2.2 ratio. There was only one statistic that worried us about the performance of this system and that was the long profitto short profit comparison. This system made nearly 90% of its profit onthe long side. What would happen to future performance if the U.S.bonds entered into an extended bear market? In addition, this system had60% winning months. Remember, know your system inside and out andhopefully you will be prepared for situations like seven consecutivelosers in a row. The historical equity curve shown in Figure 10.4 on page223 indicates smooth and consistent equity growth and illustrates a highSharpe Ratio. This is the type of equity curve that you want to see in thepast and hope to see in the future.HOW TO EVALUATE TRADING SYSTEMPORTFOLIO PERFORMANCEAll of these performance statistics should be used to determine a system's future viability. However, we must keep in mind that we are looking at a system on a market-to-market basis. Long-term success intrading can only be achieved by diversification. In addition to a microscopic market-to-market analysis, we must add a macroscopic portfolioanalysis so that we can determine system and portfolio viability. It iseasy to see how one market will perform on a system, hut it is more difficult to see how two or more markets, traded simultaneously by thesame system, interact with each other and affect the end results. Weknow if you trade two markets with one system, the total end profit is asimple summation of the individual profits. However, the overall maximum draw down figure of the two markets, in moat cases, is not thesimple summation of the individual draw downs. Here lies the beauty ofdiversification; profit increases more in proportion than maximumdraw down. If two very different markets are traded on the same system, the probability of them drawing down at the same time is extremely low.Figure 10.5 illustrates the goal of trading more than one market.When one market is losing, we hope the other market is making morethan enough to cover the loss. This is why it is so important to analyze asystem through two dimensions: individual market (microscopic) andportfolio analysis (macroscopic). Both forms of analysis don't alwaysagree with portfolio inclusion. Referring back to our pattern system, wecame up with a portfolio of two different markets. Table 10.10 shows asummary of the market by market analysis. In this analysis, it is plain tosee that a portfolio of just these two markets would be antiproductivefrom a draw down standpoint.
225
HISTORICAL TESTING—A BLESSING OH A CURSE
FIGURE 10.5 The goal of diversification (vertical= profit; horizontal = time).
TABLE 10.10
Individual Performance of the British Pound and Swiss Franc
ONE CONTRACT PER TRADETEST PERIOD 1/1/83-8/31/99S75 ALLOWED FOR COMMISSION AND SLIPPAGEIndividualMarket
TotalPL (1)
Avg PL/Yr ($)
MaxDrawDn($)
Trds/Yr
Win(%)
Gain/MrW:L +DD (%)
British PdSwiss Franc
44,20046,438
2,6522,786
24,68822,900
4445
40.5
1.21.2
Summary PerformanceNet Profit ($):Maximum Drawdown ($) :
90,36845,531
40
10.111.3
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THE ULTIMATE TRADING GUIDE
TABLE 10.11 Portfolio Performance Increased by Adding Less ThanDesirable Markets
ONE CONTRACT PER TRADETEST PERIOD l/8/83-8/31/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
Sometimes adding markets that seem to be underachievers on amarket, by market basis can help the overall performance. Table 10.11demonstrates improved portfolio performance. By manipulating andadding anti-correlated markets the overall profit increased by 39%while overall maximum draw down decreased by 5%. Some markets thatare ruled out due to their individual performance sometimes addsvalue at the portfolio level. Portfolio analysis is a must when it comes tobuilding a successful trading plan. A trading system cannot be considered good unless it can trade a basket of different and somewhat anticorrelated markets.CONCLUSIONHopefully, this chapter shed some light on the problems of interpretinghistorical system performance data. A curve fitted track record is asworthless as the paper it is printed on and can bolster false confidence ina nonrobust system. Optimization and/or reoptimization is not the answer to the ever-changing markets. There has been promising researchon adaptive parameters, which could eliminate curve fitting altogether.If you develop a trading system and most of the design was contributedby your computer and hindsight, then you should know that your designwill only work in the past. Once curve fitting has been ruled out of atrack record, in depth analysis of the track record is necessary to determine system viability. In addition to determining a system's viability,
HISTORICAL TESTING-A BLESSING OR A CURSE
227
one must analyze the track record to determine compatibility betweenthe system and the trader's psychology. You can't simply look at individual market performance to develop a trading plan. The interaction oftrading individual markets simultaneously on a system plays a big role inportfolio composition. Success in trading futures or stocks can only be attained by diversification, therefore one must look beyond individual market, performance and look at the entire picture.
