Hi everyone. I've collected and tried to summarize my understanding of acrary's posts on how to combine strategies. I will post my summarized understanding here and include as an attachment the file with the original collection of posts. The collection file is very messy and randomly organized and contains much more than just his strategy management posts. I'm not planning on spending anytime on organizing it more than this - so it's given "as is" and without links to the actual posts. Please feel free to correct any mistakes I make or misunderstandings I have and I'll try to edit them into the summary. I'll attach the summary to the next post as a text file as well.
0) Definitions Expectation of a trade = (PW * AW) - (PL * AL) Expectation of profit factor = (PW * AW) / (PL * AL) where PW = probability of a winning trade AW = average size of winning trade PL = probability of a loss AL = average size of a loss 1) Goal is Consistently Positive Results for any given Time Frame (e.g. monthly) a) This is mainly determined by Profit Factor and N Trades Baseline report of profit factor versus # of trades to achieve profitability after the number of trades Number of Trades PF 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 1.40 61.8 67.0 70.8 73.7 76.3 78.3 80.1 81.8 83.2 84.6 85.4 86.7 87.5 88.6 89.4 90.1 90.7 91.5 91.9 92.7 93.1 93.5 93.9 94.4 1.42 62.0 67.7 71.8 74.5 77.2 79.1 80.9 82.6 84.0 85.6 86.8 87.6 88.8 89.4 90.3 91.2 91.7 92.3 92.8 93.4 93.7 94.2 94.7 95.1 1.44 62.7 68.3 72.3 75.2 78.0 80.3 82.1 83.6 85.0 86.3 87.5 88.8 89.4 90.3 91.1 92.0 92.5 93.1 93.7 94.1 94.4 94.9 95.3 95.7 1.46 63.1 69.1 72.8 76.1 78.9 81.0 83.0 84.4 86.0 87.1 88.4 89.4 90.3 91.2 91.8 92.6 93.2 93.8 94.3 94.7 95.1 95.6 95.9 96.3 1.48 63.3 69.5 73.9 76.9 79.5 81.8 83.6 85.3 86.9 88.2 89.1 90.1 91.1 92.0 92.6 93.3 93.9 94.3 94.9 95.4 95.7 96.0 96.4 96.7 1.50 63.9 69.9 74.5 77.6 80.3 82.5 84.5 86.3 87.5 88.8 90.1 91.1 91.9 92.6 93.3 93.9 94.5 94.9 95.6 95.8 96.2 96.5 96.8 97.1 1.52 64.4 70.7 74.9 78.7 81.2 83.5 85.3 86.9 88.3 89.7 90.6 91.6 92.4 93.3 93.9 94.4 95.1 95.5 95.9 96.3 96.6 96.9 97.4 97.5 1.54 64.9 71.1 75.6 79.2 82.0 84.3 86.0 87.8 89.0 90.3 91.4 92.3 93.1 93.8 94.4 95.0 95.4 96.0 96.2 96.7 97.1 97.2 97.6 97.8 1.56 65.2 71.8 76.0 79.9 82.4 85.0 86.9 88.2 89.7 91.0 91.9 92.9 93.6 94.3 95.1 95.5 96.0 96.4 96.7 97.1 97.4 97.7 97.9 98.1 1.58 65.3 72.2 77.1 80.5 83.1 85.5 87.4 89.1 90.3 91.6 92.4 93.5 94.1 94.9 95.5 95.9 96.4 96.8 97.1 97.4 97.7 98.0 98.2 98.3 1.60 65.9 73.2 77.4 81.0 83.9 86.3 88.0 89.7 90.9 92.0 92.9 93.8 94.5 95.2 95.8 96.3 96.6 97.1 97.4 97.7 97.9 98.2 98.4 98.6 1.62 66.5 73.4 78.2 81.5 84.5 86.8 88.7 90.1 91.4 92.6 93.6 94.4 95.1 95.7 96.2 96.7 97.0 97.4 97.8 98.0 98.2 98.4 98.6 98.8 1.64 66.8 74.0 78.5 82.3 85.1 87.5 89.2 90.7 92.0 93.1 94.0 94.8 95.4 96.1 96.5 96.8 97.3 97.7 98.0 98.3 98.5 98.6 98.8 98.9 1.66 67.0 74.4 79.3 82.9 85.5 87.9 89.8 91.0 92.5 93.7 94.5 95.3 95.9 96.4 97.0 97.2 97.6 97.9 98.2 98.4 98.7 98.8 99.0 