umusage of lines in a telephone cable. His name was J. L. Kelly Jr., and in1956 he published his findings in a technical journal on information theory.How his findings found their way into the gambling community is unknown.Most of the big casinos do employ mathematicians to calculate odds,though, so perhaps one of them saw the article in an obscure technical journal. When the results of Kelly’s analysis were applied to gambling, thismoney management system became known as the Kelly System. It has sincebeen adapted to the stock market as a money management system as well.
In reality, the Kelly System was designed only for use on itemsthat have only two results (win or lose, true or false, on or off, etc.).This works very well for gambling, but not so well for the stock market. However, with a little adapting, its principles are applicable tothe stock market also. The Kelly System assumes that you are goingto bet a fixed percentage of your bankroll on each item. If you aremaking money, your bets will grow in size as your bankroll does. If
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you hit a bad streak and are losing, the Kelly System automaticallyreduces your actual bet size as the value of your bankroll decreases.Here is the original Kelly formula in its simplest form:Amount of bet = (W + L) × p – Lwhere W = amount you could winL = amount you could losep = probability of winningFor example, in a situation where you risk one “unit” and pay a10 percent “commission,” the amount you could win (W ) would be1.0, while the amount that you could lose (L) would be 1.1. Thisreflects the 10 percent commission, which is typical in sports betting.With these values for the variable, the Kelly formula would read:Amount of bet = 2.1p – 1.1So, in order to use the system, you would only need to knowwhat your probability of predicting winners is. For example, if youcan predict winners at a 60 percent rate, the Kelly System would tellyou to bet 2.1 × 0.60 – 1.1 = 0.16, or 16 percent of your totalbankroll on this one bet.This formula also tells you that if p is less than about 52 percent,the Kelly System would tell you not to bet at all (2.1 × 0.52 – 1.1 =–0.01); that is, if you are paying a 10 percent commission and can’tpredict 52 percent winners, then find another line of work. Ofcourse, it’s often hard to admit that you can’t predict sporting eventwinners, or day-trade the S&P futures, or whatever. Sometimes it’shard to admit the results yourself, as the following anecdote relates.A basketball bettor was having a particularly poor season and was lamentingto his friend that he had lost a good deal of money. The concerned friendsaid, “Well, why don’t you try something else—like betting hockey?” Thebettor’s reply: “Hockey?! I don’t know anything about hockey!”
At least with the Kelly criteria, this poor guy could have pluggedhis winning percentage into the formula and seen, mathematically,that he should have given up basketball betting.
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The Kelly formula can’t be directly applied to the stock marketbecause results are more complicated. Each trade doesn’t produce acomplete loss or a 100 percent profit, less commissions, as sportsor casino betting does. A stock, futures, or option trade can have aninfinite number of outcomes. Therefore, we have to adapt a little inorder to use the Kelly formula. We not only have to gauge the probability of having a winning trade, but we also have to take intoaccount how big the wins and losses are—that is, we have to factorthe average return into the Kelly formula. In this case, the Kelly formula becomes:Amount to risk =
((r + 1) × p − 1)r
where p = probability of winning and r = average win/average lossunder this strategy (where the average win and loss are computed,assuming an equal investment in each trade).Alternatively stated, r is also the average rate of return on a tradefor whatever system you are using. If you use the average rate ofreturn, then you don’t have to enforce the requirement that your historical statistical data are based on an equal investment in each trade.However, the average win and average loss statistics are often readily available for trading system summaries. For example, if you areanalyzing an S&P futures day-trading system, most system designerswill give you the percent of winning trades and the average win andaverage loss. This information can then be plugged directly into theKelly formula.Example: Suppose that we have the historical results of a trading systemand know that it has produced 35 winners and 45 losers, or a probabilityof winning of 44 percent. In addition, we know that the average winningtrade produced a profit of $1,000, and the average losing trade lost $500.This is all the information we need in order to use the Kelly formula (p =44 percent and r = 2).
Amount to risk =
((2 + 1) × 0.44 − 1)
= 0.16
2
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Thus, the Kelly criteria say that we should invest 16 percent of our totalfunds in each trade, when using this strategy.
