$$ Expectancy and Trade Comparison

Expectancy is simply R per trade (sum of R for all trades/# of trades).

A few posts back, we talked about how the stop loss placement affects position size, R-Multiples, and trade win percentage. The example was a $30 stock with a $32 target. The 30-cent stop resulted in a 6.67R profit, while the $1 stop resulted in a 2R profit.

I compare these two trades as follows.

First I want to know break even percentage trade win percentage. For the 30 cent stop, break even trade win percentage is 1/7.7 = 13%. For the $1 stop, it is 1/3 = 33%. These trade win percentages result in an expectancy of 0R per trade.

Second, I want to know the trade win percentage for the higher R-Multiple trade that would equal the max expectancy of the lower R-multiple trade. For the 2R trade, max expectancy is 2R (if you were right 100% of the time). To average 2R per trade with the 30 cent stop, you'd need to be right 39% of the time. [(3.9 *6.67) - 6.1 = 20R over 10 trades or 2R per trade].

Clearly, if I get the 30 cent stop trade right more than 39% of the time, it's always better to take that trade. But to fairly compare the trades, find the midpoint. Being right 67% of the time on the $1 stop trade = being right 26% of the time on the 30 cent stop trade. Both would have an expectancy of 1R per trade.

Finally, I decide whether I feel more confident hitting the 6.67R trade 26% of the time, or the 2R trade 67% of the time.

Drawdown is another consideration. But that is for another post.

$$ Relationship Between Position Sizing, R-Multiples and Trade Win %

For the swing/day trader, all three concepts are interrelated. The common denominator is how far away you place your initial stop loss.

Assume you risk 1% of account per trade. Assume account value is $100K. If you enter at $30 with a $29.70 stop loss and a $32 target, your risk is $1000, your position size will be (1000/.3) = 3333 shares * $30 = $100K or 100% of your account value in the trade.

If you hit your target at $32, you make $2/share or $6666. Your R-Multiple is 6.67R.

Of course, your stop at $29.70 is fairly tight, and you will be stopped out more often than with a looser stop, say $29 even. The tighter your stop, the greater the negative impact on your trade win percentage and vice versa.

If you made the same trade with a $29 stop, risking $1 a share, your position size would be 1000/1 = 1000 shares *$30 = $30K or 30% of your account value.

If you hit your target at $32, you make $2/share or $2000. Your R-Multiple is 2.0R.

To compensate for the lower R-Multiple, you will hit your target more often than you would with a $29.70 stop loss.

Bottom line, for the short term trader there is an art to placing your initial stop loss which directly affects how many shares you buy per unit of risk, what your R-Multiple reward will be compared to your risk, and how often your trade will be successful.

In a future post, I'll discuss how to compare the mathematical expectancy of the two trades outlined above.