pricing models, an extensive set of descriptive diagnostics coveringthe relationship between a given option and its various inputs (underlyingprice, volatility of instrument in question, time to expiration, etc.), and soon. Indeed, the options landscape is vast and complex and, for the mostpart, beyond the scope of this book. However, there are a number of basicoptions strategies that allow investors to adjust the risks in their portfoliosin  order  to  achieve  an  exposure  profile  that  is  better  adapted  to  theirinvestment objectives, and it is therefore important to address these in asimple, straightforward manner.
With this in mind, let’s take a look at the specific elements of optionstrading and investing that render it such a useful tool for risk control andadjustment.
Nonlinear Pricing Dynamics
Options  differ  from  cash  securities  (and,  to  a  lesser  extent,  futures)  pri-marily because of the fact that there is a wide range of contingencies thatimpact  the  payouts  associated  with  them.  The  first  and  certainly  amongthe  most  important  of  these  are  those  associated  with  time.  No  optionsexist into perpetuity (otherwise their value would in many cases be infi-nite), and all have fixed expiration dates beyond which they are no longervalid (i.e., the options buyer no longer is entitled to the rights of the optionunder the terms of the contract). Because of this, options instruments willreact differently to pertinent economic information at different points intheir life cycle, with more abrupt/less continuous pricing impacts typicallyoccurring at points close to expiration (particularly when the underlyinginstrument  is  trading  at  or  near  the  option’s  strike  price,  as  further  dis-cussed later) and more continuous patterns at earlier dates during the life-time of the instrument.
Relationship between Strike Price and Underlying Price (Moneyness)
The second critical contributing factor to option nonlinearity is a conceptcalled moneyness, or the extent to which the instrument is in or out of themoney. To calculate an option’s moneyness, you simply need to comparethe value of the underlying price to its strike price (i.e., the price at whichthe underlying instrument will change hands in the event that the holder of
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the option chooses to exercise it). Options prices will react very differentlydepending on their associated moneyness––particularly as they approachexpiration. Indeed, at expiration, an out-of-the-money option is worth zero,while  an  in-the-money  option  is  worth  the  difference  between  the  strikeprice  and  the  underlying  price  (this  is  the  option’s  so-called  “intrinsicvalue”). This dichotomy causes exponential types of movements for optionsat or near the money as underlying markets change in value and displayshifting price dispersion characteristics.
Implied Volatility
We  already  covered  the  topic  of  implied  volatility,  which,  as  you  mayrecall from Chapter 3, is a useful means of characterizing future volatility,both for the options themselves and for their associated underlying instru-ments.  Because  implied  volatility  is  as  dynamic  a  concept  as  underlyingprice, it can shift abruptly, often causing discontinuous movements in theprice  of  options  that  may  or  may  not  be  consistent  with  the  associatedmoves in underlying securities. For example, the holders of call options ona  stock  about  to  report  earnings  may  find  that  a  positive  earningsannouncement generates a less favorable price movement than is consis-tent with the release––due to the market’s belief that the stock will be lessvolatile after this announcement.
Asymmetric Payoff Functions
With  most  financial  instruments,  a  long  position  and  a  short  position  exe-cuted at the same price have pricing characteristics that are of identical mag-nitude and opposite direction. Not so with options, where the payoff charac-teristics between buyers and sellers, and thus the associated risk dynamics,diverge widely. In order to understand the underlying causes of this anomaly,it is simply necessary to review the basic dynamics of the transaction. 
Under an option transaction, the seller grants the buyer the right, but notthe obligation, to execute certain trades under specified conditions at somepoint in the future. In consideration for these rights, the seller receives a cashpremium, which is his to keep and which binds him for the life of the contractto the terms and conditions implied in the option. Once the premium changeshands, external conditions determine the fortunes of the participants.
If,  on  the  one  hand  the  market  moves  in  such  a  way  that  benefits  theoption holder, the benefits may far exceed the associated costs (expressed inthe form of premium). These benefits can be monetized in one of two ways:(1) by the sale of the option itself or (2) by taking the position in the under-lying markets, through the exercise process. Under these circumstances, theseller  of  the  option  is  faced  with  exactly  the  opposite  return  dynamics,
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potentially losing multiples of the premium taken in by virtue of movementin the underlying market.
If,  on  the  other  hand,  the  market  moves  against  the  interests  of  theoption holder, the value of the option converges to zero, causing the holderto  lose  up  to  the  entire  value  of  the  premium,  which  typically  translatesinto profits for the option seller.
