day. Thus, we should scale our trading down to have a daily standarddeviation of $1000. Essentially, we need to trade one-fifth as large as the size ofthe back-test that produced a daily standard deviation of $5000 per day.Readers should note that even small positions yield such volatility. Forexample, the current daily dollar volatility of one S&P 500 contract is over $3000.Despite the fact that this strategy is very profitable, our $10,000 capital base maynot be enough to trade a well-diversified portfolio of products. If we trade higherthan the optimal leverage, chances are it will harm results in the long run—notimprove them. Traders can see from this example why trading with small accountsis an almost certain way to end up with no money at all.As time passes, markets and strategies may become more or less volatile. Inaddition, our capital will increase with gains and decrease with losses. As a result,
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when calculating optimal volatility for our trading strategy, we must continuallyrecalculate and adjust the optimal dollar volatility statistic. While drastic changesare unlikely on a day-to-day basis, the optimal dollar volatility number is likely toshift considerably over months and years of trading.
THE PARADOX OF OPTIMAL LEVERAGEUnderstanding the benefits and perils of leverage can help investors and tradersalike. Investors can structure their stock and bond allocations more efficiently.Traders can determine their optimal risk tolerance.While the mathematics of this chapter may sound like we’ve created the perfect tool, unfortunately Vince’s optimal f, the Kelly criteria, and the optimal leverage concept we visited above are all tremendously flawed when applied to trading.For optimal leverage to be useful, the return and volatility of trading strategiesmust be known. If we know our expected return and risk with absolute certainty,then we can leverage our capital effectively.The problem arises from the fact that optimal leverage is calculated fromspecific assumptions of expected return and risk. If we use even $1 more leveragethan optimal on a portfolio, then we will actually be decreasing our median ending wealth while simultaneously taking more risk. If we use even $1 less leveragethan optimal, we will not achieve maximum ending wealth.For games with known expected return and risk such as blackjack, we knowthe edge and volatility of our bets. In such static games, optimal leverage calculations can be very helpful. But in a dynamic game such as the financial markets,we can never be certain of future expected returns and volatility despite knowinghow our strategies performed in the past. As a result, we can never be sure if we’reutilizing leverage effectively.This is why money management techniques such as the Kelly criteria or optimal f are actually a paradox. While we know optimal values of the past, we haveno certainty what will be optimal in the future. That is not to say these tools areuseless. In fact, they are very useful. Their most important use is to determine iftraders are trading larger than optimal leverage, in which case they should reducetheir trading size immediately. And if trading under optimal leverage, traders mustask themselves what the true average return and volatility of their strategy will bein the future. These questions are the true difficulties when crafting an effectivemoney management plan.Another problem is that the optimal leverage calculation assumes that everyinvestor and trader is attempting to maximize median wealth. But many academicresearchers have found that, on average, investors are more risk averse. The typicalinvestor picks reward-to-risk trade-offs that would be created by trading at only onehalf or one-third of the optimal leverage that would yield the highest median endingwealth. As it turns out, what is optimal for one person is excessive for another.
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CHAPTER
12
Solving the Trading PuzzleCreating, Testing, and Evaluating a New Trading Strategy
Now that we have the tools to create, test, and trade profitable trading strategies onstocks, futures, and relative value markets, let’s create a trading theory and then follow the process until we have a polished trading strategy.
