that its total customer assets willbe very volatile. If the war ends, customer losses could be huge, and allat the same time. Completely unrelated investments are liquidated tocover losses in other markets. Those customers trading on margin maynot meet the calls for new money, placing the brokerage firm's capitalization at risk.This situation actually happened in early 1980, when silver and goldrallied to all-time highs. The publicity given to the Hunt's silver position was so extensive that the general public was heavily committed toholding long positions.Brokerage firms will deal with this by monitoring the aggregate customer positions. When a percentage of correlated holdings exceed a safelevel, they recommend other positions, raise the house margin levels,and generally try whatever is needed to get clients out of current, highrisk positions and add diversification. They save the clients and theyserve themselves.Institutions that hold large house trading positions have the same problem. What appears to be diversified under normal market conditions maynot provide the risk protection under extreme cases—and those are themost important. A sharp loss once every three to five years is just as badas high volatility in daily performance. For many risk situations, there isno statistical evaluation. It is simply necessary for someone to reason outwhat might happen under varying circumstances.Correlations and TimeThe correlation matrix of monthly returns in Table 4-3 shows how thechoice of time periods affects the measurement of similarity betweenassets or systems. Using only the past 10 years of data, the correlationsdrop significantly when monthly values replace annual data. Thosevalues already near zero may be slightly higher without contradictingthe principle. This phenomenon is not surprising. The annual, longterm relationship between interest rates and Producer Price Index maybe predictable, but month-to-month reactions can vary. If interest ratesoverreact to an anticipated increase in prices, then daily or monthly values may move somewhat apart, while the economic relationshipremains steady. As you reduce the time period, the smaller pricechanges become more important. Noise becomes a bigger factor in theoverall pattern, and the correlation drops.Using daily data to measure correlation is likely to give you ananswer near zero for most combinations. But results over a full yearcould be very similar, and a poor choice if you are looking for portfoliodiversification.
63
Risk and Return
Table 4-3. Correlation Matrices forAnnual and Monthly Returns(1983-1992)Correlation of Monthly Returns
S&P500
S&P500
Bonds
PPI
FX
CTA
1.00
0.12
0.03
0.01
0.00
1.00
0.03
0.03
0.02
1.00
0.00
0.00
1.00
0.00
BondsPPIFXCTA
1.00Correlation of Annual Returns
S&P500BondsPPI
S&P500
Bonds
PPI
FX
CTA
1.00
0.34
0.16
0.00
0.13
1.00
0.43
0.00
0.16
1.00
0.04
0.15
1.00
0.15
FXCTA
1.00
The two correlation matrices in Table 4-3 comparethe similarity in price movement of passive portfoliosof the S&P 500, Lehman Brothers Bond Index, theProducer Price Index, a Forex group, and the MARdollar-weighted Commodity Trading Advisor Index.The monthly figures show much smaller correlationsthan the annual returns. As shorter time periods areused for evaluation, the noise of short-term movement interferes with the direction of the long-termtrend. This makes the correlations seem lower, yetsevere, volatile moves may prove that many of thesemarkets move in the same direction.
Forecasting CorrelationsAnother essential step in evaluating diversification is to forecast the correlations. Markets change, and more so in these times of globalization. Worldequity markets are becoming interrelated. A severe drop in the Japanese,German, or U.S. stock markets is likely to cause similar drops in other markets, resulting in correlated performance. This tendency can be seen by calculating individual annual correlations (using monthly data) and lookingat the trend of r. If the correlation coefficient is moving toward +1, then youwill want to decrease the use of these markets for diversification.
64
How Changing Markets and Technology Affect Results
I
99%95%
68%•*
i-
•+
Losses
0
Average
*•
-
Profits
Figure 4 . 9 . Normal versus skewed distributions. The standarddeviation (sd) measurement assumes that trading profit and losseswill be distributed evenly around the average (at 0). But most systems have unique skewed patterns. The trades of a trend-followingsystem, shown by the "X" marks on the chart, have clustered lossesand a few very large profits. The normal distribution does not showthis correctly.
Skewed DistributionsThe standard deviation assumes that profits and losses fluctuate evenlyabove and below the equity trend, as seen in Figure 4-2, which shows evenly spaced parallel lines. That is not a realistic assumption. Many trendfollowing systems are skewed to show larger profits than losses, but morefrequent smaller losses. Then a typical profit/loss trend-following distribution will show a longer "tail" to the right, indicating larger profits, and thehighest point to the left of center and below zero, indicating that the mostfrequent trades are small losses. Figure 4-9 shows the "normal" distributioncurve on the same chart as the skewed trend performance.Frequency Distribution. A practical way to display trading performance is by using a frequency distribution, or "histogram." This looks thesame as a spreadsheet bar graph, except that the bars have differentwidths. For example, Figure 4-10 shows that each of the 10 bars represents
65
Risk and Return
Figure 4 - 1 0 . A frequency distribution of performance. The 10 uneven bars eachrepresent 10% of the trades. The highest 10% profits are spread out while the losses are clustered together. A small tall to the left represents larger losses due tounavoidable price gaps.