The entire range of outcomes can be viewed as one where for the holderof the option, there is unlimited upside, with the downside being confined tothe value of the premium. For the seller, the best that can be expected is toretain the premium, while this entity faces theoretically unlimited risk if themarket moves against the short option position. This payoff matrix is largelyidentical to the one experienced between the buyer of insurance policies andthe insurers that grant them, and this is why many types of long options strate-gies are often characterized in terms of the purchase of portfolio insurance. While the market typically views the selling of options as a far morerisky activity than their associated purchase, it is, in my view, hazardous tomake  broad  generalizations  in  this  regard.  Indeed,  depending  on  marketdynamics,  there  are  certain  options  strategies  (e.g.,  the  purchase  ofextremely expensive options immediately after a market event) where therisks are in fact much greater on the long side than on the short side, underwide  ranges  of  likely  market  outcomes.  Many  of  the  more  experiencedshort sellers of options employ sophisticated hedging strategies that canmitigate most, if not all, of the key risk factors we’ve discussed. For thesereasons, the use of options is an extremely complex market strategy andone that can often lead to surprising results, even for seasoned market par-ticipants. I suggest that you proceed with the appropriate level of caution(some good software wouldn’t hurt matters either).
Leverage Characteristics
In addition to the aforementioned characteristics, it should also be pointedout that there are material levels of leverage inherent in virtually all optionstrading, that the associated leverage characteristics are dynamic and com-plex, and that (like virtually every other aspect of options trading) the exer-cise  of  drawing  broad  conclusions  regarding  the  relationship  betweenoptions and leverage is one that is full of hazards. In order to understandthis, we must again return to the rudiments of the options trade itself. 
Purchasers of options pay premiums in exchange for contingent rightsto hold specified amounts of target securities. The premium can be thoughtof in these cases as invested capital. Many investors like to think of the ratioof the underlying value to this premium as the leverage factor. For example,if an investor paid, say, $1 million for an option to buy $100 million worth of
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U.S. Treasury securities, the implied leverage in this transaction is 100 times.However, this leverage, needless to say, has much different risk character-istics than a portfolio that simply takes $1 million and uses it as collateral topurchase  $100  million  of  the  same  U.S.  bonds,  with  the  main  differencebeing  that  while  the  holder  of  the  option  cannot  lose  more  than  the  pre-mium  he  or  she  invested,  anyone  invested  in  cash  securities  at  100-to-1leverage can realize losses beyond the level of the investment.
By contrast, short sellers of options are receivers of premium and areoften  viewed  as  making  no  investment  and,  therefore,  achieving  infiniteleverage on their portfolios. The seller of the U.S. Treasury security optiondescribed in the preceding paragraph would be the net recipient of the $1million in premium and would have exposure to the same $100 million ofunderlying market risk. However, in most cases, it is entirely erroneous tocharacterize this as an infinitely levered position. In the first instance, theoverwhelming majority of options short sellers (including, in my opinion, allof the smart ones) engage in some type of hedging, whether it involves anoffsetting  position  in  the  underlying  markets,  long  options  positions  withrisk-mitigating market characteristics, or some combination of the two. Assuch, there are very few pure “short sellers” of options. Beyond this, everylegitimate brokerage firm in the world requires options sellers to post mar-gin ideally equal to the value of the premium plus an amount equal to thelikely worst-case loss that the position could experience. Finally, even if theshort  options  portfolio  in  question  is  unhedged  and  uncollateralized,  anylegitimate market participant would at least set aside sufficient risk capitalin order to fund associated losses if the position moves against them.
From these perspectives, we can reasonably conclude that the calcu-lation  of  a  leverage  factor  for  short  options  portfolios  is  a  complex  andambiguous process that is probably viewed most rationally as a function ofboth the margin collateral required to fund them and the amount of riskcapital rationally allocated to them.
Absent the necessary precautions, the naked short sale of options is inmost cases irresponsible and almost always a losing strategy over the longterm. However, if incorporated into a sound risk-control program that fea-tures some of the components we’ve mentioned, short selling of optionscan have more attractive risk-control features than long options programs,which often generate large losses while providing false comfort as to theiractual levels of exposure.
To reiterate: Options are mathematically complex and extremely idiosyn-cratic. Options markets are notorious for packaging certain types of eco-nomic  attributes  on  the  surface  while  imposing  subtle  costs  in  hiddenways. Therefore, it is critical to proceed with extreme care when enter-ing  into  an  options  strategy.  First  and  foremost,  this  means  taking  the
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trouble to understand the full measure of the associated risks. However,risk  evaluation  is  only  the  beginning.  In  order  to  guard  perpetuallyagainst myriad unforeseen outcomes in options trading, it is also neces-sary  to  thoroughly  evaluate  all  transactions  costs  implications  as  well,including commissions, bid/offer spreads, and tax considerations.