11MONEY MANAGEMENT
Money management is the most important tool to successful trading,but only about 10% of individual traders incorporate it into their trading plan. Just because a trader has a small amount of capital doesn'tmean he can't apply the ideas of money management. Many traders feelthat these concepts can only be utilized by large CTAs and institutions.This chapter argues the opposite and illustrates how money management concepts can he utilized at any capital level.Money management involves examining the concepts of risk and return in reference to investor preference. The objective is to choose a desired rale of return and then minimize the risk associated with thatrate of return. In general, there are four decisions involved in the trading process:1. Buy/sell (system or strategy).2. Which commodity or stock to trade.3. How many contracts of each commodity to trade.4. How much equity to risk at any given time.The first decision involves the mechanics of trading itself withoutreference to money management. The last three decisions apply directlyto the maximization of profit and the minimization of risk. Since 75%of the decision process deals with the management of risk and reward,75% of research time should be spent on money management and portfolio composition. Principles dealing with risk and reward should beconsidered from the outset of system development and made an integralpart of the system.
ZZ8
MONEY MANAGEMENT
229
STATISTICS—A NECESSARY TOOLStatistics is a branch of mathematics used to measure the probability ofpossible outcomes. We can use statistics to measure the risk and returnof trading an individual commodity or stock or a portfolio of differentmarkets. Most traders use net profit as their measure of return andmaximum draw down figure as their measure of risk, but with statistics we can measure risk/return in terms of all events, not just two. Inthe money management world, risk is defined as the standard deviationof returns that represents the volatility of the equity curve. The higherthe standard deviation, the less smooth the returns and curve. The deviation amount represents how much one tan make or lose on a monthlybasis. The overall objective of using statistics in money management isto minimize the standard deviation of returns with respect to the meanreturn. We plan to keep things simple in this chapter, so the only statistical tools that we will use will be mean and standard deviation.Formulasx = Variables or events (could be anything fromwidgets to monthly returns)n = Number of variables or events (a minimum ofthirty IMean = Summation of all x / Number of xStandard deviation = Square root (Summation((x - Mean)2) / n - 1)Examples for calculating the mean and standard deviation of numericalseries:xl = 400x2 = -90x3 = 200n=3xl + x2 + x3=510Mean = (xl + x2 + x3) / n = 510 / 3 = 170xl -Mean = 400-170 = 230x2 - Mean = -90 - 170 = -260x3 - Mean = 200 - 170 = 30(xl - Mean)2 = (230) 2 = 52900(x2 - Mean)2 = (-260)2 = 67600(x3 - Mean)2 = (30)2 = 900Summation((x - Mean)2) / n -1 = (52900 + 67600 + 900) / 2 = 60700Standard deviation = Square root(60700) = 264.4
230
THE ULTIMATE TRADING GUIDE
A value w i l l fall within one standard deviation above and below themean 68% of the time. With respect to our example, there is a 68%chance that future events (x) w i l l fall between the values of -94.4 and434.4. There is a 95% probability that future events will fall within twostandard deviations above and below the mean. In addition to the overall goal of maximizing profit while m i n i m i z i n g risk, money management also tries to reduce the probability of total meltdown also knownas the risk of ruin.
