmy  experience,  these  factors  offer  little  direct  solace  to  many  portfoliomanagers who often feel the pain of losses on the hedging side much moreacutely than they do when the ideas for which they have the highest levelof conviction liquidate to negative P/L. So prevalent is this trend that manyequity traders with a long orientation are convinced that they are gettingkilled on the short side of the market—even when their short trades aredoing no worse than breaking even or generating modest profits!
I have spent a great deal of time thinking about this phenomenon, andI  suspect  that  the  pervasive  reluctance  of  many  portfolio  managers  tooperate  on  the  hedge  side  of  the  market,  along  with  the  associated  ten-dency to experience heightened levels of stress over what they perceive tobe losses from this activity, is entirely psychological in nature. In my expe-rience, not only do traders perform much better statistically on the hedgeside  than  they  generally  believe,  but  their  overall  profitability  improveswith  the  proper  level  of  attention  to  hedge-oriented  trades  in  ways  thatmay be difficult to perceive.
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My friend Mo, the movie producer, is a perfect example of this type ofthinking. As is consistent with his artistic temperament, he had a tendencyto fall in love with all of the stocks that he trades. “Fine,” I told him overbeers one night (I have found over the years that beer and even strongerwaters are very useful tools of the risk management trade), “but you’d havea better chance of owning them at the right time if you could find some off-setting  shorts,  and  hang  on  to  them.”  From  time  to  time,  he’d  take  myadvice; but I could always count on him to whine about just how much hisdaring forays into the short side of the market cost him. When we finallylooked at his trading sheets, I’ll be damned if the schmuck hadn’t actuallymade money on his shorting! After I finished slapping him upside the head,I  made  him  promise  me  that  he  would  do  two  things:  (1)  Keep  shorting,and (2) shut up about it. Of course, he did neither. Looking back at theseevents,  I  suspect  that  Mo’s  move  to  Hollywood  was  just  about  the  besttrade he ever made.
Operating a balanced portfolio is a very labor-intensive operation; andin order to do so effectively, it may be necessary to spend the lion’s shareof  your  time  seeking  out  appropriate  hedges  for  your  portfolio.  Theprocess is more difficult than you might currently suspect because, amongother  things,  you  need  to  select  a  security  that  will  protect  you  fromadverse  events  without  negating  your  upside  when  your  catalyst  playsitself out. What is more, factors that qualify a position as a good hedge areneither identical nor, unfortunately, the mirror opposite of those that char-acterize your best opportunities. Often the methodology involved in iden-tifying  opposite-side  market  positions  designed  to  reduce  your  overallexposure is entirely different from that through which you would seek toidentify your highest profit positions.
Specifically, the identification of a proper hedge involves the selec-tion of a security not for its likely profitability prospects, but rather forits  ability  to  offer  protection  against  negative  outcomes  in  the  marketthat do not change your fundamental desire to hold the security on whichyou are focused from a profitability perspective. For example, if you arelong GM because you expect an overall rise in auto sales but are fearfulof an uptick in interest rates, you might consider an offsetting short in,say, Ford. However, in doing so, you run the risk that Ford benefits by anequal or greater amount than GM if auto sales do spike up. The hedginguniverse  is  rife  with  problems  of  this  nature,  and  I  don’t  believe  it’sinaccurate to state that there are almost no situations where even a per-fect hedge on paper cannot go badly awry. For these reasons, you mayspend more of your time, if you’re smart, identifying and analyzing hedgealternatives  than  you  do  identifying  profit  opportunities.  Such  a  timecommitment may not be a particularly enjoyable prospect; but if you areable  to  successfully  maintain  a  two-sided  approach  toward  portfolio
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management,  the  prospects  for  risk-adjusted  return  across  an  increas-ingly  high  level  of  capital  under  management  will  ultimately  justify  theextra effort required.