10 percent of the trades, when sorted from greatest loss to largest profit.The wide bar at the right indicates that there is a large variance betweenthe largest profits. The narrowest bar near the left shows that losses areclustered because of cutting losses short.By looking at the chart, we can say there is a 10 percent chance thatprofits on any one trade will be greater than 50 percent or less than —10percent. There is also a 20 percent chance that profits will be greaterthan 40 percent or less than -6 percent.Semivariance. A useful way of measuring risk for equity distributionsis with semivariance. This simply divides the equity into separate sets ofcontinuous profits and losses. For example, if a trading program had thefollowing sequence of profits and losses:2.5%, (1.0%), 4.1%, 3.5%, (.6%), (1.1%), (.7%), 1.5%it would be regrouped to show alternating, cumulative profits and losses:2.5%, (1.0%), 7.6%, (2.4%), 1.5%The losses can be evaluated separately, giving the probability of a drawdown based on sequences of trades, rather than the probability of a losson a single trade. This is a practical approach to evaluating risk.
66
How Changing Markets and Technology Affect Results
Risk of RuinAnother valuable measurement is risk of ruin. It is the chance of losingso much that you must stop trading. The formula that follows allows usto specify the maximum amount that we are willing to lose, constitutingruin. Before looking at the calculations, consider these premises:• In real trading, once profits accumulate, the chance of ruin decreases.The greatest risk is at the beginning.• If we plan to withdraw profits, thereby maintaining the same relativecommitment to the market, then the risk of ruin must be greater than ifwe accumulate profits and keep the trading position the same.The probability of risk of ruin is expressed as:Risk_of_Ruin = ((1 - Edge)/(1 + Edge))AUnits_Capitalwhere Edge = 2*Probability_of_Win - 1, the "trader's advantage"Units_Capital allows risk to be given relative to the size of theinvestmentExample 1. A typical trend-following system will have larger profitsthan losses and more losing trades than winning ones. IfProbability_of_Win = 40% andUnits_Capital = 1 for a $10,000 investmentRisk_of_Ruin = ((1 - .40)/(1 + .40))A1= (.60/1.40)A1= .42857 or 42.8%
If the investment is increased to $20,000, or 2 units of capital,Risk_of_Ruin = ((1 - .40)/(1+.40))A2
= (.60/1.40)A2= .18367 or 18.3%By doubling the investment, the risk of ruin decreases by 57 percent.
Profit GoalsTaking profits will reduce the risk of ruin. The closer the profit goal, theless chance of ruin:
67
Risk and Return
Risk_of_Ruin_2 = ((((1 + Edge)/(1 - Edge))*Goal) - 1)/(((1 + Edge)/(1 - Edge))A(Units_Capital + Goal) - 1)
where all the terms are the same as the previous calculation, except Goalis the profit objective in units of trading capital (profit objective dividedby one unit of trading capital).Example 2. If you traded the same trend-following system as example1, with a 2-unit investment, but had a profit goal of half of one capital unit(or $5,000), thenRisk_of_Ruin_2 = ((((1 + .40)/(1 - .40))A5) - 1)/(((1 + .40)/(1 - .40))*(2 + . 5 ) - 1 )= (((1.40/.60)A.5) - 1)/(((1.40/.60)A2.5) - 1)
= .5275/7.3165= .0721 or 7.21%Specifying Wins, Losses,and RiskTo be practical, a risk evaluation must use the performance profile of thesystem being traded. That includes the size of the profits and losses, aswell as the amount of risk the investor is willing to accept. The following formula, from Ralph Vince's Portfolio Management Formulas (NewYork: Wiley, 1990) is a summary of P. Griffin's work, The Theory ofBlackjack (Las Vegas: Gamblers Press, 1981) and a "fair approximation"of risk:Risk of Ruin = ((1 - P)/P)A(MaxRisk/A)where the following terms are defined asAvgWin is the average winning trade (e.g., $600)AvgLoss is the average losing trade (e.g., $200)Investment is the amount invested (e.g., $20,000)ProbWin is the probability (percentage) of a winning trade (e.g., .40)ProbLoss is the probability (percentage) of a losing trade (e.g., .60)MaxRisk is expressed in percent (e.g., 25% = .25)AvgWin% is @ABS(AvgWin/lnvestment)
68
How Changing Markets and Technology Affect Results
AvgLoss% is @ABS(Avgl_oss/lnvestmenf)Z is ProbWin*AvgWin% - ProbLoss*AvgLoss%A is (ProbWin*(AvgWin%)A2 + ProbLoss*(Avgl_oss%)A2)A( 1/2)Pis.5*(1+(Z/A))
Example 3.
