# «Key to Trading Profits – Matching the Probability Distribution of A Contract with An Appropriate Mechanical Trading Strategy Gary Tan Business ...»

The model works on the premise that the breaking of a prior high signifies new buying interest which in turn will drive prices even higher. Conversely, the breaking of a prior low is indication of renewed selling interests which would then force prices down. Being aligned with the flow complements the high incidence of wins given by the contract characteristics as determined in subsection 2.2. Accordingly, if the rule takes you long in the market, remain in that position until the rule takes you out. This will allow the market to work on your trade and more importantly allow one to be constantly in the market so as to be able to ride the big move when it comes as opposed to trying to “second-guess” when that might be, thus increasing the likelihood of achieving a robust win/loss ratio.

It is further assumed that one is able to buy at the ask and sell at the bid, with no slippage given that the i) contract in question is liquid and its bid-ask spread had been consistently 1 tick difference for most parts, and ii) bid-ask volume can easily absorb your trade size (in this paper this isn’t an issue since we are looking at only one contract). In other words, one can hope to get in and out of a trade at relative ease.

4. The Results

4.1 Results from Trading the Model The model generated net profits for every single year in the out-of-sample period from January 1999 to October 2008, no matter long or short positions. Combined, long and short trades netted profits of USD590,690, USD323,220 and USD267,470 respectively for the period sampled. Such sterling results were achieved on the back of robust win/loss ratios compounded by a high probability of winning trades.

Transaction costs were assumed to be USD30 per round turn. Note also that the average profit per trade of USD770 can more than cover any transaction costs and still be profitable. Consequently, slippage from execution, if any, is unlikely to have a material negative impact on profits.

Win/loss ratio is defined as gross win/gross loss and averaged 4 times for all trades, indicating the dollar value of winnings was 4 times that of losses in the period sampled. Long trades performed better than short trades, averaging 5 times compared to 4 times for shorts. The lowest win/loss ratio in a given year was still a healthy 2 times. Such robust win/loss ratios can be attributed to the efficacy of the trading model. The trading model as enumerated in section 3 is designed such that a position once initiated and profitable is allowed to run thus maximising its profit potential. Consequently, the model was able to exploit the opportunities offered by the market, thus compounding the many “small” wins envisaged by the distribution characteristics of the contract.

Such favourable win/loss ratios are certain to result in longer term profitability for any trading model that has an even chance of winning, more so when we have a high probability of wins as is the case here.

% winning trades is defined as the total number of winning trades/total number of trades and was 55% of a total of 798 trades taken during the sample period. It is further noted that annual trades generated by the model were winning at least half the time to two thirds of the time. It must also be pointed out that % wins are less International Journal of Economics and Finance Vol. 2, No. 2; May 2010 encouraging in short trades primarily because crude oil was on a long term uptrend for much of the period sampled. However, profits were still achieved every single year on short trades due to a robust win/loss ratio.

Long trades were more profitable, averaging 61% wins for the sample period. Again as explained in subsection 2.2, the subject contract exhibited significant time dependencies. By aiming to capitalise on new buying and new selling interests the trading model was able to capture the trends and reversal tendencies displayed, thus resulting in a high probability of wins.

Maximum continuous winning streak was 9 trades and totalled USD60,240 while maximum continuous losing trades totalled 6 trades and was USD10,620. Consistent with the leptokurtic nature described in subsection 2.2 drawdown was kept in check. Together with the strong win/loss ratios and higher probability of wins, the trading model provides one with positive expectations and hence the confidence to trade.

There is no open position as the last trade was closed out at the end of the sample period.

Insert Tables 4: Trading Results of Combined Trades Insert Tables 5: Trading Results of Long Trades Only Insert Tables 6: Trading Results of Short Trades Only To be sure, one can improve the results by employing risk/money management strategies such as trade sizing, trailing stops, pyramiding etc. Results can also be enhanced by the use of appropriate filters in the trade rules and by employing other confirmation signals which is out of the scope of this paper.

4.2. Results Evaluated Against the Weak Form EMH As described above, the model had consistently generated positive excess return. The question remains if these excess returns were due to the efficacy of the model or did they happen by chance? And if they were due to the efficacy of the model, just how significant are they? To address these concerns, we evaluated the results in the context of the framework developed by Peterson & Leuthold (1982), a framework that essentially evolve from the works of Samuelson (1965) and Mandelbrot (1963, 1966) and Fama (1970).