Finally,  the  most  relevant  benefit  of  a  balanced  long/short  marketapproach for those who practice this art effectively is that it is an effectivetool for explicitly controlling portfolio volatilities in a manner that is moreor less seamless to their core trading practices. For instance, a long/shortequity  player  wishing  to  increase  his  volatility  might  allow  his  net  expo-sures to fluctuate more broadly than is the norm, while a trader wishing todampen  her  P/L  swings  would  choose  to  operate  within  more  narrowbands and with a higher degree of balance. In a dual-orientation portfolio,these adjustments occur naturally within the ebb and flow of the portfoliomanagement process. By contrast, if you focus exclusively on one marketside  or  the  other,  the  process  of  controlling  volatility  through  dynamichedging is both disruptive and fraught with hazard.
POSITION LEVEL VOLATILITY
Another manner in which traders can directly control the magnitude oftheir  P/L  fluctuations  is  through  the  strategic  inclusion  of  individualsecurity  volatility  in  their  selection  criteria.  Though  the  relationshipbetween the volatility of individual securities within a portfolio and thatof the portfolio as a whole is a complex one, it is safe to assume that theselection  of  higher-volatility  securities  in  your  portfolio  will  increaseyour exposure, whereas the avoidance of these instruments will have arisk-dampening  impact.  Therefore,  during  times  when  you  wish  toincrease market exposures, one alternative at your disposal is to substi-tute away from securities with low volatility in favor of those with highervolatility  characteristics.  Similarly,  one  way  to  dampen  exposure  is  toeffect the opposite type of substitution, replacing highly volatile securitiesin  the  portfolio  with  those  that  are  more  stable  by  standard  statisticalmeasures.
While I certainly endorse the concept of both understanding individualsecurity volatility and using this as one factor in your portfolio selectionprocess, it is important to caution against overreliance on this componentof your selection methodology. As I have argued, the ideal selection crite-ria  for  any  given  investment  opportunity  is  its  incremental  impact  onprospective risk-adjusted return for the overall portfolio. Stated more sim-ply,  it  is  imperative  that  you  make  your  decisions  on  the  basis  of  whichopportunities will provide the highest level of incremental return for theamount  of  incremental  exposure  assumption  they  entail.  In  order  to  use
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this selection process as effectively as possible, the decision maker musthave  a  grasp  of  the  volatility  characteristics  of  his  or  her  prospectivetrades, but he or she also must be aware of the upside opportunities thatare implicit in the trade. Indeed, if the true criterion for investment inclu-sion is risk-adjusted return, then it is as incorrect to make decisions on thebasis of volatility characteristics alone as it is solely on the basis of returnopportunity. The ideal model incorporates both concepts, and I encourageyou  to  bear  this  in  mind  when  managing  the  volatility  characteristics  ofyour portfolio.
Also be mindful, as we will discuss in the next chapter, that one veryeffective  means  of  “normalizing”  the  exposure  in  your  account  is  to  sizeyour positions according to their volatility. For example, if you buy $1,000worth of a stock that has a 50% annualized volatility, this, in risk units, isthe rough equivalent of spending $2,000 on a stock whose volatility is 25%.Most  professional  traders  use  this  type  of  analysis  in  determining  theappropriate size of individual positions within their portfolio, and I encour-age you to do the same.
TIME HORIZON
An additional if less intuitive way of managing your portfolio volatility isthrough the manipulation of your holding periods. Specifically, the longerthat you hold positions in your account, the more volatility you are likely toexperience. To fully understand this interplay, it is important to recall therelationship between volatility and time, as set forth in previous chapters.In particular, you can convert a daily standard deviation statistic into theappropriate figure for your particular holding period by simply multiplyingthe percentage-based figure by the square root of the number of days youintend to hold the position. For example, if you plan on holding an individualsecurity with a daily volatility of 1% for 100 days, you would anticipate astandard deviation over this period of 10%. 