Using the values given after the definitions, we get
AvgWin% = @ABS(600/20000) = .03AvgLoss% = @ABS(200/20000) = .01Z = .40*.03 - .60\01 = .012 - .006 = .006A = (.40*.03A2+.60*].01A2)*(1/2) = (.00036+.00006yX1/2) = .0605P = .5*(1+.006/.0605)) = .5495Risk_of_Ruin = ((1 - .5495)/.5495)A(.25/.0605)= .8198*4.132= .4408 or 44.1%
SummaryRisk is important, but it does not have to be complex. The simplest riskadjusted measure of trading performance is the return/risk ratio, whichallows a fair comparison of values that are determined during differenttime intervals. It only requires that you use the same measure of riskand reward for all the information being evaluated.Time periods can be deceptive. All time periods smooth performance,eliminating interim equity fluctuations that could have been large. Tooffset part of this problem, the maximum drawdown is needed, whichputs an absolute value on the expected loss. Over time, even the maximum loss will be replaced by a larger loss. The longer the tested history, the less likely it will occur, but inevitably, all programs see largerprofits and larger losses than those on record.Diversification is the best approach to risk reduction. Deciding howmuch safety is gained by combining assets has been a very mathematical process; however, a simple spreadsheet program now allows anyoneto combine performance history and evaluate the return/risk ratio ofthe proposed portfolios.
Risk and Return
69
Trading cannot be successful withou-t adding common sense.Changing volatility and fundamental relationships are seen faster by aperson than by a computer. Therefore, trading requires constant watching. Risks also change; assets and trading strategies that once offereddiversification can move together. It is not as important that they offersome risk reduction on a daily basis as it is that they do not mimic eachother during a price shock.
PART 2Using Old and NewTrading Tools to AchieveReasonable Objectives
5
Profit-Taking
Ask a trend follower, "How do you trade successfully?" The answerwill be, "Let your profits run and cut your losses short." That seems toexpress the underlying philosophy behind trend-following programs.One of the most stunning examples is gold, rising from $100/oz to peakat $850/oz in January 1980. There were good opportunities to take profits at $250/oz and $400/oz, but neither of these would have been closeto the profits that were possible if you had simply held a long-term position using nearly any trend-following method. In Figure 5-1 (a), the samepattern can be seen in silver; and Figure 5-1 (b) shows an S&P move inOctober 1987 that is difficult to forget.Large profits represent what "might have been" in one price move.This chapter will show that waiting for the exception is not as good as
PROFIT-TAKINGDisadvantages• Miss big profitsAdvantages• More frequent profitable trades• Less slippage closing out trades• Less slippage than reversing a trade (e.g., long to short)• Better reward/risk ratioWhen deciding to use profit-taking, the only disadvantage is the fear of"missing the big move." Instead, trading can be improved.
73
74
Using Old and New Trading Tools for Reasonable Objectives
(a)
Figure 5 - 1 . Exceptional market moves, (a) May 1980 Convex Silver, peakingon January 21, 1980. Exceptionally large trend-following profits could have beencaptured had you been able to exit near the top. By waiting, much of the profitwould have disappeared. The high volatility near the top may have also reducedthose returns due to slippage.
returning more frequent profits. Spectacular price moves do not occuroften enough to be worth sacrificing a good, everyday plan. In addition,the great risk associated with a major move requires a constant investment that is too big to be reasonable for the few times it will serve toprotect an infrequent occurrence.