As any mechanical trading system must yield zero profits under the weak form efficient market conditions, the null hypothesis must be zero and any non zero results deemed a contradiction. Additionally, a zero benchmark seemed in order given that futures trading are a zero sum game, Leuthold (1976). Further, Samuelson (1965) argued that “on average … there is no way of making an expected profit” and Fama (1970) also ruled out excess profits under the assumptions of the weak form efficient market. Bachelier (1900) also concluded that "the mathematical expectation of the speculator is zero" and he described this condition as a "fair game." Accordingly,

**the following hypothesis is tested:**

Ho: mean profit = 0 Ha: mean profit ≠ 0 A trading system that consistently produces losses can just as easily be used to consistently produce profits by adopting a contrarian approach, i.e. by simply buying on a sell signal and selling on a buy signal. Such a move would obviously result in an opposite effect of the same magnitude.

**Accordingly, a two-tailed Z-test is chosen to measure the significance:**

(n 30) (8) where is the actual mean gross profit/loss from the Model, is the expected mean gross profit/loss (= 0), is the variance of gross profits per trade and n is the number of round-turn trades.

As tabulated in Tables 4, 5 and 6 the calculated z-statistic for combined trades, long trades and short trades in the sample period was 9.43, 8.61 and 5.34 respectively. For all years in the sample period, combined trades generated net profits significantly different from 0 at the 1% level.

Long trades also exhibited the same results as above for all years. Short trades were more erratic but most years were still significant, at least at the 10% level.

The results indicate that the null hypothesis should be rejected, at least at the 10% level. The ability of the model to generate significant excess profits suggest non random price movements and accordingly, it can be concluded that the Light Sweet Crude Oil futures failed the weak form efficiency test.

International Journal of Economics and Finance www.ccsenet.org/ijef

5. Conclusion This study confirmed that it is possible to match the distribution of a contract with an appropriate trading strategy to provide a competitive edge. Simple trading rules that are complementary to the distribution of the contract, when consistently applied, can systematically produce excess profits in the long run. The appeal of mechanical trading methods lies also in that they help set the rules and remove or at least keep guesswork and emotions to a minimum, thereby making simulation easy.

To be sure there can be more than one trading rule that matches any given distribution and vice versa. Perhaps the successful trader differs from the unsuccessful one, not because of the superiority of one model over another, but because he or she has found a model that is in-tune with his or her basic personality, outlook and experience sets. Because these models of market success are drawn from our fundamental views and aversions, I suspect they are far less amenable to modification than is commonly appreciated, which explains why market participants can and do get different results from trading identical models.

References Bachelier, L. (1900). Theory of speculation (Thesis presented for the degree Docteur ès Sciences Mathèmatiques, Academy of Paris). Translated by Boness, A.J.

Brock, W., Lakonishok, J. & LeBaron, B. (1992). Simple technical trading rules and the stochastic properties of stock returns. Journal of Finance, 47(5), 1731–1764.

Cheung, Yin-Wong, & Menzie D. Chinn. (2001). Currency traders and exchange rate dynamics: A survey of the US market. Journal of International Money and Finance, 20(4): 439–71.

Fama, E. F. & Blume, M. E. (1966). Filter rules and stock market trading. Journal of Business, 39, 226–241.

Fama, Eugene F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2): 383–417.

LeBaron, B. (1994). Technical trading rule profitability and foreign exchange intervention. Department of Economics University of Wisconsin.

Leuthold, R.M. (1976) On the methodology of testing for independence in futures prices. Journal of Finance, 31:984-85.

Levich, R. M., & Thomas, L. R. (1993). The significance of technical trading rule profits in the foreign exchange market: A bootstrap approach. Journal of International Money and Finance, 12(5), 451–474.

Malkiel, Burton G. (1996). A random walk down Wall Street: Including a life-cycle guide to personal investing.

(Sixth edition). New York and London: Norton.

Mandelbrot, B.B. (1963). The variation of certain speculative prices. Journal of Business, 36:394-419.

Mandelbrot, B.B. (1966). Forecasts of futures prices, unbiased markets, and Martingale models. Journal of Business, 39:242-55.

Peterson, P.E. & R.M. Leuthold. (1982). Using mechanical trading systems to evaluate the weak form efficiency of futures markets. Southern Journal of Agricultural Economics.

Samuelson, P.A. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review 6:41-49.

Sweeney, Richard James. (1986). Beating the foreign exchange market. Journal of Finance, 41(1):163–82.