This is very useful information, as it allows us to increase the sizeof our trades when our account size is increasing and forces us to cutback on the size of our trades when the system is losing. Despite thatbenefit, the Kelly criteria have some problems, in that they assumethat you are investing sequentially; that is, you are using the systemfor one trade at a time.However, most investors are trading several things at a time. Forexample, suppose you are trading option volume alerts, watching forincreasing option volume and then buying stock in anticipation ofcorporate news events, as described in Chapter 4. At times, theremay only be a few of these situations, but at other times there may bemany of them. If the Kelly criteria told us to invest 20 percent of ourfunds in each one trade, what would we do if there were more thanfive trades that needed to be positioned at one time? One solutionmight be to trade on margin, but a more conservative approachwould be to use what is called the risk-adjusted method. In thismethod, the amount invested in a trade is the Kelly percentage of theavailable equity in the account.Example: Suppose that we computed the Kelly criteria, and they say toinvest 20 percent of our capital in each trade. Then, incorporating the riskadjusted method into the trading would result in the following amount ofcapital being invested in each trade.TradeNumber
Available Capitalbefore This Trade (%)
Capital Investedin This Trade (%)
Available Capitalafter This Trade (%)
123etc.
1008064
201612.8
806451.2
Thus, if Kelly criteria say to invest 20 percent, then the first trade wouldconsume 20 percent of our whole equity. That leaves 80 percent of ourequity to be invested. The next trade would then be 20 percent of the avail-
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OTHER IMPORTANT CONSIDERATIONS
able equity—or 20 percent of 80 percent (16 percent) of the entire account.In terms of the whole account, 20 percent would be invested in the firsttrade and 16 percent in the second trade, leaving 64 percent of the accountas available equity. The third trade would require 20 percent of 64 percent,and so forth.
The main problem with this sequence of money management isthat the first trade is bigger than the rest, but it is the only way toguarantee that you don’t overinvest and still adhere to the Kelly criteria. Moreover, if a lot of trades are going into the account at one timeand all might be negatively affected by the same event (news orvolatility, for example), this method automatically scales back the sizeof each new position. This reduces the tendency to overtrade a particular system at any one time. In addition, as time passes and tradesare opened and closed, the sizes of the trades will tend to even out.Using the risk-adjusted method will even allow you to combinedifferent strategies (which presumably would have different Kellypercentages). For each new investment, you merely use the apropriate Kelly percentage and apply it against the remainingequity in the account in order to determine how much to invest inany particular trade.In summary, then, the Kelly criteria can be coupled with the riskadjusted method to produce a useful and impartial way to help youmanage your money as you establish each new position.
Speculative Trading ProceduresIn this book, many of the trading opportunities identified are speculative in nature. If you are using option volume, option premiums, orthe put–call ratio as a predictive indicator, you are most likely goingto take an outright position, as opposed to a hedged strategy. Therefore, it would be pertinent to discuss the general philosophy of trading an outright position.In a broad sense, outright speculative positions are the easiest tomanage—you are generally long a security (stock, futures, calls, orputs), and all you have to do for follow-up action is to adhere to some
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sort of a stop loss. In reality, though, an outright trading positionneeds more management than that—from initial selection to finalsale. In some cases, there is no underlying—sector index options, forexample—so options are then the only choice. However, when thereis a choice, the only way to logically make it is to evaluate the optionswith a mathematical model. You must know the relative price of anoption before you trade it. If the options are too expensive, youmay then decide to trade the underlying instead.In order to decide if the options are “too expensive,” you musthave some gauge against which to measure the current option price.That gauge, of course, is volatility. You should compare the currentimplied volatility of the options to the recent historical volatility of theunderlying. In addition, you should also compare the current impliedvolatility with recent implied volatilities. An example should help inunderstanding this procedure.Example: A trader is going to buy “the market.” He can either buy OEXoptions or S&P 500 futures. With OEX at 550, these are the relevant statistics:OEX: 550Option545 call550 call555 call
Implied Volatility (%)131211
Historical volatility: 9Given this information, it appears as if the options are overpriced, andso the trader might opt to buy the S&P 500 futures instead of any of theseoptions. However, a little more investigation reveals that the OEX optionsalways seem to have an implied volatility that is higher than the historicalvolatility. In fact, over the past few months, OEX implied volatility hasranged between 11 percent and 18 percent. Thus, implied volatility is currently near the lower end of that range.Moreover, looking at historical volatility in the same context, the traderfinds that over the past few months, historical volatility has ranged between6 percent and 13 percent; so it is currently near the center of that range.