99.1 1.68 67.3 74.8 79.7 83.5 86.3 88.4 90.3 91.7 92.8 93.9 94.8 95.6 96.2 96.7 97.1 97.6 97.9 98.1 98.4 98.6 98.8 98.9 99.0 99.2 1.70 68.1 75.5 80.6 83.9 86.7 88.9 90.8 92.1 93.3 94.4 95.3 95.8 96.6 97.0 97.4 97.8 98.1 98.4 98.6 98.7 98.9 99.1 99.2 99.3 1.72 68.3 75.9 80.8 84.3 87.2 89.4 91.0 92.5 93.8 94.7 95.6 96.2 96.8 97.3 97.7 98.1 98.3 98.5 98.7 98.9 99.1 99.2 99.3 99.4 1.74 68.8 76.4 81.3 84.9 87.7 89.9 91.6 93.0 94.1 95.0 95.8 96.6 97.1 97.5 97.9 98.2 98.4 98.7 98.8 99.1 99.2 99.3 99.4 99.5 1.76 68.9 76.9 81.6 85.6 88.0 90.1 92.0 93.4 94.4 95.5 96.2 96.8 97.2 97.6 98.1 98.4 98.6 98.8 99.0 99.2 99.3 99.4 99.5 99.5 1.78 69.0 77.2 82.4 85.9 88.6 90.8 92.3 93.7 94.8 95.7 96.5 97.0 97.4 97.9 98.2 98.5 98.8 99.0 99.1 99.3 99.4 99.5 99.6 99.7 1.80 69.5 77.6 82.4 86.3 88.9 91.2 92.7 94.1 95.2 96.0 96.7 97.1 97.8 98.1 98.4 98.7 98.9 99.1 99.3 99.3 99.5 99.6 99.6 99.7 1.82 70.0 78.0 83.0 86.7 89.3 91.3 93.1 94.3 95.4 96.2 97.0 97.4 98.0 98.3 98.5 98.8 99.0 99.2 99.3 99.4 99.5 99.6 99.6 99.7 1.84 70.0 78.2 83.4 87.2 89.8 91.9 93.4 94.7 95.6 96.5 97.2 97.6 98.1 98.4 98.7 98.9 99.1 99.3 99.4 99.5 99.6 99.6 99.7 99.7 1.86 70.5 78.9 83.9 87.5 90.2 92.2 93.9 95.1 95.9 96.7 97.3 97.9 98.3 98.6 98.8 99.0 99.3 99.3 99.5 99.6 99.7 99.7 99.8 99.8 1.88 70.7 79.2 84.3 87.9 90.5 92.4 94.1 95.3 96.1 97.0 97.5 98.1 98.4 98.6 98.9 99.1 99.3 99.4 99.5 99.6 99.7 99.8 99.8 99.8 1.90 70.9 79.4 84.6 88.2 90.9 92.9 94.3 95.5 96.4 97.2 97.7 98.2 98.5 98.8 99.1 99.2 99.3 99.5 99.5 99.7 99.8 99.8 99.8 99.8 1.92 71.4 79.8 85.2 88.5 91.4 93.1 94.7 95.8 96.6 97.2 97.9 98.3 98.7 98.9 99.1 99.3 99.5 99.5 99.6 99.7 99.8 99.8 99.8 99.9 1.94 71.7 80.3 85.5 88.9 91.6 93.4 94.9 95.9 96.9 97.5 98.0 98.5 98.8 99.0 99.2 99.4 99.4 99.6 99.7 99.7 99.8 99.8 99.9 99.9 1.96 72.0 80.6 85.8 89.4 91.9 93.7 95.2 96.3 97.1 97.8 98.2 98.5 98.9 99.1 99.3 99.4 99.6 99.6 99.7 99.8 99.8 99.9 99.9 99.9 1.98 72.5 80.8 86.1 89.4 92.0 94.1 95.4 96.4 97.1 97.9 98.3 98.6 99.0 99.2 99.3 99.5 99.6 99.7 99.8 99.8 99.8 99.9 99.9 99.9 2.00 72.3 81.1 86.4 89.9 92.5 94.2 95.8 96.6 97.4 97.9 98.4 98.8 99.1 99.2 99.4 99.5 99.6 99.7 99.8 99.8 99.9 99.9 99.9 99.9 2.02 72.7 81.5 86.4 90.2 92.8 94.5 95.8 96.7 97.5 98.0 98.6 98.9 99.1 99.3 99.4 99.6 99.7 99.8 99.8 99.8 99.9 99.9 99.9 99.9 2.04 73.2 81.8 87.1 90.4 92.9 94.7 96.1 97.0 97.7 98.2 98.7 99.0 99.2 99.4 99.5 99.6 99.7 99.8 99.8 99.9 99.9 99.9 99.9 99.9 2.06 73.3 82.0 87.4 90.8 93.3 95.0 96.2 97.2 97.9 98.4 98.7 99.0 99.2 99.4 99.5 99.7 99.7 99.8 99.9 99.9 99.9 99.9 99.9 99.9 2.08 73.3 82.5 87.7 91.2 93.6 95.1 96.4 97.4 98.0 98.4 98.8 99.2 99.3 99.5 99.6 99.7 99.8 99.8 99.9 99.9 99.9 99.9 99.9 99.9 2.10 73.9 82.5 88.1 91.4 93.7 95.4 96.5 97.4 98.0 98.5 98.9 99.2 99.4 99.5 99.7 99.7 99.8 99.9 99.9 99.9 99.9 99.9 99.9 99.9 2.12 73.9 83.1 88.2 91.8 94.1 95.6 96.8 97.6 98.2 98.6 98.9 99.2 99.4 99.6 99.7 99.7 99.8 99.8 99.9 99.9 99.9 99.9 99.9 99.9 2.14 74.3 83.2 88.7 91.8 94.1 95.8 96.9 97.7 98.2 98.7 99.0 99.3 99.5 99.6 99.7 99.8 99.8 99.9 99.9 99.9 