CREATING THE STRATEGYFrom my experience in trading, it appears that large moves are often followed by threeto five days of follow-through. Buying the market after a big rise seems to lead toprofits, as does selling after large drops. But how should we measure these moves?The traditional volatility breakout method attempts to exploit this tendency bybuying markets after a large one day price gain and selling markets after a large oneday price loss. Is one day really enough data to define a trend, or do we need to lookat three to five days of market returns? Our new system will broaden the scope ofthe typical volatility breakout strategy by analyzing multiple period returns for generating buy and sell signals.I decided to look at volatility breakouts in a different light. In a typical volatilitybreakout system, longs are taken if today’s close is greater than:Price reference + num ⭈ volatility measurewhere price reference is usually yesterday’s close or today’s open, num is a positive number, volatility measure is either the standard deviation of closes, standard321
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deviation of returns, or average true range. But I believe it’s shortsighted to analyze one day returns for short term breakouts.What if the market makes two consecutive above-average price moves in thesame direction? Are those moves important?I believe they are. As a result, I search for all breakouts over multiple days’price movement to generate trading signals.Each day, evaluate for all values of x from 5 to 20:New volatility breakout logic:Buy if close – close of x days ago > num ⭈ SQRT(x) ⭈ standard deviation of pricechanges over the past 100 daysSell if close – close of x days ago < –1 ⭈ num ⭈ SQRT(x) ⭈ standard deviation ofprice changes over the past 100 daysEach trading day, I search for buy and sell signals by calculating signals fromthe rules above for all values of x from 5 to 20. We start by comparing the five-dayprice change with the standard deviation of price changes over the past 100 days.If the price change is greater than num times the standard deviation, we have apotential buy signal. If the price change is less than negative num times the standard deviation, we have a potential sell signal. After running the five-day pricechange through our model, we compare the six-day price change. After evaluatingthe six-day price change, we examine the seven-day price change, then the eightday price change, the nine-day price change, and so forth until we have comparedthe 20-day price change.In each case, we compare the price change to the product of multiplyingthree values: a constant num, the square root of the number of days in the pricechange, and the 100-day standard deviation of price changes. The num parameterwill determine the sensitivity of price moves that generate trading signals. Smallervalues will generate more frequent buy and sell signals, while larger values willgenerate relatively infrequent signals. From the normal distribution, we know thatroughly 95 percent of values will be contained within ±2 standard deviations. Ifwe require moves greater than two times the standard deviation, we should expecttrading signals roughly 5 percent of the time (or one out of every 20 days, approximately once a month).We can use the standard deviation to project price changes over multipledays. To accomplish this transformation, we need to multiply the standard deviation by the square root of the number of days in our new price change interval. Forexample, suppose the standard deviation of daily price changes is $1. We wouldexpect 68 percent of future one-day price changes to lie within ±$1, 95 percent tolie within ±$2, and 99 to lie within ±$3.We can make similar predictions aboutfuture two-day price changes by multiplying the standard deviation by the squareroot of 2. We would expect 68 percent of future two-day price changes to lie within±$1.41, 95 percent to lie within ±$2.83, and 99 percent to lie within ± $4.24. This
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method can be extended to predict any number of days’ price changes. The graphin Figure 12.1 depicts how our ±2 standard deviation confidence interval increaseswith the number of days’ returns into the future.It is possible to generate conflicting signals using this method as we look forsignals when running x between 5 and 20. For example, the five-day price changemight generate a long signal due to a recent rally. At the same time, a previoussharp decline might cause the 15-day price change to generate a sell signal. Inthese cases, the longer term signal always overrides the shorter term signal. Wewould take the short entry associated with the 15-day price change and ignore thelong entry associated with the five-day price change.In Figure 12.2, we can see signals of our new volatility breakout strategyapplied to Eurodollar futures. The signals utilize the new entry mechanism for theparameter num = 1.0. A quick, sharp sell-off in mid-October triggers a short entry.After a significant decline, a rally from the market’s bottom in late Decembercauses a long entry to be initiated in early January. The strategy stays with the longposition through the end of April.Our new volatility breakout strategy can probably be improved by adding anexit rule to signal when trades have run their course. So, in addition to the entryrules, we will exit long and short positions using a trailing stop. We’ll trail our best
Two Standard Deviation Confidence Intervals120
110
100
90
49
46
43
40
37
34
31
28
25
22
19
16
13
7
10
4
1
–2
–5
–8
–11
–14
–17
–20
80Days from Today
FIGURE
12.1
Two Standard Deviation Confidence Intervals. Note that the confidence intervals do not increase in a linearfashion with time. Instead, they increase at a rate proportional to the square root of time.
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FIGURE
12.2
New Trading Strategy Applied to Eurodollars. Both a short entry in mid-October and a long entry in early January produceprofits.
position profit by two times the 100-day standard deviation of price changes. Ifwe’re long and prices fall from the highest high seen during the trade by twice the100-day standard deviation of price returns, we’ll exit our long position. If we’reshort and prices rise from the lowest low seen during the trade by twice the 100day standard deviation of price returns, we’ll exit our short position. Using thistrailing exit will help ensure that we close losing trades early and that winningtrades will be closed with a profit before prices turn, leading to a losing trade.
