Changing Bet Size after Winning or Losing

One of the key money-management decisions you have to make is how you will change your bet size as your account equity evolves in time. Your trade-off is between equity growth and smoothness of the equity curve. This section presents some common "betting" strategies and their impact on the equity curve.

Two references will fill in the background on betting strategies. Bruce Babcock's book on trading systems examines different betting strategies. Jack D. Schwager's interviews with market wizards shows that many indicated that they reduced the size of their trades during losing periods. These references (see bibliography for details) should convince you that changing bet size can be as important as your system design.

222 Ideas for Money Management

The premise behind changing bet size is that you can use the out­come of the last trade to predict the outcome of the next trade. This im­plies that winning and losing trades come in streaks. However, it is easy to show mathematically that successive trades are independent. Hence, on average, it is difficult to justify the premise behind changing bet size. Despite this mathematical fact, most traders will tell you there are psy­chological benefits to reducing trade size during a drawdown. You can be conservative and assume losing trades will come in bunches, though winning trades may not. Under this assumption, you could generate a smoother equity curve by changing bet size.

A simulation will help us to examine the effect of different betting strategies on the smoothness of the equity curve. We will use the stand­ard error calculations to have a uniform basis for the comparison. We chose ten trades at random, half of them winners, and sampled these trades at random to construct 14 sequences often trades each. On each sequence, we then tested the following four strategies:

1. Constant contracts: always trading two per signal.

2. Double-or-half: if the previous trade was a winner, trade four contracts. If the last trade was a loser, trade one contract.

3. Half-on-loss: if the previous trade is a loser, trade one contract. If the last trade was a winner, then trade two contracts again.

4. Double-on-loss: if the previous trade is a loser, trade four con­tracts. If the last trade is a winner, then trade two contracts again.

We started with $100,000 in each portfolio. Every strategy was tested on precisely the same trades. We ran 14 simulations, for a total of 140 trades, and then averaged the equity curves for each trading strat­egy. We compared the averaged curves for each strategy to the average curve for trading two contracts per trade. Finally, we used linear regres­sion analysis to calculate the standard error.

You should conduct a larger simulation with your data to find the strategy you like. In particular, be aware that the double-on-loss is the riskiest strategy. If you are hit with an unusually long string of losses, this strategy will produce the largest drawdowns.

Table 7.13 shows the effect of changing the bet size after each trade. The strategy of halving trade size to one contract after each losing trade produced a 21.6-percent reduction in the standard error of the eq­uity curve for only a 2.4-percent profit penalty. Thus, we got a substan­tially smoother curve for a relatively small reduction in profits.

Changing Bet Size after Winning or Losing 223

Table 7.13 Effect of betting strategies on standard error of average equity curve

Strategy	Number of Contracts after Wins	Number of Contracts after Loss	Average Ending Equity (S)	Percentage Change in Equity	Standard Error ($)	Percentage Change in Standard Error
Constant			110,377	—		—
Half on loss			107,692	-2.4		-21.6
Double or			112,699	2.1	1,366	40.8
half
Double on			115,746	4.9	1,488	53.4
loss

The double-or-half strategy increased ending equity on average by only 2.1 percent, but the standard error increased by nearly 41 percent. You would expect this strategy to show sharp gains if winning trades come in bunches. Hence, the equity curve will be rougher and the in­crease in standard error is no surprise.

The double-on-loss strategy was the riskiest, as you can see by a more than 53-percent increase in standard error. The equity curve (see Figure 7.3) shows that this strategy can produce steep drawdowns. Al­though this strategy had the highest ending average equity, this was only 5 percent greater than the constant contract strategy. Hence, the relative risk reward does not seem worth the aggravation.

This limited simulation supports the opinion expressed by many accomplished traders that they like to reduce trade size during draw­downs. Table 7.13 clearly shows that the half-on-loss strategy had the best reward-to-risk performance. Some traders suggest that they defer accepting new signals during drawdowns, but ignoring new signals may cause you to miss just the signal you need to boost equity.

Table 7.13 shows that the fixed contracts strategy is also a reason­able choice. Certainly, when you are starting off, you may wish to con­sider this strategy to keep life simple. Eventually, as you feel more con­fident and have more equity, you can move on to other more elaborate strategies.

Note that when you use a fixed 2-percent stop to calculate a vari­able number of contracts, you are automatically adjusting position size to equity and volatility. If you have losing trades, equity will drop and bet size will decrease. Similarly, after profits, your bet size will increase. Hence, this strategy will produce a different equity curve. The calcula­tions here should provide a starting point for you to explore other com-

224 Ideas for Money Management