99.9 99.9 99.9 99.9 2.16 74.4 83.8 88.6 92.1 94.4 96.0 97.1 97.8 98.4 98.8 99.1 99.3 99.5 99.6 99.7 99.8 99.8 99.9 99.9 99.9 99.9 99.9 99.9 99.9 2.18 74.6 83.9 88.9 92.4 94.5 96.1 97.2 97.8 98.5 98.9 99.2 99.4 99.5 99.7 99.7 99.8 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 2.20 74.8 84.1 89.1 92.6 94.8 96.2 97.3 98.0 98.5 98.9 99.3 99.5 99.6 99.7 99.8 99.8 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 "It's just a Monte Carlo sim using 100,000 passes per table entry and plugging in the profit factor as a multiplier for the winning trades. Sum the winners and losers until you've reached the number of trades in the pass. Then see if the pass is a winner or loser. The percentage in the table is the number of winners in relation to the 100,000 passes." 2) Determine Modified Sharpe Ratio (EV/STD) for each Strategy "The modified sharpe ratio can be thought of as a z score. The higher the number, the closer we are to achieving consistent profitability. In my case I want to be 99% sure of making a profit each month. So if I were to look it up in a normal distribution table I'd know the Z score I need is approx. 2.58 or a modified sharpe ratio of 2.58." 3) Use Brute-Force to determine the optimal ratios of the strategies in the portfolio that will maximize the portfolio Sharpe ratio. "In the end what I found I had to do was develop a program to do all these passes. It weighs each model from 1 - 100 units and determines the optimal modified sharpe ratio. Then it determines the ratio between each of the methods to determine how much of each should be traded. If I have 4 models it'll do tests on all four of them, five, six, 10, 50, etc... In the end it gives me the optimal balance for the best modified sharpe ratio. For my trading I had to use 8 very good models to get the number up to 2.58 so that's why I trade against 8 models."
4) Determine position size based on normalized volatility levels. "For daytrading I just calculate the range (high - low), then average it for the past ten days. I use ten because I want my model to cut back on size pretty quickly if the volatility jumps. Then I divide the highest historical 10 day volatility (approx. 48 pts.) by the current volatility (ex. 8 pts) to come up with a multiplier (ex. 6). The model would then apply 6 contracts for the next trade. This is not the final size used to trade... By doing so, I can see if the same level of opportunites persist from period to period." 5) Determine Max Drawdown and Use MOnte-Carlo Analysis to determine Minimum Required Capital "M = Min. Required Capital A = Average loss P = Per-cent risk DD = Drawdown to recover at 95% of Monte Carlo Sims in decimal ex. .2 = 20% M = (A/P) * (1/(1-DD)) A = average loss of 1,000 P = 1% risk per-trade DD = 19% drawdown at 95% level I use the 95% level as a cutoff because I'd stop trading a system at that point." 