TESTING THE NEW STRATEGYNow that the idea is quantified, we’ll move to the testing phase and evaluate theperformance of the strategy defined above on 19 futures markets. Our strategy isapplied only on market sectors that display a natural tendency to trend: currencies,interest rates, petroleum, grains, and softs (excluding cocoa and orange juice).Testing is performed on two versions of our new volatility breakout strategy.Version #1 includes only the entry mechanism. Version #2 adds the trailing stop tothe entry mechanism. We need to tweak our system to determine if the results are
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New Volatility Breakout StrategyEntry only
Net profit
Sharpe Ratio
K-ratio
Num = 1.0
$6,560,399
0.51
0.30
Num = 1.5
$7,454,859
0.57
0.23
Num = 2.0
$6,185,323
0.51
0.05
Entry plus trailing stop
Net profit
Sharpe Ratio
K-ratio
Num = 1.0
$8,741,153
0.74
0.42
Num = 1.5
$6,345,168
0.58
0.39
Num = 2.0
$4,390,501
0.51
0.17
FIGURE
12.3
Table of Net Profit, Sharpe Ratio, and K-ratio for New Volatility Breakout Strategies. Smaller values of thenum parameter coupled with the trailing stop produce the highest profitability.
stable across varying parameters. To test the stability of the num parameter of ourstrategy, we run the profitability tests by varying num from 1 to 2, in incrementsof 0.5. The corresponding net profit, Sharpe ratio, and K-ratio of all versions andparameter sets are noted in Figure 12.3.The results elucidate much about our strategy. First, by adding the trailingexit, we increase reward to risk measures such as the Sharpe ratio and K-ratio.While net profit is sacrificed for two of the three values of num, the benefit is lessrisk. Second, it appears that smaller values of num outperform larger values ofnum. We conclude that our strategy is robust across parameters and that performance is likely to remain profitable in the future.Our next decision is whether we should combine multiple versions of thestrategy with multiple parameter sets to achieve improved reward-to-risk frombenefits of diversification. Because the signals from the two versions of this strategy are so highly correlated, we choose to skip combining multiple strategy versions together. Instead, we will trade the new volatility breakout entry with thetrailing stop and num parameter of 1.0. Figures 12.4a and 12.4b details the performance of our new volatility breakout strategy.
DETERMINING OPTIMAL LEVERAGEThe equity curve in Figure 12.4a highlights the performance of our new strategyfor selected futures markets. We earn $8,741,153 over 145 months, for an average of $60,284 per month. Our monthly volatility of returns, calculated by takingthe standard deviation of monthly profit and loss numbers from the performanceback-test, is $282,620. Using the optimal leverage formula from Chapter 11, wedetermine the optimal volatility for a hypothetical $100,000 portfolio:
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Avg.BarsWin1816181819211820
Avg.BarsLoss56566555
–17,936–18,943–16,996–18,663–20,082–18,144
181718191918
656565
–18,485
19
7
–18,923–17,295–18,725–17,449
20161817
5675
Net Profit:Drawdown:K-ratio:
Jan-01
Dec-01
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-90
0–2,000,000
Jan-92
6,000,0004,000,0002,000,000
Jan-91
Equity
Avg.Loss–17,258–17,772–18,958–17,057–18,760–21,188–18,369–17,986
Jan-00
Trading Strategy Evaluation (Futures)Strategy Name: New volatility breakout strategyParameters:Num = 1.0, trail best position profit by 2 sigmas of 100 price changesDescription:Enter when 5 to 20 day return greater or less than Num sigmas, 2 sigma trailing exitRun Dates:1/1/1990 – 12/31/2001#Avg.Sharpeof%Avg.ProfitAvg.Market Net Profit K-ratio Ratio Max DD Trades Win Contracts Per Con. WinFXAD179,4200.01 0.10 –618,070 257 3721.363231,301BP–124,375 –0.08 –0.06 –769,925 254 3614.31–3630,380CD852,8600.24 0.41 –265,090 244 4335.899833,814JY547,5130.17 0.29 –276,250 252 3610.8116335,047SF–599,700 –0.10 –0.31 –657,463 254 2913.68–16537,866RatesED1,858,175 0.23 0.80 –345,800 205 4368.0613248,385TY337,3600.12 0.16 –235,312 268 3723.075634,825US490,9060.17 0.26 –225,031 240 3817.0912135,472StockSPMetalsGCHGPLSLEnergyCL701,1200.14 0.36 –395,470 244 3922.4013036,192HO253,7810.05 0.12 –625,216 247 3819.335533,068HU546,6720.10 0.25 –368,189 256 3718.0311835,072GrainsC353,0500.12 0.17 –379,513 251 3561.152239,030S–289,838 –0.13 –0.16 –668,063 235 3626.19–4831,978W377,3250.14 0.18 –402,050 259 3744.233434,322MeatsFCLCLHPBSoftsCCCT189,9350.01 0.09 –626,855 230 3420.854037,739JOKC886,3160.15 0.41 –391,144 220 3910.8637139,790LB2,075,208 0.16 0.77 –272,816 273 4022.7833745,806SB105,425 –0.03 0.06 –663,623 219 3743.581233,283Average 460,0610.08 0.20 –430,836 232 3525.987734,38810,000,0008,000,000
Portfolio Statistics8,741,153Sharpe ratio:–1,141,172Correlation to breakout:0.42Correlation to 10-40 MA:
0.740.630.54
© 2002 Lars Kestner – All Rights Reserved
FIGURES
12.4a
Performance of Final New Volatility Breakout Strategy. The new Volatility Breakout Strategy produced profits in all 12 yearsof our back-test.