A Test for Profit-TakingThis chapter will show that a simple rule for taking profits is better than waitinguntil the trend changes, which also means that profits will be taken beforethe "big" moves reach their peak. This will be done by testing a moving
Profit-Taking
75
Figure 5 - 1 . [Continued) Exceptional market moves, (b) The S&Pdrop of October 1987. Trend followers should have been short beforethe sharp drop, but the volatility of the following day would have madeit difficult to justify holding a trend position. Looking back, it is clearthat the trend was over on October 19. After that, a trend follower wasjust giving back profits waiting for a reversal.
average system with profit-taking measured as a percentage of price. Othermore complicated tests could look at different trading strategies as well asdifferent profit-taking measurements, some based on volatility. First it isimportant to see that the idea of taking profits is sound.How It Was TestedA simple exponential moving average system was tested using Telerate'sTeleTrac, and the results were compared and plotted using a spreadsheet.The formula for the trend was
76
Using Old and New Trading Tools for Reasonable Objectives
@exp_ma(price,period) = ema[1] + sc*(price - ema[1])
where @exp_ma is the exponential moving average function, saved asexpperiod is the number of days over which @exp_ma is calculatedema[1] is yesterday's exponential trend valueprice is today's closing pricesc is the smoothing constant, sc = 2/(period +1)Six trend speeds were tested: 5, 10, 15, 25, 50, and 75 days. This distribution was selected to even out the percentage changes between thetime periods in each test.The trading and profit-taking rules were:1. Buy on the close when the exponential moving average turns up; sellwhen it turns down.2. Close out the trade if the unrealized (open) profits, as of the closingprice, are greater than a preset profit level, PT = p x close, where pis a percentage. Exit the trade at the closing price of the day.3. Do not reset a trade in the same direction once profits have beentaken.If the daily high and low prices had been used, profits could havebeen taken at the moment the profit was reached, instead of at the close.This could have improved results for many trades. But in this basicapproach, all trades were exited at the close. If you use the interbankmarket, intraday data, or any 24-hour price stream, you will want totake profits as soon as they reach the target level. Here, we will onlylook at decisions made on the daily close of trading.Profit-Taking LevelsTo be certain that all levels of profit-taking were included in only a fewtests, profit levels began at 100 percent of the trade entry price, thenwere divided by 2 until performance deteriorated. Because prices neverdoubled, no profits were taken at the 100 percent level, and those resultswill be used as a control to measure improvement. Profit-taking levelswere:100%, 50%, 25%, 12.5%, 6.0%, 3.0%, 1.5%For the serious technician, this method is also convenient for comparing the frequency of profit-taking events with a normally distributedsample.
77
Profit-Taking
Measuring the ResultsAlthough many traders judge success by the size of profits, these testscompare profits with risk. The goal is to find the greatest returns for thelowest risk. Portfolio managers would recognize this as "risk-adjusted"returns, discussed in Chapter 4. A better risk-adjusted return can beconverted to higher profits simply by increasing the leverage, or reducing investment reserves, because of the lower relative risk. Expressingresults in this way also allows investors to judge clearly how much riskthey are willing to accept.In this example, normal commissions and slippage were applied totrades, but analysts must be careful to use realistic values for transactioncosts to get correct results for their own trading. Profits, losses, and riskare shown in points. Risk is measured as one standard deviation of thedaily accumulated profits and losses.The following three markets were tested:From
To
January 1988
February 1993
Deutsche Mark Index February 1988
February 1993
Hang Seng Index
Unilever
November 1987 November 1992
Coding the TestsThe TeleTrac code is shown in Box 5-1. This can also be done using aspreadsheet; however, it is important not to reenter a trade in the samedirection once a profit is taken. You can solve this problem by keepingone spreadsheet column for the underlying trend direction (e.g., +1 forlong and -1 for short), and another column to show whether that position is active (+1 if holding the trade, 0 if closed out using profit-taking).It is tricky, but it can be done. Strategy testing programs, such asOmega's TradeStation or TeleTrac make it much easier.
