# Optimization metric that takes into account number of trades vs expectancy

In optimizing my automated trading system I find that certain combinations while increasing the expectancy:

(AverageWin * ProfitableTradesRatio) - (AverageLoss * (1 - ProfitableTradesRatio))


Reduces the number of trades the strategy is making.

So although the expectancy increased dramatically, the number of trades went from 2,000 to just 40 over a 3 year backtest period which is not acceptable frequency of trading.

What performance metric can I optimize to balance this. I'd like to increase the expectancy without reducing the number of trades significantly.

EDIT: Further analysis shows that this is not only a problem with expectancy but other metrics like Max Drawdown that I'm measuring which also decreases as the numbers of trades decrease.

What method can I generically apply to adjust for this? This is not to be confused with SomeMetric "Per Trade". Simply dividing a metric by the number of trades does not seem to allow me to optimize that metric such that I can identify performance gains that have not decreased the frequency of trading.

If this doesn't make much sense, here's some data to illustrate. This is an optimization for "parameter" column (each row is an optimization run). I'm not sure how to identity whether there is any meaningful increase in expectancy (or decrease in max drawdown) by increase said "parameter" since the number of trades depletes along with each metric.

 parameter  total trades    expectancy    expectancy per trade  max drawdown
0          710             233.2957746   0.328585598           -1.389104131
2          640             158.53125     0.247705078           -1.799492989
4          559             129.9463327   0.232462134           -2.127999294
6          478             106.6945607   0.223210378           -1.463252512
8          402             134.6641791   0.33498552            -1.364193967
10         349             176.0601719   0.504470407           -1.196254362
12         303             134.4224422   0.443638423           -1.114376551
16         225             193.6222222   0.86054321            -0.657900215
20         181             242.3480663   1.338939593           -0.558306147
25         135             514.6296296   3.812071331           -0.493760619
30         106             47.16981132   0.44499822            -1.471772548
35         85              206           2.423529412           -1.482912119


I can't tell if it's worth decreasing the trading frequency for these performance gains. Anything under 300 trades in 3 years is not even an acceptable frequency of trading.

• I'm not sure I understand: you want to have a utility function or metric that increases the number of trades? Or do you want to increase the number of bets made? – Bob Jansen Nov 4 '14 at 17:37
• I think what I need is a way to identity "the point of diminishing returns" of increases in expectancy as the number of trades gets reduced. For example if the first increase of 10 in expectancy reduced the trades by 100, but the second increase of 10 reduces the trades by 500, then the second increase is not worth taking. – Vazgen Nov 4 '14 at 22:32

I think the problem is not that you optimize a wrong criterion, but the trading strategy itself. Compare this to testing a hypothesis: if you reject at p-value of 1% then the proportion of true discoveries among all discoveries is, say, 70% (high "expectancy"). If you reject at 10% then the true discovery proportion is 40% (lower "expectancy"), but you make a lot more rejections ("trades").

Of course, one would prefer having a lot of rejections and a high "expectancy", but for that you need to modify the testing procedure itself as opposed to changing the cutoff p-value.

• I'm not sure I understand, my last statistics exposure was a while ago in college. See my comment above, does that reword the question to allow for a simpler answer? – Vazgen Nov 4 '14 at 22:40
• You can tabulate the (expectancy, number of trades) pairs and find the one that looks ok, but you still won't be able to increase the number of trades w/o sacrificing the expectancy. – James Nov 6 '14 at 0:20