327
12.4b
AverageAverageMax DD Num Trades–517,360252–201,536178#DIV/0!#DIV/0!#DIV/0!#DIV/0!–462,958249248–483,208#DIV/0!#DIV/0!–488,609236
19911992
1993
1994
K-ratio0.220.130.280.220.620.14
1995Year
1996
1997
Sharpe Ratio0.361.190.490.272.010.12
Average Avg. Profit% Win Per Contract36182977#DIV/0!#DIV/0!#DIV/0!#DIV/0!38101363#DIV/0!#DIV/0!37190
Net Profit by Year
Performance Breakdown by YearYearNet ProfitK-ratio Sharpe Ratio499,97319960.410.991,024,74119970.170.73559,70919980.100.15433,14719990.070.8520002,394,993–0.070.222001143,2560.151.16
AverageSharpe Ratio0.090.31#DIV/0!#DIV/0!0.240.06#DIV/0!0.33
AverageLoss–17,961–14,386#DIV/0!#DIV/0!–17,958–18,963#DIV/0!–18,357
Avg. Bars Avg. BarsLossWin186154#DIV/0!#DIV/0!#DIV/0!#DIV/0!186195#DIV/0!#DIV/0!186
1998
2000
2001© 2002 Lars Kestner – All Rights Reserved
1999
Num. ofNumber of Profitable PercentLength Windows Windows Profitable1448055.56%1 Month1428861.97%3 Months13910374.10%6 Months12493.23%12 Months13312712296.06%18 Months121121100.00%24 Months
AverageWin33,68129,670#DIV/0!#DIV/0!34,77735,110#DIV/0!39,155
Performance of Final New Volatility Breakout Strategy. The new Volatility Breakout Strategy produced profits in all 12 years of our back-test.
FIGURES
0
500,000
1,000,000
1,500,000
2,000,000
1990
Net Profit944,797795,198139,256732,121144,832916,671
2,500,000
Breakdown Statistics (Futures)New volatility breakout strategyNum = 1.0, trail best position profit by 2 sigmas of 100 price changesEnter when 5 to 20 day return greater or less than Num sigmas, 2 sigma trailing exit1/1/1990 – 12/31/2001Breakdown by Market Sector
Average AverageNet Profit K-ratio171,1440.05671,6100.13#DIV/0! #DIV/0!#DIV/0! #DIV/0!500,5240.10146,8460.04#DIV/0!#DIV/0!814,2210.07
3,000,000
Year199019911992199319941995
MarketSectorFXRatesStockMetalsEnergyGrainsMeatsSofts
System Name:Parameters:Description:Run Dates:
Net Profit
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Optimal dollar volatility = capital ⭈ average dollar return/dollar volatilityOptimal dollar volatility = $100,000 ⭈ $60,284/$282,620 = $21,330Our calculations suggest the optimal dollar volatility is $21,330 per monthwhile our back-test above produces monthly volatility of $282,620. Based on thesecalculations, we need to scale down our position size by trading only 7.5 percentas much (approximately one-thirteenth) as the size that generated the profit andloss figure in our back-test. Remember, the number of contracts traded on anyentry is based on dividing $10,000 by the 100-day standard deviation of dollarprice changes. If using the $10,000 input results in monthly volatility of $282,620per month for our portfolio of futures in this strategy, then to create our desiredleverage when trading $100,000 we multiply $10,000(7.5%) = $750. Thus, for a$100,000 trading account, we should trade the following number of contracts eachtrade to maximize our median wealth:Contracts to trade = $750/100 day standard deviation of dollar price changesNow comes the hard part. We know that the values above are optimal usinghistorical profit and loss performance data. What about going forward?I will arbitrarily cut the optimal leverage in half, just as a cushion for whatmay lie ahead.Adjusted new strategy contracts/shares to trade = $375/100-day standarddeviation of dollar price changesIf we trade using a numerator of $375 for determining position size, we canexpect ($60,284)(7.5%)/2 = $2261 return per month, with monthly volatility of($282,620)(7.5%)/2 = $10,598 as we trade our strategy going forward. Real-timenumbers that deviate far from these benchmarks should trigger caution. Whentrading in real time, large deviations away from results seen in historical testingwould suggest that we have either made a mistake in our calculations or the strategy is deteriorating in live trading. Either situation can be disastrous for traders.