While the plain implication of this interplay is that your volatility is adirect, positive function of your holding periods, the specifics of this rela-tionship will vary from security to security, from one situation to the next.Herein lies both the opportunity and the hazard. As indicated previously,attempts to deconstruct the risks associated with individual positions intosingle  volatility  numbers  require  us  to  make  certain  simplifying  assump-tions about the manner in which volatility expresses itself in the market-place that simply don’t hold true in real-life situations. The most glaring ofthese oversimplifications is one that suggests that actual price fluctuationswill  distribute  themselves  evenly  across  time.  This,  of  course,  is  seldom
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the  case.  For  example,  the  previously  referenced  security  with  dailyvolatility of 1% that we intend to hold for 100 days might generate enoughprice fluctuation within a week or two to account for the entire 10% volatil-ity we would expect over the period. This would be particularly true wheninformation  pertinent  to  the  valuation  of  the  security  is  concentratedwithin specific dates, such as earnings reports. In these cases (which, bythe  way,  account  for  the  vast  majority  of  market  activity),  not  only  theholding  period  for  individual  securities  will  determine  how  much  of  thevolatility you capture in your trading, but also the timing of your entry andthe exit points.
Counterintuitive  though  it  may  seem,  the  idiosyncratic  manner  inwhich volatility distributes itself across time actually creates opportunitiesto control risk through the management of holding periods. As an example,consider the case of the day-trading methodology that has come into main-stream popularity over the past several years: Day traders, by definition,are usually in and out of their positions within a single trading session; andby operating with holding periods that are typically measured in terms ofhours, if not minutes, they often miss even the core of single-day volatilitythat  is  implicit  in  our  one-day,  one-standard-deviation  statistic.  Thus,  byextending  their  holding  periods  from  intraday  to  overnight,  day  tradersoften stand to increase their exposures by much more than that implied bya simple, linear expansion of their holding periods. Of course, day traderswishing to modify the amount of time they are willing to hold positionsfor the purpose of decreasing their market exposures have much less lat-itude.  Any  move  to  shorten  holding  periods  that  already  fail  to  extendbeyond one trading session is not likely to reduce the risk of loss in indi-vidual  securities  and  may  in  fact  increase  it––due  to  such  unavoidablemarket  factors  as  commissions,  bid/offer  spreads,  and  other  types  oftransactions costs.
By contrast, those whose holding periods extend beyond one day havea better opportunity to use this variable as a means of targeting the appro-priate  exposure  levels  in  their  portfolios.  Once  again,  a  useful  rule  ofthumb is that your exposure will increase and decrease as a function of thesquare  root  of  the  number  of  days  you  hold  the  position.  Thus,  the  riskassociated with holding a position for a week (five trading days) is slightlymore than double (i.e., the square root of five) the risk that would be asso-ciated with a single day; a position carried for a month would be just overfour  times  the  daily  amount  (i.e.,  the  square  root  of  twenty);  and  so  on.What is more, you can achieve additional refinements to this formula bybeing  mindful  of  the  information  calendar,  leading  to  opportunities  foradjusting exposure upward and downward as appropriate, around the tim-ing  of  the  release  of  pertinent  market  information,  such  as  earningsannouncements and economic reports.
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Finally, just as there is diminishing risk impact available in the adjust-ment of high-velocity day trading, so too do the impacts reduce themselvesat the other end of the spectrum. Specifically, if your trading style typicallyinvolves retaining positions for intervals of several months or longer, themodification of your holding periods by even very large, percentage-basedamounts is unlikely to have much of an impact on the management of yourexposures. The reason for this is that over longer holding periods, volatil-ity  patterns  tend  to  smooth  themselves  out,  converging  toward  the  equi-librium levels that in most cases can be ascertained through close obser-vation  of  such  factors  as  historical  pricing  patterns  and  options  impliedvolatility  levels.  Under  these  circumstances,  traders  and  investors  arelikely to capture the full measure of the volatility inherent in each of thesecurities they hold in their portfolio. However, it is still possible for long-term investors to use holding periods as a means of controlling exposures,specifically  by  increasing  and  decreasing  their  position  sizes  around  theanticipated release of economic information that may be pertinent to theirposition profile, as suggested earlier.