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OTHER IMPORTANT CONSIDERATIONS
Given this additional information—that implied volatility is near thelower end of its normal range, and that it is normally higher than historicalvolatility—the trader would opt to buy the calls instead of the futures.
Another decision that must then be made is which option tobuy. As mentioned earlier in this chapter, buying the short-term inthe-money option is usually the best choice. The trader obtainsleverage because he owns an option, but he does not spend a lot fortime value premium. The number-one reason that option buyerslose money is that they buy options that are too far out-of-themoney. These options also may have too little time remaining. Thismistake can cause the trader to lose money even though the underlying may move in his favor. Whereas with the in-the-money option,he will almost assuredly make money if the underlying has a favorable move.As for actually buying the position, be careful about using marketorders in options unless (1) you are trading a very liquid option, suchas OEX or IBM, or (2) you are placing a small order of 10 contractsor less. Otherwise, limit orders would serve you better in the longrun. You may find that you can often “split” a market (i.e., buybetween the bid and the offer), especially in a moderately activeoption. Don’t be stubborn about using limits, though. If you areattempting to buy a very thin (illiquid) option, the market makers mayjust raise their offer when they see your bid, for they don’t really wantto take a position.Risk management, through stops, of an existing position isanother important factor, especially in speculative trading. Not onlymust you adhere to a stop loss of some sort, but you should also havea plan for taking partial profits at times along the way. I generallyprefer to set my stops based on technical support and resistance levels in the chart of the underlying security. Some traders who buyoptions set stops based on the option price; this can mean that timewill stop them out or that they sell their options when the underlyingis sitting right on a support level—not a good idea. However, whenthey are trading in-the-money options, they don’t have to worryabout time decay so much, so they can use the underlying’s technicallevels to place their stops.
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If you are trading options, use a mental stop; if you are tradingstock or futures, you can use an actual stop. A mental stop meansthat you don’t actually have a stop-loss order on the floor of anexchange; but when the underlying hits your mental stop price, youcan evaluate the situation at that time. If it seems that the positionshould be sold, then you can decide on a market or limit order. Ingeneral, if your mental stop has been violated and if the stock orfutures contract seems to be headed in the wrong direction, a marketorder is best. However, if the stock or futures seem stable, you mighttry to use a limit order to exit the position.Perhaps even more important than limiting losses is managingprofits. Everyone wants to follow the conventional wisdom to “limityour losses and let your profits run.” Actually doing this is easier thanit might appear, despite conventional wisdom to the contrary. Mosttraders know the anguish of seeing a position move in their favor,thereby generating an unrealized gain, only to have it fall back andstop them out. To me, this is far more devastating than taking aprofit too early, although we can attempt to get the best of bothworlds. There are two ways to do this: (1) take partial profits and (2)use a trailing stop.Some traders take partial profits on a strict basis. For example, ifthey own options, they may sell a part of the position if they get a 25percent profit. Then they would sell a similar portion if they get a 50percent profit. Then they would attempt to hold the remainder witha mental stop. Other traders prefer to take profits based on theunderlying’s action—if it hits resistance or spurts ahead too fast, theytake partial profits on their position. In either case, this is the correctapproach, for it allows them to take some realized gains but still letstheir profits run.The other technique that protects profits is the trailing stop.Once a position begins to move in your favor, raise your stop price,whether it be a mental or an actual stop. Initially, you use a fairlytight stop in a trading position. But, if you are taking partial profitsalong the way, you might not want to keep the trailing stop as tightwhen you raise it. That is, when things are going your way, leavesome extra room for a small correction to take place without stopping you out.