In Conclusion
Traders are the new alchemists. Our job is to predict the unpredictable. Day afterday we attempt to turn lead into gold. When we fail to predict the unpredictable, westress and we worry. After all, the near impossible task of forecasting financial markets is our job.If readers retain one idea after reading this book, it should be that practicallyeverything can be analyzed with numbers. Integers and digits make the world goround—not only in markets, but in every facet of life. Rarely does a situation present itself where quantitative analysis cannot help explain an event or predict anoutcome. Numbers may not explain everything, but when analyzing financial data,this analysis can lead to trading success. Hopefully, the contents of this book haveconvinced you not to take anything at face value—certainly nothing that can be tested or solved mathematically.We’ve examined trading stocks, financial futures, metals, meats, grains, petroleum products, cotton, cocoa, sugar, currencies, interest rate term structures, creditspreads, volatility, and even the relationship between stocks and commodities. Iftrading cheddar cheese futures becomes the next hot market, I will be there to analyze it and trade it using the exact same approaches I described in this book. Thereinlies the beauty of quantitative trading: the portability of strategies and methods.My years of experience have taught me that nothing in trading comes easy.There will always be profits, but you have to work hard to stay ahead of others.Growing up in Louisiana, I had a tennis coach who made us work on our physicalconditioning, often spending over 20 minutes at the end of the day sprinting aroundthe court. We all hated this workout and sometimes questioned its merits. I vividlyrecall his screams, “You know what they are doing in New Orleans right now? Theyare doing sprints! If you want to beat them, then you have got to outwork them!”
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In Conclusion
He was right. In every profession, sport, and academic discipline, people areworking to improve themselves. They’re becoming faster, stronger, and smarter asevery day goes by. Heed these works of advice—if you want to beat your competitors, you need to outwork them.I want to leave readers with one thought. In The General Theory of Employment,Interest, and Money, John Maynard Keynes writes:Worldly wisdom teaches us that it is better for reputations to fail conventionally than to succeed unconventionally.
Keynes suggests that those who succeed are more likely to do so unconventionally. However, those who choose the path of unconventional methods will havetheir success dismissed by others as chance and will be disparaged in their defeat.I urge anyone attempting to thrive in such an inclement endeavor as trading to follow Keynes’s advice. Think for yourself and travel on paths never journeyedbefore. I hope that trading success will bring you personal satisfaction and thatyour failures will cause you to rise and try again.Best wishes and good trading.
References
Chapter 1: Introduction to Quantitative TradingAndreassen, Paul. 1988. Explaining the Price-Volume Relationship. Organizational Behavior andHuman Decision Processes 41: 371–389.Arnold, Curtis. 1995. Curtis Arnold’s PPS Trading System. McGraw Hill.Black, Fischer, and Myron Scholes. 1973. The Pricing of Options and Corporate Liabilities. Journalof Political Economy 81: 637–654.Blume, Marshall, Jeremy Siegel, and Dan Rottenberg. 1993. Revolution on Wall Street. W. W. Norton& Company.Bulkowski, Thomas. 2000. Encyclopedia of Chart Patterns. John Wiley & Sons.Burke, Gibbons. 1993. Tom DeMark: Technical Guru Breaks Out to the Upside. Futures, Sept. 1993,34–40.DeBondt, Werner, and Richard Thaler. 1985. Does the Stock Market Overreact? Journal of Finance40: 793–807.DeMark, Thomas. 1994. The New Science of Techn