DIVERSIFICATION
One proven way to control portfolio exposure is through the manipula-tion of diversification. While the mathematics of this concept are vagueat  best,  the  idea  itself  is  intuitive:  The  more  diverse  the  portfolio,  thelower  its  risk  profile.  In  turn,  diversification  itself  can  be  diffused  intotwo  separate  components:  (1)  the  number  of  securities  included  in  agiven portfolio, and (2) the similarity of the pricing characteristics acrossthese securities.
As  is  the  case  with  the  other  methods  to  adjust  portfolio  exposure,diversification  can  be  used  as  a  tool  for  two-way  risk  control,  allowinginvestors to adjust their risk profiles upward or downward as the specificsituation requires. This means that investors wishing to increase their riskprofile can accomplish this objective by reducing the number of positionsin the portfolio or by selecting securities that have more common pricingcharacteristics, or some combination of the two. Conversely (and perhapsmore typically), diversification can be used as a tool for exposure reduc-tion by a program that features larger numbers of securities and ones withmore  diverse  economic  characteristics.  To  illustrate,  an  account  with  asingle security obviously is as undiversified as a portfolio can get, whereasone that featured, say, a hundred names across various market sectors wouldlikely  display  some  characteristics  of  diversification,  taking  the  form  ofsmoother return streams on both the upside and the downside—particularly
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across longer time horizons, which are more likely to yield a full range ofmarket conditions.
However, while it is easy to maintain a running count of the number ofsecurities held in a given portfolio, establishing the level of pricing simi-larity between securities is a complex process, often more an art than a sci-ence. A good qualitative starting point is the rudimentary economics of thesecurities  themselves.  For  example,  if  you  are  trading  equities,  you  canassume that in order to achieve a meaningful level of diversification, it willbe  necessary  to  hold  positions  across  a  number  of  industries—ideallythose that are subject to different business cycles. Similarly, if you are trad-ing  commodities,  a  portfolio  of  materially  different  asset  classes  (e.g.,grains  and  energies)  is  likely  to  generate  higher  levels  of  diversificationthan  one  that  is  focused  in  a  single  set  of  “substitutable”  product  types(e.g., wheat and corn). These dynamics also carry forward to the remainingsegments of global capital markets, most notably fixed income and foreignexchange.
In  addition,  it  is  important  to  be  aware  of  the  actual,  statisticallyobservable correlations among the securities you are trading, which willbe inversely related to the level of diversification you are able to achievein your portfolio. In other words, the higher the level of correlation amongthe individual securities in your portfolio, the lower the benefits of diver-sification you are likely to derive. Intuitively, this makes sense, and the useof correlation analysis is entirely compatible with the fundamental strat-egy of selecting securities with differing underlying economic characteris-tics. However, while the qualitative approach to constructing a diversifiedportfolio  may  in  most  cases  appear  to  be  sufficient,  correlation  analysiswill add accuracy and precision to the process. Often enough, the appar-ent commonalities (or lack thereof) among positions in your portfolio willbe  deceiving,  and  you  will  inevitably  run  into  situations  where  financialinstruments that have little or no economic overlap are in fact highly cor-related, as well as those where seemingly closely related securities offerwidely divergent pricing characteristics. In these cases, quantitative cor-relation analysis  can  be  of  enormous  assistance  in  the  development  andmaintenance  of  a  portfolio  diversification  profile  that  is  consistent  withyour objectives for risk-adjusted return. 