RISK OF RUINThis statistical term is used to describe the probability of a trader losing all of his or her trading capital. Risk of ruin is a basically a function of three different variables: amount of capita] risked per trade,percentage of wins, and the win to loss ratio of the trading system. Theamount of money that is risked per trade is governed by money management, whereas the other two variables are quantified by the trading system you wish to trade. The risk of ruin is heavily concentrated in theearly stages of trading a system. The higher the bet or (risk) per tradethe higher the risk of ruin. If you start out with $20,000 and bet $5,000on each trade, you are ruined if your first four trades are losers. Theprobability of this occurring is a function of the bet size and the probability of success of the trading system (for simplification we assumethat the amount that we win or lose is the same and constant). If thechance of losing on the first trade is 45%, then the probability of havingfour losing trades in a row is (45%) 4 (We raised our chance of loss by thenumber of losing trades necessary to cause ruin right off the bat. 1 orapproximately 4%. If you bet less, than the probability of ruin decreases. Instead of betting 35,000 per trade, you bet $2,500 then theprobability of ruin right of the bat is (45%) 8 or .17%.If a trader is profitable in the early stages of trading and has increased his initial capital, then four losses (consecutive or net) can nolonger ruin him (if his bet size remains constant). Even though thenumber of consecutive losses needed to cause ruin increases over time,so does the probability of more consecutive losses. The following formula gives the probability of eventual ruin (PR) over the long run:PR = (1 - TA / 1 + TA)IUwhere TA is the trader's advantage (percent wins - percent losses) and1U is the initial trading units. If a trader's initial capital is $20.000and the bet size is $5,000 then IU = four. The probability of eventualruin for the following scenarios is:
MONEY MANAGEMENT
231
Total capital:Bet size:Trading advantage:Probability of ruin:
$20.000$ 6,00010%44.8%
Total capital:Bet size:Trading advantage:Probability of ruin:
$20.000$ 2.500
Total capital:Bet size:Trading advantage:Probability of ruin:
$20,000$ 2,00010%13.4%
Total capital:Bet size:Trading advantage:Probability of ruin:
$20,000$ 1,00010%1.8%
10%
20.1%
These numbers are only valid if you are trading on a one contractbasis. The risk of ruin changes dramatically if the number of contracts vary. In addition, these equations assume that the amount wonwhen you win is always the same and always equal to the amount lostwhen you lose. As we had stated previously, risk of ruin is a functionof percent wins, win to loss ratio, and bet size. So far we have ignoredthe win to loss ratio. In the real world, most profitable trading systemshave leas than 50% wins and win:loss ratios greater than 1.2; therefore, leading to the fact that wins and losses are not always of thesame magnitude. Ralph Vince, in his book Portfolio Management Formulas (New York, 1990), offers risk of ruin equations that take thisfact and others into account.Risk of ruin is an interesting figure, hut does not provide much insight in how to manage or trade one's account effectively. What have welearned from risk of ruin and the examples? Self-preservation is bestachieved by not betting the farm. If you bet (risk a percentage of equity) sensibly and trade a system with positive expectation, then theprobability of ruin is quite small.CAPITAL ALLOCATION MODELYou now have the tools necessary to understand our Capital AllocationModel. First we will demonstrate how to allocate capital across a singlemarket portfolio using a small sample of data and then we will use thesame approach on a portfolio of two markets. At the end of the chapter,we will demonstrate the effectiveness of the capital allocation model ona real system on medium- and small-sized accounts.Remember our goal is to maximize profit while minimizing risk. Thisgoal must be attained without going outside the barriers of acceptablerisk. To attain this goal, we must know how much money to allocate toeach market and the number of contracts that we should trade. In themodel, capital is a function of equity, mean monthly returns, and market
332
THE ULTIMATE TRADING GUIDE
risk. Equity is simply the initial capital that we have to start trading.In these examples, returns are not compounded; we use the initialtotal capita] for all calculations. Mean monthly returns is the amountof money that we can expect from our system on a monthly basis. Market risk is the amount of money that can be lost on a trade on a dailybasis.Money managers use several different measures to monitormarket risk;• Mean range: Find the mean of the ranges over a previous 3 to 50days. Convert the mean to a dollar value. For example, if the meanrange in the Swiss Franc of the previous 10 days is 40 points andthe Swiss Francs are worth $12.50 a point, the dollar value of riskin equal to $500, The probable amount that the market will move isequal is the average range for the past x days. This isn't always thecase, but you need probabilities to build your allocation modelupon.• Mean change in closes: The mean change in closes over a previous3 to 50 days will be more representative of the risk since thisvalue will give the expected risk for holding a position.• Mean change in closes down vs. mean change in closes up: Themean change in down closes over a previous time period represents the risk associated with holding a long position.• Standard deviation of closes: The standard deviation of closesgives a more accurate picture of risk because it shows the amountof daily variability within a 68% confidence interval, This is amore involved calculation, but with today's computers this shouldnot pose a problem.However measured, risk is the most important variable to track andis the main component of the capital allocation model.Single Market PortfolioThe first step in the model is to come up with a system that has a positive expectation of returns. This system can trade stocks or futures, itreally doesn't matter. Before allocating capital we need to measuremean monthly return and market risk on a one contract basis. In addition, we need to know how much of our equity we want to risk on eachtrade. At this point, we don't know how much equity to risk becausethat is what we are searching for. However, we do know the boundariesof acceptability.