6) Determine rolling correlation between strategies. Determine likelihood of correlations being accurate by looking at the standard deviation of the correlations. "Notice in the two model result there is a 12 month rolling correlation. To do this I use a minimum of 48 months of results. The rolling correlation starts after the first 12 months and then keeps figuring them for each month until the end of the data. The total of all the rolling months is then divided by the number of months tested. The number in the report is the average correlation. I also figure the standard deviation of the correlation for each two model pair and add/subtract it from the average to figure out how stable the correlation is." "In a practical sense what I'm interested in is the average correlation + 1 std. dev. being below .5. I have a program around here somewhere where I processed trades at different correlations and found that below +.5, it's better to trade separately. Above +.5 it's better to save the better model and either combine the second model with it or discard it if it can't be integrated." 7) If you are using fixed percent trades, you can lower the drawdowns by decreasing the percent at risk. "Notice how every time I hit the performance goal I reduce the risk per-trade. This is done to lower the expected drawdown. In testing I've found if you use fixed % risk per-trade the best way to lower the drawdown is to lower the average losing trade. At this level the only tool is the % risked." 8) Determine the Minimum Capital Required for the combined system (see 5) 9) Adjust the trading values by the Free Money Ratio to use the entire account and increase the percent return while reducing the percent drawdown. "I call this the free money ratio. If you noticed on the minimum capital required to trade the 5 systems it only amounted to about $187,000. Since the account had $500,000 all the extra money isn't really working very hard. (The initial return was 75.3% and the DD was -7.1%) The free money ratio is: FR = account funding / minimum capital required in this case: FR = 500,000 / 187,000 FR = 2.673 To use this you multiply the original projected drawdown @95% confidence by the FR to come up with a new target drawdown. In this case the 95% drawdown was 7.6% * 2.673 = 20.31% Using this new drawdown target we re-run the mmgt report using a larger risk amount until it's close to the new target. We also use only the min. account required for the initial capital. In this case I upped the risk per-trade to .75% and set the initial capital to $187,000. You can see from the report the 95% drawdown level is 18.2% so I could have upped the risk per-trade a little more. What we're doing is saying of the original 500,000 most of it (313,000) is not going to be actively traded. Because of this it will have no risk and no return. The rest will be actively traded at the free money ratio. The return at the higher risk is 287.2% on the $187,000. While the drawdown at the 95% level is 18.2%. We then convert the %'s into dollar returns. Return = 187,000 * 2.872 = 537,064 