As a final point, it is important to be mindful of the diminishing bene-fits  of  diversification.  In  particular,  as  you  spread  your  portfolio  over  aneverwidening set of individual securities, the impact on risk adjustment ofthe addition or removal of an individual asset will decrease. At some pointin  the  process,  the  portfolio  will  take  on  the  characteristics  of  an  index;and  the  addition  (or,  for  that  matter,  removal)  of  individual  transactionsmay actually have the opposite effect of the one that is intended. In addi-tion (and at the risk of stating the obvious), the more positions you have in
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your portfolio, the more work you have to do with respect to both analysisand position management; and this implies a diminishing edge with everyincremental position that you add in the name of diversification. Presum-ably, if diversification never enters your mind, you will only put on tradesthat  you  believe  have  met  the  full  measure  of  your  criteria  for  effectivereturn generation. As you add positions in order to diversify, by definition,you begin to relax these criteria. At some point, this will begin to cut intoyour profit profile; and in extreme cases, you run the risk of obliteratingany opportunities you might have otherwise had to make money from youroriginal investment hypothesis. 
For these reasons, I suggest that you establish a base level of positionsthat  you  are  comfortable  managing  and  increase/decrease  your  diversifi-cation levels by nominal amounts as a means of adjusting your exposure atthe margin. The selection of this base number of positions is largely a qual-itative process for which no formula is likely to generate the appropriateanswer. The number should be sufficient to avoid an undue level of posi-tion  concentration  while  at  the  same  time  allowing  you  to  devote  theappropriate  level  of  attention  to  each  individual  position.  Whether  thishappy  medium  can  be  achieved  with  5  positions  or  50  is  a  function  of  anumber of variables, including the complexity of the markets in which youoperate, the level of resources you have at your disposal to manage yourbook, and your own personal portfolio management style. The point is thatyour use of diversification as a tool of risk control should not cause you tostray from your base number of positions by more than, say, 50%. Thus, ifyou  comfortably  manage  5  positions  under  normal  circumstances,  yourefforts to engineer your diversification should generate a range of as manyas 7 or 8 or as few as 2 or 3. Similarly, if your base number is 50, the rangemight be 25 on the low end and 75 on the high.
LEVERAGE
A widely discussed but often misapplied concept of risk control is that ofleverage. Indeed, there has been so much misinformation about leverage inthe discussion of financial markets over the years that it is, in many ways,difficult to find the appropriate point for introducing it into our discussion.However, as leverage, when properly measured, is undoubtedly part of therisk management landscape, it is essential for portfolio managers to haveat least enough understanding of the concept to enable them to grasp itsimpact on their portfolio exposures. 
Therefore, I begin with a simple definition. For our purposes, leveragecan be defined as the ratio of the economic value of a given portfolio to
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the amount of capital available to fund it. Because leverage, no matterhow it is defined, is always expressed as a ratio, its level can be controlledthrough manipulation of both the numerator and the denominator. Specifi-cally,  individuals  wishing  to  increase  their  leverage  can  do  so  by  eitherincreasing  the  value  of  the  assets  in  their  portfolio  or  decreasing  theamount of associated capital allocated to fund it, or by some combinationof the two. Similarly, a decrease in leverage can be brought about by anycombination of reduced asset size and increased capitalization.
As a general rule, leverage and portfolio volatility are positively cor-related.  However,  there  is  a  virtually  unlimited  set  of  exceptions  to  thisrule. For example, because the numerator of the leverage calculation is sim-ply the total aggregate value of the positions in the portfolio (i.e., withoutregard to market direction), a given market-neutral, long/short portfolio withvery minimal risk has a higher degree of leverage than one that simply con-tained the long positions in the same portfolio––in spite of the fact that thelatter is likely to be the more risky market profile. Beyond this, leverage sta-tistics  have  vastly  different  implications  across  asset  classes  and  acrossinstrument classes within a given asset class. For example, the use of a spec-ified amount of leverage in a fixed-income portfolio will generally have less-acute  impacts  than  will  the  same  profile  in  equities,  due  to  the  fact  thatequity  markets  routinely  have  higher  levels  of  volatility.  For  identical  rea-sons, within the fixed-income group, leverage will be more impactful at thelong end of the yield curve than it will for short-term trading instruments.
