## Multiple contracts allow you to make larger profits when you are right.

However, the drawdowns are larger if you are wrong. You are betting that with good risk control, the overall profits will be greater than the drawdowns. An essential requirement is that your account equity must be sufficiently large to permit trading multiple contracts. Your risk control guidelines must permit multiple contracts to benefit from this approach. If your account permits you to trade just one contract at a time, then this approach must be deferred until your equity has increased.

Multiple contracts also allow you to add a nonlinear element to your system design. This means the results of trading, say, five contracts using this nonlinear logic are better than trading five contracts using the usual linear logic. The linear logic trades one contract per signal. The nonlinear logic uses a price-based criterion such as volatility. The volatility rule buys more contracts when volatility is low. Markets often have low volatility after they have consolidated for many weeks. If a strong trend develops as the market emerges from the consolidation, then the nonlinear effect is to boost profits significantly.

### A simple example illustrates these ideas.

Assume that your account is so large that trading up to 15 contracts in the 10-year T-note market is well within your risk control guidelines. For example, with a 1 percent risk per position and a $1,000 initial money management stop, you would need $1,500,000 in equity to trade 15 T-note contracts. This assumes that the 15-lot margin is also within your money-management guidelines.

Consider a simple moving average crossover system using 5-day and 50-day simple moving averages. The trade day is one day after the crossover day. You will buy or sell on the next day’s open if you get a 5/50 crossover tonight after the close. Use a $1,000 initial stop on each contract and allow $100 for slippage and commissions.

Let us compare system performance with one contract versus variable contracts, rising to a maximum of 15 contracts. The test period is from January 3, 1989, through June 30, 1995, using a continuous con-tract. Table 2.6 compares four variations of the 5/50 crossover system. The column labeled “fixed 1 contract” shows the results over the test period for always trading one contract per trade. The next column, “fixed 15 contracts” shows the calculated results for always trading 15 contracts per trade. The column, “variable #1” trades a maximum of contracts with the contracts added at the open on successive days. The “variable #2” trades a maximum of 15 contracts with all the contracts bought on the same day. The volatility in dollars here is four times the average 20-day true range. The volatility divided into $15,000 gives the number of contracts. Thus, variable #2 uses a volatility-based criterion for calculating the number of contracts, always trading 15 or less.

Let us compare the net profit produced by the four strategies. It should come as no surprise that the absolute amount of profit increases as we trade more contracts. However, as the next row of Table 2.6 shows, the maximum intraday drawdown also increases as we trade more contracts. The ratio of net profits to maximum intraday drawdown shows whether we gain anything by trading multiple contracts. This ratio is 3.47 for a fixed contract trading strategy. The ratio increases to 4.7 or 5.1 for the variable contract strategies. This is a 39 to 47 percent improvement, a strong reason to consider multiple contracts. Hence, profits can increase without proportionately increasing drawdowns.

#### Observe from Table 2.6 that the largest losing trade for variable #1 is considerably less than simply trading a fixed number of 15 contracts.

Similarly, the largest losing trade in variable #2 is less than always trading 15 contracts. This too confirms the benefits of going to the multiple-contract strategy.

The total number of trades remains the same for the fixed-1, fixed-15 and variable #2 strategies since all the contracts are bought on the same day. The number of trades increases for variable #1 since not all the contracts are bought on the same day.

The average trade for each strategy is relatively high, suggesting that this simple model seems to catch significant trends. The average trade is higher when all the contracts are bought at the same time. This is merely an artifact of system design. As pointed out before, the average trade does not provide a measure of variability in system results.

The standard deviation per trade is naturally smaller when we trade one contract at a time rather than all at once. The standard deviation in trade returns increases as the number of contracts increases. As Table 2.6 shows, there is higher volatility in trade returns ($36,721) for fixed 15-contract trading than either of the variable contract strategies. This means volatility can be reduced by trading a variable number of multiple contracts, rather than a fixed number of multiple contracts. This is another desirable design goal.

#### Dividing the average trade profit by the standard deviation in trade profitability yields a composite picture of model performance.

The higher this number, the more desirable the system. For the fixed 1-contract strategy, this reward to risk ratio is only 0.09, and it increases to 0.24 for the variable #2 strategy. Remember, however, that the volatility in trading profits increases significantly with multiple contracts.

The last line of Table 2.6, the downside volatility, explains that the increased volatility occurs due to rising profits of winning trades. Note that the fixed 15-contract downside volatility is the highest, followed by variable #2 and variable #1 strategies. There is not a large difference in downside volatility between the fixed 1-contract strategy and variable #1 strategy, which buys one contract at a time but on multiple days. Note also that the standard deviation of all trades (including winning trades) is much greater than the downside volatility. Thus, rather than all volatility being undesirable, note that adding multiple contracts increases upside volatility more than downside volatility. Increasing upside volatility is easier to cope with than sharply rising downside volatility.

In summary, if your account equity and mental makeup permit, consider the benefits of a multiple contract strategy.