expected profit Risk = 187,000 * .182 = 34,034 expected max dd at 95% confidence we then use the return and risk with the total account return = 537,064 / 500,000 = 1.074 or 107.4% expected return risk = 34,034 / 500,000 = .068 or 6.8% expected drawdown @ 95% As you can see by doing this the return was boosted and the drawdown reduced. You can do this everytime the account hits a new equity high and compound the return to much higher levels. This works because returns do not grow at a linear rate."
10) Example Outputs from Programs a) Model Allocation Program "Model 1 - ES/Model131 Model 2 - ES/Model122 Model 3 - NQ/Model131 Model 4 - ES/Model111 Model 5 - ES/Prod8 Test period from 07/01/01 to 08/31/05 Single Model Results Modified Model # Sharpe Weighting ------- --------- --------- 1 0.7600 1.00 2 0.5454 5.80 3 0.4326 6.20 4 0.4718 3.80 5 1.0326 1.00 Two Model Results Modified 12 Month +1 -1 Model # Sharpe Weighting Roll Cor. Std. Dev. Std. Dev. Std. Dev. ------- --------- ------------- --------- --------- --------- --------- 1 2 1.0291 3.00 1.00 -.1753 0.1655 -.0098 -.3408 1 3 0.8279 4.60 1.00 0.1220 0.1982 0.3202 -.0763 1 4 0.8986 1.00 1.00 0.0240 0.2425 0.2665 -.2186 1 5 1.2977 1.00 1.00 0.0324 0.3168 0.3493 -.2844 2 3 0.7195 1.40 1.00 0.0014 0.3238 0.3251 -.3224 2 4 0.6295 1.00 1.00 0.1073 0.2491 0.3563 -.1418 2 5 0.8160 1.00 1.00 0.1372 0.2475 0.3847 -.1104 3 4 0.5235 1.00 1.00 0.1010 0.2520 0.3530 -.1510 3 5 0.7669 1.00 1.00 -.2054 0.2267 0.0213 -.4322 4 5 1.0336 1.00 1.00 0.0069 0.2763 0.2832 -.2695 Three Model Results Modified Model # Sharpe Weighting ------- --------- ------------------- 1 2 3 1.1021 8.60 3.40 1.80 1 2 4 1.1376 9.80 3.40 9.00 1 2 5 1.4511 5.80 1.40 9.00 1 3 4 0.9659 8.20 1.80 9.00 1 3 5 1.4528 3.80 1.00 7.80 1 4 5 1.3934 5.80 2.60 9.40 2 3 4 0.8385 2.20 1.80 7.00 2 3 5 1.3774 1.00 1.40 7.00 2 4 5 1.1763 1.40 4.20 8.20 3 4 5 1.2990 1.40 2.60 7.40 Four Model Results Modified Model # Sharpe Weighting ------- --------- -------------------------- 1 2 3 4 1.2066 9.00 3.40 1.80 9.00 1 2 3 5 1.5768 4.20 1.40 1.40 8.60 1 2 4 5 1.4826 5.80 1.40 3.00 8.20 1 3 4 5 1.4821 3.80 1.00 2.20 7.40 2 3 4 5 1.4119 1.00 1.40 2.20 6.60 BSTMODL5 10-13-2005 Page 2 Five Model Results Modified Model # Sharpe Weighting --------- --------- -------------------------------- 1 2 3 4 5 1.6072 3.00 1.00 1.00 1.80 5.80 Best Overall Combination Modified Money Management Model # Sharpe Contract Multiplier --------- --------- ------------------------------------------ 1 2 3 4 5 1.6072 0.5172 0.1724 0.1724 0.3103 1.0000" b) System Performance Report " Projected Performance Report for 12 Months Inital Capital 500,000.00 Minimum Capital Required @95% DD 186,753.61 Fixed % Risk MMgt of 0.30% per-trade Outcome 72.1% Drawdown 4.8% Income to Drawdown Ratio 14.9 Trades Per-Month 35.0 Expected Profit Factor 1.80 Per-cent Months Profitable 92.6% Model 1 ES/Prod8 Average number of trades per-month 10.9 Std. Dev. of # of trades per-month 4.4 Average