Sweeney, R. J. (1988). Some filter rule tests: Methods and results. Journal of Financial and Quantitative Analysis, 23, 285–300.

Taylor, M. P. & Allen, H. (1992). The use of technical analysis in the foreign exchange market. Journal of International Money and Finance, 11(3), 304–314.

www.cmegroup.com/trading/energy-metals/ www.esignallearning.com Troncone, Vincent. (2006). the 1 Point Rule. www.pennies-from-heaven.us.

Notes Note 1. The author gratefully acknowledged the helpful comments of Professor Ralf Zurbrugg on an earlier version of this paper.

1999 22,140 -2,670 24,810 34,410 -9,600 4 89 55% 279 694 481,420 3.79 2000 41,740 -2,670 44,410 62,120 -17,710 4 89 47% 499 1,262 1,592,118 3.73 2001 30,360 -2,670 33,030 47,190 -14,160 3 89 51% 371 992 984,562 3.53 2002 25,420 -2,700 28,120 41,670 -13,550 3 90 51% 312 773 598,210 3.83 2003 30,800 -2,670 33,470 53,740 -20,270 3 89 52% 376 1,269 1,609,899 2.80 2004 45,800 -2,370 48,170 69,310 -21,140 3 79 53% 610 1,697 2,880,241 3.19 2005 71,860 -2,250 74,110 95,240 -21,130 5 75 60% 988 1,911 3,650,691 4.48 2006 71,090 -2,490 73,580 97,540 -23,960 4 83 59% 887 1,804 3,255,460 4.48 2007 84,870 -1,740 86,610 102,670 -16,060 6 58 66% 1,493 2,740 7,508,475 4.15 2008 166,610 -1,710 168,320 202,520 -34,200 6 57 58% 2,953 6,278 39,408,386 3.55 1999-2008 590,690 -23,940 614,630 806,410 -191,780 4 798 55% 770 2,308 5,325,164 9.43 Notes: (1) Net Profit = Gross Profit – Transaction Costs; (2) Transaction costs is assumed to be USD30 per round turn; (3) Gross Profit = Gross Win – Gross Loss; (4) Gross Win = Gross Total Dollar Value of Winning Trades; Gross Loss = Gross Total Dollar Value of Losing Trades; Win/Loss Ratio = Gross Win/Gross Loss; Total Number of Trades = Total Number of New Trades; % Win Trades = Total Number f Winning Trades/Total Number of Trades; Mean Profit = Average Gross Profit per Trade; Z-Test is two-tailed.

1999 17,440 -1,320 18,760 21,920 -3,160 7 44 75% 426 680 462,121 4.16 2000 22,400 -1,350 23,750 32,050 -8,300 4 45 51% 528 1,216 1,479,845 2.91 2001 11,490 -1,320 12,810 19,750 -6,940 3 44 52% 291 748 559,922 2.58 2002 18,170 -1,350 19,520 25,620 -6,100 4 45 56% 434 828 684,910 3.52 2003 16,350 -1,350 17,700 26,970 -9,270 3 45 60% 393 947 896,559 2.79 2004 27,400 -1,170 28,570 35,800 -7,230 5 39 64% 733 1,418 2,010,441 3.23 2005 46,680 -1,140 47,820 56,040 -8,220 7 38 71% 1,258 1,998 3,990,624 3.88 2006 31,870 -1,230 33,100 43,450 -10,350 4 41 61% 807 1,680 2,820,865 3.08 2007 62,610 -870 63,480 68,520 -5,040 14 29 72% 2,189 3,184 10,136,431 3.70 2008 68,810 -870 69,680 86,160 -16,480 5 29 55% 2,403 4,396 19,320,585 2.94 1999-2008 323,220 -11,970 335,190 416,280 -81,090 5 399 61% 840 1,950 3,800,610 8.61 Notes: (1) Net Profit = Gross Profit – Transaction Costs; (2) Transaction costs is assumed to be USD30 per round turn; (3) Gross Profit = Gross Win – Gross Loss; (4) Gross Win = Gross Total Dollar Value of Winning Trades; Gross Loss = Gross Total Dollar Value of Losing Trades; Win/Loss Ratio = Gross Win/Gross Loss; Total Number of Trades = Total Number of New Trades; % Win Trades = Total Number f Winning Trades/Total Number of Trades; Mean Profit = Average Gross Profit per Trade; Z-Test is two-tailed