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OTHER IMPORTANT CONSIDERATIONS
I previously said that it wasn’t so hard to limit losses and let yourprofits run. To limit your losses, set a reasonable stop to begin withand have the discipline to adhere to it. I prefer to risk no more thana fixed percentage of my account on any particular trade—about 3percent, or maybe less. I am talking about position trades here—notday trades (where I would risk less). Then use the trailing stop to letprofits run. Don’t be lured by targets, and don’t fall prey to youremotions when profits are building up. In my experience, targetsdon’t do anything except get you out of a position that is about tomake a long run. Staying with one or two super-trending trades ayear can make all the difference in the world.As for the specific stop, I use the 20-day simple moving averageas a mental closing stop. It is mental because there’s not an actualstop order on the trading floor. It is closing because I want the stockto have violated the stop at the close of trading. See Figure 7.2 forexamples of closing stops. There are so many intraday feints that Iprefer to use closing stops (some traders even use two-day closingstops; that is, the stop has to be violated on a closing basis for twoconsecutive days). Closing stops are also easier for traders who mightbe employed in another profession. All you have to do is checkwhere your stock is trading with about 10 minutes to go in the trading day. If it has violated your stop, then exit your position. Or if youmiss the close on any given day, then see where the stock closed andexit on the opening the next morning if the stop was violated.There are variations on the type of stop that could be used.Chandelier stops and parabolic stops are designed to “hug” the current price more closely if a very strong, parabolic-style move develops, and they incorporate the recent volatility of the underlying. Idon’t think one type of stop is necessarily any better than another(although the idea of incorporating volatility inherently makes sense),but the real point is use a trailing closing stop.In summary, some axioms are difficult to accomplish—such as“buy low, sell high” (and, I might add, you don't necessarily act in thatorder). But cutting your losses and letting your profits run is something that everyone can accomplish without much difficulty, merelyby setting an initial stop to cut losses if necessary. Then, if profitsdevelop, using a trailing stop to let them run.
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Figure 7.2EXAMPLES OF CLOSING STOPS
Trailing sell stop(you are long)
Trailing buy stop(you are short)Not stoppedNot stopped
StoppedoutStoppedoutNot stopped
Not stopped
Actual Trading ExamplesOn the following pages, there are some rather extraordinary historical examples of actual positions that I have been involved in at onetime or another; some of you may call these “war stories.” Theseexamples will help to illustrate some of the points regarding judgment, timing, and luck in the stock and options market. I once heardJack Schwager (author of Market Wizards) say that no one evergives bad examples of their theories or systems, just good ones.That’s a good point, so some of these examples are of losing tradesas well as winning ones. Even experienced traders might enjoy theseexamples, perhaps because they had similar positions themselves.
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The previous section discussed the usage of stops. Of course, no matterhow carefully you plan to set stops, there is very little that you can do if notrading takes place. One of the most severe trading gaps that I personallyexperienced was in the stock of Cities Service Company, back in 1982. Allduring 1981 and 1982, there had been a myriad of oil company takeovers,many at very inflated prices. Two of the biggest were Conoco (which waseventually acquired by DuPont after outbidding both Seagrams and Mobil)and Marathon Oil (which was acquired by U.S. Steel).In 1982, Gulf Oil made a bid for Cities Service at $63 per share. Ashead of the arbitrage department for Thomson McKinnon, I began toacquire a position. Not only was the stock selling at a wide discount to theeventual tender price—it was selling in the mid-50s—but out-of-the-moneyputs were expensive as well. So we sold puts naked and bought stock. Mostof the arbitrage departments on Wall Street did the same, and then we alltendered our stock to Gulf Oil. After that, one could only sit and wait untilthe appropriate date, when Gulf would take in the stock and pay out cash.Unfortunately, that day never came. For reasons that were never specified, Gulf decided to back out. Rumors had begun to spread that somethingwas amiss, but no one could really sell their Cities Service stock because virtually all of the shares in existence had been tendered to Gulf. That madematters worse; the only thing that traders could do was buy puts for protection, but those quickly became so expensive as to be prohibitive. A fewCities Service shares were trading in the cash market, but they were few andfar between. By and large, though, most arbs still felt the deal was going togo through.It was as if Gulf Oil was out to exact the maximum amount of pain, asthey waited until a Friday afternoon to make it official—they were, in fact,withdrawing their offer and were releasing all shares that had been tenderedto them. Trading halted in Cities Service and didn’t reopen until the following Wednesday because of order imbalances (not a very good showing bythe NYSE’s specialist system). When it finally opened, it opened at 30,down 22 from the last trade!The aftermath of this Cities Service blown deal was, at the time, one ofthe biggest single disasters that Wall Street trading firms had ever suffered intheir own accounts. Some smaller trading houses went out of business; evenIvan Boesky’s firm was in dire straits, needing to borrow money to stayafloat until somebody could rescue the stock.Cities Service executives, who were basically as much in the dark asanyone else during Gulf’s nefarious internal board meetings, set about tofind another suitor. They did, in Occidental Petroleum (OXY), who bought
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the company a few months later for about $50 per share. This preventeddisaster for any arbs who had the staying power to hold onto their stock during the worst of the mess. Even though we lost money, our loss was onlyabout a tenth of what it might have been had OXY not rescued us all. Tothis day, I refuse to buy Gulf Oil products.
