Monthly Equity Curve: Filtered Breakout for DM

-1000

Months (2/88-6/95)

Figure 7.1 Monthly equity curve for deutsche mark trading one contract.

commission is shown in Figure 7.1. This system had a steady increase in equity with several significant retracements. We imported the monthly equity curve into a spreadsheet and analyzed the interval change in eq­uity over 1, 3, 6, and 12 months. Those data appear in Table 7.5.

Some simple calculations will show the usefulness of Table 7.5. As­sume that the monthly average return is zero and that monthly equity changes are normally distributed. Most trend-following systems have losing streaks lasting six months or less. Hence, to estimate downside

Table 7.5 Interval equity change analysis for the deutsche mark over 90 months (2/88-6/95)

Interval Analysis	1 Month	3 Months	6 Months	12 Months
Maximum gain ($)	7,963	7,413	7,213	7,650
Maximum loss ($)	-3,137	-3,925	-5,263	-3,889
Average ($)			1,297	2,111
Standard Deviation ($)	1,471	2,263	2,667	2,928

214 Ideas for Money Management

potential, let us look at the worst loss over the 6-month interval. The maximum loss over six months was -$5,263, which is 3.5 times the monthly standard deviation of $1,471, rounded up to $1,500. We will use the 3.5 figure as a guideline, and round it up to 4. Thus, we will plan for a drawdown of four times the standard deviation of monthly equity changes. We know from statistical theory that the probability of getting a number larger than four times the standard deviation is quite small, about 6 in 100,000.

Now for a $50,000 account trading one deutsche mark contract for this system, our projected "worst" drawdown is 12 percent (= ($1,500 x 4) / $50,000). Using the same estimate for the upside, our "best" upside annual performance would be 12 percent. Thus, our most likely per­formance band will be ±12 percent. We can make this "linear" assump­tion because we are trading just one contract per market. Let us see how the system performed on an annual basis, assuming the account was re­set to $50,000 at the beginning of each year.

Table 7.6 shows that the performance band of ±12 percent was generally a good estimate. The 10.5 percent drawdown trading just one contract (1990) is worrisome. To cut the figure in half, trade this system with an account equity of $100,000. However, doubling the equity will halve your return, and you will have to decide your comfort level be­tween returns and drawdowns.

Now that you have some feel for how to deal with a single contract, let us consider the impact of trading multiple contracts. One method of selecting the number of contracts is to fix your hard-dollar stop, and then to use market volatility to determine the number of contracts. In such systems, the number of contracts is inversely proportional to vola­tility. When market volatility is high, you trade a smaller number of con- Table 7.6 Annual return for DM system, $50,000 equity at start of year

Year

Percentage Return ($50K account)

Percentage Drawdown ($50K account)

11.5 8.1 -6.5 15.3 -2.1 5.6 -2.9

-1.9 -2.5 -10.5 -5.0 -10.2 -2.4 -5.4

Interaction: System Design and Money Management 215

tracts, and vice versa. We have discussed volatility-based calculations be­fore, such as for the long-bomb system in chapter 5. If volatility is $2,000, you buy five contracts for a $10,000 hard stop. If volatility tri­ples to $6,000, you buy just one contract. You can use any measure vola­tility, such as the 10-day SMA of the daily range.

In trading terms, the volatility is often low at the start of a trend after the market has consolidated for a few months. Your volatility-based criterion will trade more contracts, giving you a big boost if a dynamic trend occurs. Conversely, near the end of a trend, the volatility is usually higher, and you will buy fewer contracts. Thus, any false signals near the end of a trend will have a proportionately smaller impact.

If the volatility-based logic worked perfectly, you would have greater exposure during trends and smaller exposure during consolida­tions. Thus, your overall results should improve "nonlinearly" with vari­able contracts versus trading a fixed number of contracts each time. For example, trading, say, eight contracts using a volatility-based entry crite­rion may be better than just trading a fixed number of eight contracts at every signal. You hope to achieve greater returns with smaller draw­downs (higher profit factor) using the volatility-based contract calcula­tions. Figure 7.2 shows the effects of using a volatility-based multiple contract system using the breakout system for the deutsche mark. Com­pare this equity curve to the curve in Figure 7.1 for one contract.

The annual returns for the multiple-contract strategy are shown in Table 7.7. The multiple-contract system made more than five times the profit of the single-contract system. The system traded a maximum of eight contracts, and an average of three contracts. The drawdowns were, on average, only three times higher. Thus, there was a significant im-

Table 7.7 Annual return for deutsche mark system, $50,000 equity at start of year, multiple contracts

Year	Percentage Return ($50K Account)	Percentage Drawdown ($50K Account)
	102.8	-4.0
	44.5	-5.9
	-24.7	-43.6
	-15.1	-11.8
	-6.2	-30.5
	20.6	-6.0
	-15.7	-23.4

216 Ideas for Money Management