The ResultsThe raw values (in points) of the test results are shown in Table 5-1 (a)-(c).The trend speed is the far left column and the profit-taking level is givenalong the top. The profit and risk in the "100%" column represent thetrend system performance with no profit-taking. In each row of each ofthe three tables, there are tests that show increased profits; however,
78
Using Old and New Trading Tools for Reasonable Objectives
Box 5-1. TELERATE TeleTrac CODE (USINGTHE CLOSE ONLY)1 item2 date3 close4 speed5 exp6 buy7 sell8 buysell9 openbs10 ptlevel11 ptrule12 strategy13 realized14 openpl15 netpl16 risk17 ratio
"DMXData used is the D-mark"DATA(date,880201,930226,item)(indexed as a %)"DATA(close,item)40Speed of the moving averageExponential MA calculationExp_ma(close,speed)Buy signal ruleexp-exp[1 ]>0&exp[1 ]-exp[2]<0Sell signal ruleexp-exp[1]<0& exp[1]-exp[2]>0Trade strategy rulesTrade(buy,sell,sell,buy)Open trade profit or lossOpen_PL(buysell,close,0,0)Profit-taking level in %3.0Profit-taking ruleopenbs* 100/close>ptlevelTrade(buy,sell I ptrule.sell.buy I ptrule) Final strategy rulesClos_PL(strategy,close,0.001,0.001) Realized PL with trans costsOpen trade PL on new strategyOpen_PL(strategy,close,0,0)Net PLrealized + openplStd_dv(netpl,1200)Risk = 1200 day standard devReward/risk rationetpl/risk
The code shows the calculation for the exponential moving averageusing the "study" Exp_ma. The code first tests the simple trend changelogic without profit-taking and calculates the open-trade profit,openbs. It compares the open-trade profits with the profit-taking level,then creates a new buy-sell rule named strategy.If the high and low prices are used to take profits on longs and shorts,lines 11 and 12 are replaced by the following three lines:ptlong(openbs[1]+high-close[1])*100/close>ptlevelptshort (openbs[1 ]+close[1 ]-low)*100/close>ptlevelstrategy Trade(buy,sell I ptlong.sell.buy I ptshort)
these are also accompanied by increased risk. Table 5-2 presents the HangSeng results as the return/risk ratio, making it easy to see whether thecombination of risk and return gives better performance.Generalizing theProfit-Taking PatternsThe values for the Hang Seng Index given in Table 5-1 are plotted inFigure 5-2. The slowest trend (75 days) showed best performance at theprofit-taking level of 12.5 percent, the 50- and 25-day trends were best
70
Profit-TakingTable B - l . T e s t Resultsa. Hang Seng Results in PointsH A N G S E N G I N D E X , ]January 1,1988, to February 1 6 , 1 9 9 3 (in H a n g Seng points)MA
100%
50%
25%
12.5%
6%
3%
1.5%
Days Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
51015255075
11091221984744397524
46035833410526451298743
11091221984744397524
48656493436229911776907
118613351063861432442
44944846306926262181951
1010940657655423338
42843437210314361813328
1099710397335268175
3174186915651106341-33
770328319359257190
1652166613585969-256
325328244222258231
46035833410526451298743
b. Deutsche Mark Results in PercentDEUTCHE MARK IMM INDEX, February 1,1988, to February 26,1993 (in percent)100%MADays Profits Risk
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
51015255075
9.838.7923.4737.7639.6118.53
4.096.348.0412.0112.757.17
9.838.7923.4737.7639.6118.53
4.096.348.0412.0112.757.17
10.479.9626.7337.9250.2434.00
4.046.578.5911.9114.4910.42
5.7911.0026.5830.9326.005.87
4.637.369.499.978.002.98
10.8810.1525.9022.7921.591.80
4.987.589.908.687.352.35
9.838.7923.4737.7639.6118.53
4.096.348.0412.0112.757.17
50%
25%
12.5%
6%
1.5%
3%
Profits
Risk
c. Unilever Results in PointsUNILEVER, November 4,1987, to November 23,1992 (in points)100%MADays Profits Risk51015255075
240-1040-3420-3360-3620-10060
50%
25^53
6%
12.5%
3%
1.5%
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
Profits
Risk
24013871313 -1040-342016301149-3360967-36201190 -10060
13871313163011499671190
240-1040-3420-3360-3620-9710
13872401313-8901630 -24401149 -2010967-368 01190 -11560
13871313163011499431092
4 330300-2480-940-3260-8080
15761377164511078571313
6350353012006430310-2200
180112601214841366610
56204960101046402940-2600
141711081232676431921
at 6 percent, the 15-day was best at 3 percent, and the faster speeds werestill improving at 1.5 percent. Because slower trends allow larger profits to accumulate, it makes sense that profit-taking levels will also begreater. Fast trends need comparably smaller targets.The consistency of the results is also reassuring. We can have moreconfidence in a method that begins with a logical premise and is confirmed by testing.
80
Using Old and New Trading Tools for Reasonable Objectives
Table 5-2. Hang Seng Reward/Risk RatioBecause risk declines faster than profits, the reward/risk ratioImproves. By using leverage, a better ratio can be turned into higherprofits for lower risk.MA Days
100%
50%
Reward/Risk Ratio12.5%25%
51015255075
4.154.784.173.563.271.42
4.154.784.173.563.271.42
4.104.864.103.474.112.05
4.455.164.674.015.162.81
6%
3%
1.5%
3.904.845.304.296.761.87
4.125.704.913.081.330.17
5.085.085.570.270.27-1.11
Reasons for Profit-TakingThe following are strong arguments for profit-taking:• Profit-taking has smaller slippage