C = f(E,m,r)
MONEY MANAGEMENT
233
where C = Amount of capital to risk to achieve an acceptable risk/Reward ratioE = Iterative amounts of equity to risk on each trader = Current market riskm = Mean monthly returnIn this example, we will allocate capital to only one market and thenlater move to two markets. After we have tested our system on a onecontract basis, we need to measure E, m, and r at the beginning of a period (month, week, day). Let's say that our bond system made $6000over the past six months, therefore our mean monthly return would be$1000 ($6000/6 months):JanuaryFebruaryMarchAprilMayJuneTotal
$2000
-$1000-$1500$3000$2000S1500S6000m = S1000
We will use the 30-day average true range as our measure of marketrisk. For demonstration purposes, let's assume that the average truerange for the past 3D days is 36 points. Thirty-six bond points is theequivalent of $1125.r = $1125
Let's pretend that we are a money manager and we have $100,000 toplay with and we would like to achieve 20% return on this capital, butwe don't want to have an end-of-month draw down greater than 3%. Weknow the bounds of acceptability, but we have no idea of how muchmoney to risk on each individual trade. By looking at historical performance of our system and current risk in the market, we can create several different portfolios (or what if scenarios) by allocating differentlevels of equity to be risked on an individual trade basis. We will optimize our risk parameter to achieve an acceptable risk/reward ratio. Inthis example, our portfolio will simply consist of different lot sizes(number of contracts) of bonds.
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THE ULTIMATE TRADING GUIDE
TC = $100,000 (total capital)
E = Varying amounts of acceptable individual trade riskE = (TC * allowed risk per trade)$5000 at 5% ($100,000 * 5%)$4000 at 4%$3000 at 3%NUMC = Number of contractsNUMC = E / rPortfolio 1
E = (TC*5%) = $5000NUMC = $5000/$1125 = 4(can't have fractional parts)Portfolio 2E = (TC*4%) = $4000NUMC = $4000 / $1125 = 3PortfoliosE = (TC*3%) = $3000NUMC = $3000 / $1125 = 2
r = $1125
r = $1125r = $1125
Next measure the return on all available portfolios:
Portfolio 1Portfolio 2Portfolio 3
ROR = rate of returnROR = (mean monthly return * NUMC) / Total CapitalROR = ( m * NUMC)/TCROR = ($1000 * 4) / $100,000 = 4% = 48% yearlyROR = ($1000 * 3) / $100,000 = 3% = 36% yearlyROR = ($1000 * 2) / $100,000 = 2% = 34% yearly
Next measure the risk on all available portfolios by referring back toour monthly return values:
January
Return$2000
February
-$1000
MarchAprilMayJuneJuly 1st
-$1500S3000$2000$1500we are here at this point in time
MONEY MANAGEMENT
Portfolio 1January
NUMC = 4Return$8000
235
ROR = 48%Four Contract BasisAttained by multiplying Jan's performance by NUMC
February-S4000March-$6000April$12000May$8000June$6000Mean montly return = 4% standard deviation 7.26%68% of time: monthly returns will be between -3.26% and 11.26%Portfolio 2
NUMC = 3ROR = 36%ReturnThree Contract BasisJanuary$6000February -$3000March-$4600April$9000May$6000June$4500Mean montly return = 3% standard deviation 5.5%66% of time: monthly returns will be between -2.5% and 8.5%
Portfolio 3 NUMC = 2 ROR = 24%ReturnTwo Contract BasisJanuary$4000February-$2000March-$3000April$6000May$4000June$3000Mean montly return = 2% standard deviation 3.6%68% of time: monthly returns will be between -1.6% and 5.6%If you, as a money manager, had informed your clients that your goalwas to achieve 20% per year with at most a 3% end-of-month drawdown, then Portfolio 2 would be your choice:
236
THE ULTIMATE TRADING GUIDEC=f(E.m,r)
C = 4% of $100.000 or $4000 to risk on each trade.