Loss per-trade -368.72 Std. Dev. of average loss 200.39 Contract Multiplier 1.000 Model 2 ES/Model122 Average number of trades per-month 4.4 Std. Dev. of # of trades per-month 1.7 Average Loss per-trade -368.83 Std. Dev. of average loss 199.98 Contract Multiplier 0.172 Model 3 NQ/Model131 Average number of trades per-month 6.9 Std. Dev. of # of trades per-month 2.6 Average Loss per-trade -293.18 Std. Dev. of average loss 201.89 Contract Multiplier 0.172 Model 4 ES/Model111 Average number of trades per-month 4.3 Std. Dev. of # of trades per-month 1.6 Average Loss per-trade -263.87 Std. Dev. of average loss 300.41 Contract Multiplier 0.310 Model 5 ES/Model131 Average number of trades per-month 8.6 Std. Dev. of # of trades per-month 3.4 Average Loss per-trade -517.44 Std. Dev. of average loss 338.08 Contract Multiplier 0.517 MMGT31 10-13-2005 Page 2 Confidence Profit Level Result Return Factor DD ---------- ------------ -------- ------ ----- 2% Level 644,313.31 128.9% 2.35 8.7% 4% Level 594,774.06 119.0% 2.26 7.9% 5% Level 577,904.94 115.6% 2.23 7.6% 6% Level 563,535.69 112.7% 2.20 7.4% 8% Level 540,561.44 108.1% 2.16 7.1% 10% Level 521,521.75 104.3% 2.12 6.8% 12% Level 506,130.66 101.2% 2.09 6.6% 14% Level 492,332.34 98.5% 2.07 6.4% 16% Level 480,016.84 96.0% 2.04 6.2% 18% Level 468,996.69 93.8% 2.02 6.1% 20% Level 458,824.31 91.8% 2.00 5.9% 22% Level 449,289.69 89.9% 1.98 5.8% 24% Level 440,477.19 88.1% 1.97 5.7% 26% Level 432,010.44 86.4% 1.95 5.6% 28% Level 424,153.69 84.8% 1.93 5.5% 30% Level 416,626.69 83.3% 1.92 5.4% 32% Level 409,403.97 81.9% 1.91 5.3% 34% Level 401,938.84 80.4% 1.89 5.2% 36% Level 395,022.81 79.0% 1.88 5.1% 38% Level 388,437.50 77.7% 1.86 5.0% 40% Level 381,887.50 76.4% 1.85 5.0% 42% Level 375,817.19 75.2% 1.84 4.9% 44% Level 369,608.31 73.9% 1.83 4.8% 46% Level 363,606.56 72.7% 1.82 4.8% 48% Level 357,638.69 71.5% 1.80 4.7% 50% Level 351,781.56 70.4% 1.79 4.6% 52% Level 345,898.81 69.2% 1.78 4.6% 54% Level 340,254.44 68.1% 1.77 4.5% 56% Level 334,566.31 66.9% 1.76 4.4% 58% Level 328,992.34 65.8% 1.74 4.4% 60% Level 323,309.06 64.7% 1.73 4.3% 62% Level 317,357.16 63.5% 1.72 4.2% 64% Level 311,388.56 62.3% 1.71 4.2% 66% Level 305,317.91 61.1% 1.70 4.1% 68% Level 299,412.59 59.9% 1.68 4.1% 70% Level 293,217.72 58.6% 1.67 4.0% 72% Level 286,991.19 57.4% 1.66 3.9% 74% Level 280,443.19 56.1% 1.64 3.9% 76% Level 273,741.19 54.7% 1.63 3.8% 78% Level 267,165.44 53.4% 1.62 3.8% 80% Level 259,891.84 52.0% 1.60 3.7% 82% Level 252,304.16 50.5% 1.58 3.6% 84% Level 244,767.30 49.0% 1.57 3.6% 86% Level 236,351.00 47.3% 1.55 3.5% 88% Level 226,959.34 45.4% 1.53 3.4% 90% Level 216,806.45 43.4% 1.51 3.3% 92% Level 205,528.02 41.1% 1.48 3.2% 94% Level 191,378.52 38.3% 1.45 3.1% 95% Level 183,738.47 36.7% 1.44 3.0% 96% Level 174,045.44 34.8% 1.41 3.0% 98% Level 147,877.77 29.6% 1.36 2.8%"
For a summary of his Strategy Formation posts see my other thread at: http://www.elitetrader.com/vb/showthread.php?s=&postid=1328890#post1328890