Because  of  these  complexities,  I  highly  recommend  that  you  seeksome  sort  of  partnership  with  trustworthy  and  options-savvy  individualsbefore including options in your portfolio mix (even if these are your bro-kers). Even then, it’s best to start out small, carefully evaluating the rangeof outcomes you experience (both expected and surprising) at small levelsof  risk  capital.  Through  this  process  and  over  time,  you’ll  be  in  a  betterposition to discern which conditions are most conducive to your successin these markets and which aren’t likely to work to your advantage. In turn,this  will  place  you  in  the  best  position  to  incorporate  options  into  yourinvestment activities efficiently and to separate yourself from the untoldranks of those whose use of these markets serves as little more than fod-der for market professionals who make a living by simply understandingthe inefficiencies with more precision than the masses do.
GREEK ALPHABET SOUP
I am currently working with an equity options trader who uses options to try tocapture short-term trading flows in the equity markets—much in the same waya run-of-the-mill short-term U.S. equity trader would with stocks. Equities havebeen very volatile lately, and he’s made a particular effort to keep his portfo-lio neutral in terms of directional market exposures. The standard way of doingthis  in  options-land  is  to  achieve  something  called  delta-neutrality—a  condi-tion under which put and call positions (long and short) offset one another interms of their reaction to moves in underlying markets. He has been quite thezealot about this, and, as such, we were both surprised at how badly he wasgetting nicked in a recent wicked market rally. On further inspection, we spot-ted the problem: The options he was holding that had a negative delta (mean-ing they would tend to move in the direction opposite that of the underlyingmarket—something  almost  exclusively  associated  with  long  puts  and  shortcalls) had much higher betas than did his long delta positions (long calls andshort  puts).  As  a  result,  though  his  overall  options  position  was  neutral  interms of raw dollars, due to the beta mismatch, his portfolio had a very deeplyembedded short bias. From now on (so I told him and he agreed), he’d have tomonitor his beta-adjusted delta position.
Reminds me of that old bumper sticker that remains one of my faves: “My
karma ran over my dogma.”
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These are just a few of the methodologies available to portfolio man-agers  wishing  to  seize  more  direct  control  of  their  portfolio  exposures.There  are  others,  of  course,  but  those  we’ve  covered  are  the  most  basicones available. Moreover, there’s precious little, in my experience, in theway of risk control that can’t be achieved through the use of these tools.While I caution yet again against overapplication of these tools as a port-folio  strategy  (while  it’s  relatively  easy  to  get  caught  up  in  investmentmethods  that  have  a  primary  orientation  toward  risk  control,  such  anapproach  is  clearly  suboptimal  to  one  that  features  enlightened  positionselection and execution management), when applied strategically to situa-tions  that  merit  the  specific  adjustment  of  portfolio  exposure,  they  canhave a significant, positive impact on your experience as an investor. 
In closing, while we are moving in a rather linear fashion from a pas-sive, uninformed view of risk management to one that is active, based onthe benefits conferred by the power of information, I caution against mak-ing changes to your risk profile simply for the purpose of change itself. 
In  the  words  of  John  Milton,  “They  also  serve,  who  only  stand  and
wait.”
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CHAPTER  7
The RiskThe RiskComponents ofManagementan IndividualInvestmentTrade
Trifles make perfection and perfection is no trifle.
—Michelangelo Buonarti to a friend
Having  for  the  moment  exhausted  my  inventory  of  anonymous
British rockers to exploit, I now ask you to take a journey deeperthrough  the  past  and  to  consider  the  experience  of  Michelangelo:the man who put the Renaissance in the term “Renaissance man.” It is dif-ficult to imagine another individual who so dramatically altered the land-scape  of  human  perception  in  so  many  diverse  and  beneficial  ways  andover such a long, difficult period of time. Forsaken by his benefactors (theMedicis),  nearly  skewered  by  the  Savonarola,  indentured  for  decades  bypopes,  and  disdained  by  more  popular  contemporaries  (ranging  fromLeonardo  to  Raphael),  Michelangelo,  over  his  long  lifetime,  neverthelesssucceeded  in  reinventing  the  related  fields  of  painting,  sculpture,  andarchitecture. Don’t expect to draw any direct, market-related wisdom fromhis example because guys like him don’t make great traders. Their mindsweren’t made for such lowbrow nonsense.
But  Michelangelo,  toiling  away  for  decades  at  his  craft,  focusing  onthe details of the task—an earthly figure here, a cherub there—until theentire history of creation is told on a ceiling, had given us the gift of someinsights that we surely can use. Let’s focus our attention now on that mostbasic component of an investment program: the individual trade. Here, wewill  attempt  to  determine  whether  by  focusing  on  trifles  we  can  add  alittle  dose  of  perfection  to  the  portfolio  management  canvas  on  whichwe paint.