Two-Market PortfolioWe will use the same allocation model and apply it to the same system,but this time we will trade the bonds and soybeans. Table 11.1 showsthe performance of the bonds and beans for the past six months.First step is to measure the current market volatility. We will usethe same measure of volatility as we did in the first, example of our capital allocation model (thirty-day average true range). The currentvolatility for the bonds is $1125 and $400 for the beans. The next step isto create a range of different portfolios that reflect different levels ofequity risk.Before we do this step, we should discuss the concept of normalization. The manner in which we calculate the number of contracts of acertain market incorporates the notion of normalization. Due to the factthat we are using a constant amount of equity to risk on each trade andthat we measure the amount of risk for each market, we trade more contracts of a less risky commodity than we do for one that involves morerisk. If we are risking $1000 per trade and the market risk for thebonds is $500, then we would trade two contracts of bonds. Now if werisk the same amount of money in the beans and the market risk forthis commodity is $250. then we would trade four contracts. We havenormalized the number of contracts from one market to another basedon risk. The normalization process allows us to compare apples to apples and oranges to oranges. We are trading the same units of risk forthe soybeans as we are for the bonds.Table 11.2 shows the different portfolios and their returns based ondifferent amounts of risk. Table 11.3 shows the risk in terms of standard
TAB1E 11.1
Performance of Bonds and Beans
Monthly Returns
Bonds ($)
Beans ($)
JanuaryFebruaryMarchAprilMayJune
2.000(1,000)(1,600)3,0002,0001.500
(200)
Mean monthly return (one contract basis)
1,000
125
200300
(450)700200
MONEY MANAGEMENTTABLE 11.2
237
Return for Different Portfolios
deviation of trading this different portfolios. Portfolio 1 would probably bethe choice of most money managers, due to its low standard deviation anddecent return.Now let's test a real system with this same capital allocation model.In this test, we will measure market risk on a daily basis and allocatecontracts for the following trade in the same manner as we demonstrated in the previous examples. We will wait until the next trade andchange the number of contracts if necessary. Realisation, time framesare up to the preference of the trader/manager. We haven't seen an advantage of reallocating on a smaller time frame than on a trade-bytrade basis. In our previous examples, we reallocated on a monthly basisto make things easier for demonstration purposes. As in our previousexamples, we will create three separate portfolios reflecting three different levels of individual trade risk. We tested the Donchian systemthat was explained in Chapter 9 on the Japanese Yen and U.S. bondswith our capital allocation model and $100,000 initial capital. Table11.4 shows the portfolios of bond and yen with their respective monthlyreturns and standard deviations. The optimal portfolio is the one thatfits within the trader's or money manager's realm of acceptability. Arisky money manager would have a different portfolio than one that ismore conservative. Which portfolio would you choose?A hundred thousand dollars is a lot of money, what if a trader onlyhad $20,000? Could a email trader apply these concepts to his trading.Definitely! That is the beauty of the capital allocation model—it thinksfirst in terms of risk and then in terms of reward. Let's test the samesystem on the same portfolio, but this time let's utilize $20,000 as ourtotal capital parameter. We could optimize risk parameters and create arange of different portfolios, but at this level of equity if we don't use atleast 5% of risk per trade, we won't get any trades. In addition, we willincorporate the old adage, "If you can't stand the heat, get out of thekitchen." If the market risk exceeds $1000, we will not take on any newtrades until the market cools down. This is another important reason to