Beyond  this,  certain  derivative  instrument  classes  are  designed  toengineer precise leverage for investors because they offer trade-offs thatinvolve both the cost of the investment and the probability of their bring-ing  about  a  favorable  outcome.  Most  notable  among  these  is  options,which we will discuss in the next section. However, speaking in terms oftheir implications for leverage, it is important to note that options providewide ranges of methods for amplifying or reducing leverage, which cannotbe characterized in any simple manner for the purposes of understandingtheir impacts on portfolio exposure.
For complex portfolios that cut across asset and instrument classes, therelationship between leverage and portfolio exposure is a complex one forwhich no specific formulas are applicable. However, most portfolios are lessthan complex and have a much narrower and more stable focus. Whereverthis is the case, it is a fairly safe assumption that increased leverage translatesfairly  directly  into  increased  portfolio  exposure,  and  vice  versa.  From  thisperspective, leverage is clearly a very useful tool for risk control––providedthat whatever steps you take to either lever up or delever your portfolio areundertaken in a balanced manner. Be aware that any actions you take to useleverage to control your risk will have disproportionate impacts if the asso-ciated increases or decreases in position sizes are not distributed in a fairly
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even manner across the entire portfolio. A good rule of thumb is that anyleverage-based adjustments should not alter the core economic compositionof the portfolio, only the overall size of the investment.
On  the  whole,  it  is  safe  to  conclude  that  manipulation  of  leverage  isone  of  the  more  powerful  mechanisms  at  your  disposal  to  manage  yourexposures: increasing it by some combination of larger position sizes andsmaller capital basis, and decreasing it by reduced position sizes or capitalinjections. However, it is important to be mindful of the constraints thatwill  apply  to  your  leverage  activities.  If  you  are  trading  your  personalaccount, you should really view your leverage exclusively as a function ofthe total pool of investment capital at your disposal. Any smaller numberis really an artificial constraint, and any larger figure implies borrowing: apractice (I strongly discourage) that, while broadening your capital base,actually increases your leverage at any level of investment. If you are trad-ing professionally, using the capital of other individuals and institutions tofund your activities, you should be acutely aware that the capital at yourdisposal is not a concept you can directly control.
In terms of the ranges of investment sizes available to traders, theseare  bounded  from  below  by  zero  and  from  above  (for  most  markets)  bysome combination of market regulation, credit considerations, and otherexternal factors. For example, in the U.S. equity markets, it is well-knownthat Federal Reserve Regulation T limits the size of a given portfolio (cal-culated on a gross basis as the sum of long and short positions) to twicethe  amount  of  capital  posted  in  the  account  in  question.  Futures  tradersare  constrained  from  a  leverage  perspective  by  margin  requirements,which are ostensibly tied to the amount of volatility inherent in the under-lying instrument in question. Over-the-counter derivative leverage is deter-mined contractually by the parties to the transaction and can often signif-icantly exceed the leverage available in exchange-traded markets.
OPTIONALITY
As we just noted, one of the most powerful ways of managing the marketexposure  for  a  given  portfolio  is  through  the  use  of  options.  Indeed,because options can be constructed in so many different ways to addressmyriad exposures, it is possible to use these instruments to create virtuallyany type of risk profile that is desired––from those that are very sensitiveto movements in underlying securities to those whose value is largely inde-pendent of underlying price and instead are tied to other market factors,such as the level of volatility that is perceived to exist within the instru-ment in question. Moreover, particularly for short sellers of options, there
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are infinite numbers of strategies for which the associated market expo-sure is virtually unlimited. 
For  these  reasons,  an  entire  branch  of  market  science  has  evolvedaround the concept of options trading, featuring dozens of similar yet dis-tinct