## Total Equity Contribution Ii

Instead of just looking at the profit contribution, it also is possible to look at how many of the movements in a time series can be explained by the movements in

Time

FIGURE 16.4

The equity curve for Charity II.

Time

FIGURE 16.4

### The equity curve for Charity II.

another time series. To do this we use the Pearson correlation coefficient which returns a value between 1 and â€” 1, very much like the correlation coefficient. The difference between the Pearson correlation coefficient and the normal correlation coefficient is that the Pearson correlation coefficient requires that one of the variables be dependent on the other variable.

This means that if two markets have a Pearson correlation coefficient close to 1, almost the entire move of the dependent market can be explained by what is

TABLE 16.3

 Strategy summary End Eq (\$) 37,797,489 Total (%) 3,680 Year(%) 20.59 Max DD (%) -28.89 Lrg Loss (\$) -1,690,564 Lng Flat (m) 23.29

800523 820521 840518 860516 880513 900511 920508 940506 960503 980501

Time

800523 820521 840518 860516 880513 900511 920508 940506 960503 980501

Time

FIGURE 16.5

### The drawdown for Charity II.

going on in the independent market. With a Pearson coefficient close to 0, the two markets move independently of each other. Tests like these are very common in the stock market, where many analysts look at how many of the movements in a particular stock can be explained by the movements of the market as a whole.

Note that this is a way of trying to explain how much of a particular stock's move can be explained by the move in the market, which is not the same as a stock's beta, which indicates how much a stock is likely to move, provided a certain move in the market. For instance, a stock with a beta higher than 1, say 2, is likely to move twice as much in the same direction as the rest of the market, but not all of that move must be explained by the move of the marketâ€”which is what we measure with the Pearson coefficient.

In this case, we do it the other way around and look at how much of the total equity can be explained by the total equity from a certain market/system combination. This is an especially good method to use when we have the possibility to trade the same market with several different systems and would like to narrow down the portfolio a little bit. What we look for is, first of all, markets that influence the total equity positively. We are also careful to choose markets that seem to be too good to be true, because this might make the portfolio too dependent on the performance of a few markets, when traded on previously unseen data in real-time trading. A major difference between this method and the correlation/covariance method is that with this method we are, so to speak, working backwards, because we first trade every market/system combination we can think of in one mega portfolio and then deduct all the unwanted market/system combinations from that portfolio, one at the time.

Before we get started, however, I need to throw in another word of warning. Just as with the other techniques, this method is very computationally intensive and time consuming once you have everything up and running in Excel. Not only that, but to get everything up and running you also need to export from TradeStation the trading results for every market/system combination you can think of. Now, this wouldn't be that bad if it weren't for the fact that TradeStation does not have a way to apply the same system to several markets (or otherwise manipulate several markets) all at once. At this point, it takes me about a minute (and I'm becoming pretty quick at this) to set up one market/system combination from a set of predefined workspaces that I have built. Imagine doing this on several 1 OO-market/system combinations.

It is a drag, to say the least. Another way to illustrate this include the fact that there seems to be no way to set the starting date once and for all, or once and for all to define a particular contract as a futures contract, or to default as hidden all data streams but the first one. To do all this it takes me at least 20 mouse clicks (conservatively counting) for each market to set up the chart with the necessary system. I will tell you, I am not writing a book like this just because I think it is fun to tinker around with TradeStation.

Nonetheless, Table 16.4 shows the Pearson correlation coefficients together with the equity contribution factors for 23 different markets traded with the SDB system over the time period January 1980 to October 1999. Again, the initial markets were picked in such a way as not to use those obvious ones already used in many of the previous examples. Table 16.5 shows the summarized results for this portfolio. The initial equity was set to \$1,000,000 and the percentage risked per trade was set to 1.5%. As usual, \$75 was deducted for slippage and commission. With these settings, the strategy produced an ending equity of close to \$29,000,000, corresponding to a percentage return of close to 19% per year. So far so good, but a maximum drawdown of close to 40% and a longest flat time of more than 47 months would have made this a very difficult portfolio to trade in real life.

From these 23 markets, I deducted the six markets with the lowest (Au dollar, soybeans, platinum, live cattle, cocoa, and British pound) and the three markets with the highest (rough rice, Eurodollar, and cotton) Pearson correlation coefficients, ending up with a portfolio consisting of sugar, Nikkei index, natural gas, municipal bonds, lean hogs, lumber, coffee, copper, gold, feeder cattle, crude oil, Canada dollar, corn, and wheat. These I then traded with a fixed fractional setting of 2%. (With fewer markets, we can increase the risk per trade somewhat, because the strategy now should be a little more efficient, while at the same time our overall margin requirements have decreased.)

 TABLE 16.4 I Initial markets for Charity III. Market Contributing Pearson Au dollar -5.46 -0.6592 Sugar 0.66 0.0561 Soybeans -2.52 -0.4445 Rice 15.85 0.9508 Platinum -22.93 -0.8640 Nikkei index 7.55 0.8741 Natural gas 12.86 0.9137 Municipal bonds 3.80 0.8302 Lean hogs -0.13 -0.3184 Live cattle -2.09 0.1241 Lumber 8.83 0.6967 Coffee 28.58 0.7810 Copper 5.40 0.9064 Gold 5.19 0.6305 Feeder cattle 1.84 0.8413 Eurodollar 0.64 0.9099 Cotton 20.97 0.9098 Crude oil 32.29 0.8362 Canada dollar -1.82 0.2626 Cocoa -9.60 -0.6489 Corn 6.79 0.7143 British Pound -4.17 -0.5608 Wheat -2.54 0.4263

Table 16.6 shows the result from trading this portfolio. The ending equity is close to \$40,000,000, corresponding to a percentage return of more than 20.50% per year. The drawdown has decreased to a tolerable 29%. The longest flat time also has decreased considerably but is still, at close to 31 months, a little too long.

Table 16.6 shows the result from trading this portfolio. The ending equity is close to \$40,000,000, corresponding to a percentage return of more than 20.50% per year. The drawdown has decreased to a tolerable 29%. The longest flat time also has decreased considerably but is still, at close to 31 months, a little too long.

TABLE 16.5

Initial strategy summary for Charity III.

Strategy summary

End Eq (\$)

29,016,313

Total (%)

2,802

Year (%)

18.96

Max DD (%)

-39.29

Lrg Loss (\$)

-823,050

Lng Flat (m)

 Strategy summary End Eq (\$) 38,565,334 Total (%) 3,757 Year (%) 20.72 Max DD (%) -29.07 Lrg Loss (\$) -1,579,683 Lng Flat (m) 30.81

All in all, however, this is not too bad for a one-system strategy, traded on a bunch of markets that were basically chosen because they had not been used before or because they were plain average.

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