The preceding story illustrates how unexpected losses can occurwhen a stock gaps. Not only that, it shows that the unexpected canstrike any position. No matter how careful your planning and analysis, and no matter how many others doing independent analysisagree with your position, there are just no guarantees, period. However, life does have its strange twists, and you must keep alert foropportunities at all times. It does no good to mope and become mentally weakened by such a loss as the Cities Service deal inflicted.Time and again, I have seen a very good opportunity follow right onthe heels of a major loss.The Cities Service deal blew apart in early August 1982. By late August,another deal was formulating for the stock of Martin-Marietta. There was avague bid for the company—a bid that not many arbs were taking seriously.However, Martin-Marietta stock traded up to near 40, and options werevery expensive. At the time, our independent floor broker on the Philadelphia Stock Exchange (PHLX—which is where Martin-Marietta options weretraded) called to show us a seemingly very attractive trade: we could buy thestock at 40 and sell the September 35 calls for 8. This was a huge premiumfor an option that had less than a month of life remaining, so we took thetrade in size. The downside breakeven for this trade was thus 32 at September expiration.As the next few weeks progressed, the chances of a real bid for MartinMarietta seemed to weaken, and the stock fell to the 33–34 area. This wasperilously close to the break-even point; but since we were approaching thisfrom a risk arb point of view, the position was held in its original form. Thepremiums remained large on the options. Even with the stock at about 331⁄2on Wednesday of expiration week, the Sep 35 calls were trading at a priceof more than a dollar.At that point, option volume increased significantly and option premiums picked up even more, although the stock itself didn’t move much at all.After a series of internal meetings with the executive vice president overseeing the arbitrage, who encouraged us to play the situation aggressively if we
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really liked it, we covered the Sep 35 calls that we were short. This was theoretically illogical, of course, since the options were so expensive; moreover, it left us completely exposed on the downside.The next day, Bendix Corporation emerged as a major factor and bid$45 for Martin-Marietta. Within a matter of two weeks, they had purchasedthe stock and the arbs received their cash.
The point of the Martin-Marietta story is a subtle one, in terms oftrading. The actual strategy employed was extremely risky, but that’sthe game we had elected to play in risk arbitrage. The example is notmeant to demonstrate that you should unhedge your hedged positions, but rather to show that you should operate your strategies consistently. Both Cities Service and Martin-Marietta were aggressivepositions. To have changed strategies after the Cities Service dealblew would have been a mistake.Of course, you don’t always get such a great chance to recoverfrom major losses. I was once asked at a seminar to describe my besttrade and my worst trade. I chose the following as my worst trade,not only because of the result, but also because of the trading mistakes that were made.Nineteen eighty-six had been a pretty good year for risk arbitrage, even forthose of us who were operating without access to Drexel Burnham’s MikeMilken’s deals. That was the heyday of leveraged buyouts, and many dealswere consummated via that method. For those needing a definition, a leveraged buyout occurs when an entity interested in taking over a companyuses the company’s own assets as collateral for the buyout of the company.The collateral often took the form of “junk bonds,” which were marketed byMr. Milken’s group at Drexel. For those wanting a more in-depth description, see the movie Wall Street or read the books, Den of Thieves, byJames Stewart, or Barbarians at the Gate, by Bryan Burrough and JohnHelyar.One week in late November, there was a rumor that Gillette was goingto be taken over. The stock traded up to 60 on the rumor, and options gotvery expensive, as volume increased in both the stock and the options. Theperson who did the research for our arbitrage department liked theprospects, and I liked the opportunity to sell some of the expensive put premium. Thus, we wound up both buying the stock and selling the puts. Afterthe close of trading on Friday, I realized that we had accidentally doubled
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our purchase of stock. I was working the order, and the research directorwas also working the same order, through another broker. This wasn’t a crisis, though, as we usually added to a position for several days if we continued to like it.Saturday morning, I picked up a copy of the New York Times and sawthe headline “Ivan Boesky Arrested.” Uh oh. Over the remainder of theweekend, arbs everywhere speculated on the severity of the beating that themarket, and arb stocks in particular, would take on Monday. As it turnedout, the market was actually quite calm on Monday, so it appeared thatnothing untoward was going to happen.However, by Tuesday, the attitude had changed; and there was nothingbut scrambling going on to exit from as much inventory as possible, all overthe street. Heavy losses were taken by most arbs in the next week or two,reducing a good year to a less-than-average one. We eventually exited thelast of our Gillette at prices under $50 per share.