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At the risk of stating the obvious, your trading/investment success canbe viewed as nothing more than a financial scorecard of the buy and selldecisions you make in your portfolio, as measured across all asset classesand as weighted by such factors as investment size and market volatility. Itfollows  that  whosoever  achieves  a  systematic  mastery  of  the  science  oftrading  stands  a  great  chance  of  achieving  even  the  most  ambitious  ofinvestment objectives, while those who fail to do so will find themselves ata most bothersome disadvantage in this regard. In turn, if you wish to max-imize  your  performance  in  the  markets,  it’s  important  to  develop  a  solidand consistent quantitative handle on your performance at the level of theindividual transaction. In this chapter, we discuss ways you can accomplishthis task with relative ease.
YOUR TRANSACTION PERFORMANCE
The basic methodology for portfolio review at the trade level involves col-lecting  and  analyzing  components  of  your  individual  transactions,  basedon  aggregation  of  such  pertinent  information  as  time,  date,  underlyinginstrument, price, quantity, and counterparty. If you are able to gather thisdata  in  a  manner  that  is  efficient  to  the  subsequent  analysis,  as  will  bedescribed later in this chapter, you can then evaluate it for insights as tothe drivers of your success over any given period. It is my experience thatthis can have important implications for effective portfolio management,enabling  those  responsible  for  this  process,  among  other  things,  to  geartheir  resources  toward  those  components  and  conditions  that  are  mostlikely to produce the desired outcomes and away from those tied to theirareas of greatest frustration.
The  collection  of  transactions-level  information  is  a  more  difficultundertaking than the data-gathering processes we’ve covered so far. Princi-pally, this is due to the size of the task. Many portfolio managers trade veryactively,  and  the  practical  difficulties  associated  with  collecting  multipledata elements for each transaction can be manifold. Also, the information-gathering  process  can  be  subjective,  even  down  to  the  definition  of  whatconstitutes a trade. For example, if you buy 100 lots of a position, executingit across 10 trades over several hours, is this 1 trade or 10? Further, if thistransaction is viewed as a single trade but has multiple counterparties andprices involved, how can you classify these attributes with consistency?
Transactions-level  analysis  is  rife  with  bothersome  details  such  asthese, but the benefits you can derive from resolving these difficulties ren-der the effort well worth the hassle. To further set your mind at ease onthis score, I will begin this chapter by describing a methodology designed
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to  rid  you  of  many  of  the  ambiguities  inherent  in  the  exercise.  With  theappropriate  set  of  assumptions  in  hand  and  with  an  associated  commit-ment  to  the  process,  I  believe  it  is  possible  to  analyze  your  tradingdecisions  and  modes  of  operation  in  ways  that  can  spotlight  correctableinefficiencies  and  facilitate  the  scaling-up  of  unusually  effective  compo-nents, often with significant positive implications for your bottom line. 
As has been the case with the rest of our data gathering and analysis,we will begin by establishing the appropriate analytical framework, thenattempt  to  create  tools  that  characterize  and  measure  performance  effi-ciency, and finally point out alternatives for modifying trading/investmentbehavior when opportunities identified in your transactions-level analyticsindicate  the  need  to  do  so.  The  first  step  is  one  of  identifying  and  main-taining the appropriate data from your trading records.
Key Components of a Transactions-LevelDatabase
In  order  to  perform  effective  analysis  on  the  transactions  that  compriseyour portfolio, it is plainly necessary to gather and to store all discernableand relevant aspects of the individual trade. The recommended attributesthat should be included in the data set are:
• Instrument name.• Date and time of transaction.• Buy/sell indicator.• Price.• Quantity.• Executing broker/counterparty.• Commission.• Order type (e.g., market, limit, stop, etc.).• Native currency denomination.
In addition, depending on the type of instrument traded, it may be neces-sary to record:
• Maturity (for fixed income) or expiration (for futures and options) date.• Coupon rate and frequency (fixed income).• Put/call indicator (for options).• Strike price (for options).
While  these  informational  elements  will  more  or  less  completelydefine  a  given  transaction  (at  least  for  most  types  of  trading),  there  areother  indirect  pieces  of  information  that  you  need  not  record  for  each
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trade but that will be implicit in the information already gathered and thatyou  should  by  all  means  include  in  your  subsequent  analysis.  Theseinclude:
• Asset class.• Sector designation.• Security-specific  data  (volume,  correlation,  volatility,  shares  out-
standing, etc.).