TABLE 11.3
Risk for Different Portfolios1 Contract
JanuaryFebruaryMarchAprilMayJune
Bonds ($)
1 ContractBeans ($)
2,000(1.000)(1.500)3,0002,0001,500
(200)200300(450)700200
Total ($)
Return (%)
1,800
1.8
(800)(1.200)2,5502.7001,700Average return;Standard deviation:
-0.8-1.2
Total ($)
Return (%)
2.62.7
1.71.11.7
Average monthly return range: -0.6% to 2.8%Portfolio 1
4 ContractsBonds ($)
10 Contract!Beans ($)
JanuaryFebruaryMarchAprilMayJune
4.000(2,000)(3.000)6.0004,0003,000
(1,400)1,4002,100(3,150)4.9001,400
2,600(600)(900)2,8508.9004,400Average return:Standard deviation:
2.6-0.6
-0.92.98.94.42.93.6
Average monthly return range: -0.7% to 6.5%PortfolioJanuaryFebruaryMarchAprilMayJune
2
2 ContractsBonds ($)
7 ContractsBeans ($)
6,000(3,000)(4,500)9.0006,0004,500
(2,000)2,0003.000(4,500)7,0002,000
Total ($)
Return (%)
4,000(1,000)(1,500)4,50013.0006.000Average return:Standard deviation:
4.0-1.0-1.54.513.06.54.35.3
Total ($)
Return (%)
Average monthly return range: -1.1% to 9.6%Portfolio 3
4 ContractsBonds ($)
12 ContractsBeans ($)
JanuaryFebruaryMarch 'AprilMayJune
8,000(4,000)(6.000)12,0008.0006.000
(2,400)2,4003.600(6,400)8.4002,400
5,600(1,600)(2,400)6,60016,4008,400Average return:Standard deviation:Average monthly return range: -1.4% to 12.4%
5.6-1.6-2.46.616,48.45.56.9
MONEY MANAGEMENTTABLE 11.4
Portfolio 1Portfolio 2Portfolio 3
239
Results of One Allocation Model at Different Levels of RiskCapital toRiskon Each Trade (%)
Monthly AverageReturn (%)
Monthly StandardDeviation (%)
345
3.5
13.217,822.7
4.6
6.0
trade as many anticorrelated markets as possible. If one market heatsup, then capital can be transferred or redistributed to the markets thatare still trading at an acceptable risk level. Table 11.5 shows the performance of trading the bonds and yen on our Donchian system with$20,000 as our initial capital and our "get out of the kitchen" overlay. Wealso ran the same system on the same markets but on a one-contractbasis (Table 11.6).The capital allocation model increased profits by 49% and decreased overall maximum draw down by 6%. Does this happen to everysystem that the allocation model is applied to? No. Some systems don'treact in a positive manner to this model and this is why it is so important to develop trading systems in concert with money managementconcepts. Capital allocation models are as numerous as different trading systems
TABLE 11.5 Performance of Donchian-Based System Utilizing the CapitalAllocation ModelVARIABLE N U M B E R OF CONTRACTS PER TRADETEST PERIOD 1/l/83-8/31/99S75 ALLOWED FOR COMMISSION AND SLIPPAGE
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THE ULTIMATE TRADING GUIDE
TABLE 11.6 Performance of Donchian-Based System without the CapitalAllocation ModelONE CONTRACT PER MARKET PER TRADETEST PERIOD 1/1/83-8/31/99$75 ALLOWED FOR COMMISSION AND SLIPPAGE
COMPOUNDING RETURNSCompounding is the process of allocating capital based on current portfolio (or account) equity. Current portfolio equity takes into consideration past winning and losing trades and initial equity. Compounding isa great concept if there is a lot of money involved; it expands and contracts allocated capital based on current portfolio equity. If a tradingplan is successful, more money is allocated to each trade, whereas if atrading plan is in the pits, less money is allocated to each trade. Remember, we said that compounding is a great