There were several reasons that this Gillette trade ranks in mymind as my worst trade, and none of them really have to do with thebad timing of Ivan Boesky’s arrest occurring right after we had takenthe position. First, there was the matter of the double purchase ofstock. Second, we didn’t sell much stock on Monday, while the market was stable. I might argue, by the way, that I don’t always feel thatI know how the market will react to a certain piece of news. I normally let the market show me which direction it will take (this haskept me from some bad guesses over the years). However, in thisparticular case, the market seemed to take a whole trading day tomake up its mind, an almost unheard-of occurrence in the volatilemarkets of the 1980s and 1990s. In any case, there was a chance tosell Gillette stock at a small loss on Monday and lessen risk in the faceof the Boesky news. The fact that no one else was selling, either,should not have been a real consideration, but it was. The third mistake was a more personal one, and is not necessarily related to themanagement of a trading position; but it was in taking a large risknear the end of the year when our compensation was based on profits for the total year.On top of all those problems, there was the fact that the randomevent—Boesky’s arrest— could and did occur at just the wrong time;and it blew the position out of the water. I believe that’s what’s called
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Murphy’s Law, to a large degree. Moreover, there was no onetrade—à la the Martin-Marietta deal—that allowed traders to bounceback from the losses of December 1986, although the first half of1987 was generally very profitable for arbs and traders alike.When I didn’t sell the Gillette on Monday, it was the same as saying, in effect, that I didn’t believe in my own analysis (which was thatthe Boesky arrest would be bad for arb stocks). It wasn’t the same ashaving researched a company’s prospects and having a definitive,statistical or mathematical opinion to go by—it was more of a gutfeeling, which can be wrong at times. However, if you do have awell-researched opinion, you should stand your ground. That is thepoint of the next section.An important aspect of trading is believing in your own methodology, if you are convinced that you have adequately researched it.You need to have enough conviction in your own ideas and methodsso that you can profit from them. It is possible to discover somethingthat the majority of the investment community has overlooked orhas chosen to ignore. I don’t mean some small stock that no oneknows about—that kind of information is generally of an “inside”nature. Nor am I talking about deciding that some patently obviousfact will make a stock move. I mean a public fact that, for one reasonor another, is just not being acted upon by the majority of traders.The next two examples demonstrate the wrong approach and theright approach.In 1973, Disney began to rerelease some of its classics for the first time inyears. My neighbor went to see whatever the current release was—perhapsCinderella, I really don’t remember. He was so convinced that this was asuperior strategy on Disney’s part that he went out and bought the stock.Over the next year, which encompassed one of the century’s worst bearmarkets, the stock fell over 50 percent. Now, that’s not bad luck, that’spoor analysis. Didn’t the entire world have the chance to evaluate theimpact of Disney’s releases and factor that into the stock price? Of course,they did. So there was no advantage in his “information.”
This was clearly an “obvious” analysis, poorly researched; on theother hand, the next example is about information that is not readilyapparent to the average trader. If you have taken the time and the
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effort to thoroughly analyze a position, you should check yourresearch with someone who is knowledgeable and is a person youcan trust. If your analysis holds up under that scrutiny, then do not beafraid to act on it. You must realize that most useful technical indicators were invented by individuals; had they not had the conviction toact on their research, they might have missed out on a golden opportunity. Such ideas might involve buying or selling volatility when no