Again, while it is not necessary to gather and include this informationin  your  database,  it  is  important  to  be  aware  of  its  existence,  to  identifysources for these statistics, and to set up a framework for subsequent cap-ture of this data. For example, let’s assume that for reasons of simplicity ortargeted-market  advantage,  a  portfolio  manager  restricts  her  universe  ofsecurities traded to, say, the Standard & Poor’s (S&P) 500. In order to ana-lyze transactions-level performance for this portfolio, it would be useful toknow something about the volume of these securities, not to mention theirvolatilities,  betas,  sectors,  and  other  market  characteristics.  However,  itwould be neither necessary nor indeed efficient to record these statisticsevery time the portfolio manager executed a trade in one of these names.Rather,  this  information  is  best  obtained  from  other  sources,  includingelectronic-pricing mechanisms such as Reuters and Bloomberg, as well asfinancial print publications, such as Barron’s.
Defining a Transaction
As a final consideration in setting up your trade-level analysis tool kit, youmust decide what among your transactions activity specifically constitutesa “trade.” This is particularly important for active traders (including pro-fessionals)  who  very  often  maintain  a  core  position  in  a  given  securitywhile scaling up and down the exact quantities they are holding at any timeon  the  basis  of  market  conditions.  For  example,  an  experienced  trader,anticipating a sustained market rally, might put on a core position of 100S&P 500 futures with the expectation of holding it for several weeks. 
However, within this time interval, he might reduce or expand this posi-tion as the relative prospects for such a rally become more or less apparentover time. For the purposes of subsequently analyzing this trade, it will benecessary to determine which elements of this sequence fully comprise thetransaction.  Is  it  each  individual  execution?  Is  it  the  position  as  a  whole,with each execution folded into it? Perhaps some combination of the two?Unfortunately,  there  is  no  universally  correct  answer  to  this  question,and there are trade-offs no matter which method you adopt. As a rule, I leantoward an approach under which a single transaction is defined as the set
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of executions that establishes and liquidates a given position without cross-ing  over  either  from  long  to  short  or  from  short  to  long.  In  the  precedingexample, the unit of the trade would include every execution that comprisedthe initial position size of 100 lots along with any trades that either increasedor  reduced  the  position  down  until  it  reached  or  transcended  the  zerothreshold. If the portfolio manager actually reversed his position during thissequence, the execution that reversed the position would be split into twocomponents:  one  that  took  the  account  down  to  zero  (which  would  beincluded  as  part  of  the  original,  initiating  trade),  and  the  other  that  estab-lished a new short, with the latter being defined as the beginning of a newtrade that would be in place until the account was then flat the position.
This approach has the advantage of grouping into a single transactionall individual executions that were tied to a common theme (in the exam-ple  provided,  a  belief  that  a  benchmark  index  will  rally);  however,  thisarguably comes at the expense of some precision. This is particularly trueif the portfolio manager believes that the scaling up and down of a tradeheld for longer durations is strategic enough to merit separate analysis.
If you choose to group your executions in the manner just described,you will need to assign a single price to the transaction in order to performthe  types  of  analyses  contemplated  in  this  chapter.  You  needn’t  botherbeing particularly creative here, and the best approach is probably one thatis called “weighted average” in the nomenclature of statistics or “volumeweighted average price” (VWAP) in the nomenclature of the markets. Thisnumber is derived by multiplying the number of shares or contracts by theprice, across each execution, summing these figures, and dividing by theoverall  number  of  shares  or  contracts  grouped  into  the  transaction.  Forexample,  if  you  buy  30  shares  of  IBM  at  120  and  70  shares  at  121,  youwould multiply 30 by 120 and 70 by 121, add the two products, and dividethe total by 100. The result of 120.7 is a good proxy for the average execu-tion price of the transaction.
The alternative approach involves defining each individual executionas  a  distinct  trade.  This  is  the  most  granular  level  at  which  to  conductanalysis and arguably offers the highest level of precision. However, thismethodology also carries some hazard—particularly for traders putting onlarger  position  sizes  who,  due  to  liquidity  constraints  and  other  factors,may  require  several  executions  in  order  to  establish  and  liquidate  theirfully  invested  position  sizes.  For  instance,  in  our  S&P  example,  due  toprice sensitivity, a portfolio manager wishing to establish a long position of100 contracts might choose to do so across several individual executions,across several hours. In the trader’s mind, this may very well be a singletransaction;  however,  when  he  subsequently  attempts  to  determine  itsstatistical characteristics, it will be impossible to reconstruct it into a unitthat is conducive to analysis. Moreover, statistics (which we will describe
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