Expectancy is the average amount you can expect to win (or lose) per trade with your system when a large number of trades are taken. To calculate your trading expectancy, you need to know three things - your win percentage, your average win, and your average loss. The calculation is as follows:
Expectancy = (Probability of Win * Average Win) -
(Probability of Loss * Average Loss)
It's a simple equation, but knowing the size of your trading
edge, as shown by a large positive expectancy, can be quite powerful.
Performance Measurement | Portfolio A | Portfolio B | Portfolio C | Portfolio D | Portfolio E | Portfolio F |
% Win Rate | 90% | 80% | 50% | 45% | 40% | 40% |
Average P/L Ratio | 0.1 | 0.5 | 1 | 2 | 2.5 | 3 |
Expectancy | -0.01 | 0.20 | 0.00 | 0.35 | 0.40 | 0.60 |
% Win Rate:- Let's say you are buying 10 stocks out of which 5 are the winner and 5 are looser that means your win rate is 5/10=50%
Average P/L ratio:- Let's say in the above example you
are investing 10000 for each stock and for winner stocks on an average you are
making 3000 and for losing stocks you are making a loss of 1000. So average P/L
ratio=3000/1000=3
Expectancy:- It is nothing but the combined measurement
of the above two parameters. So let's say win rate is 50% and the average P/L ratio is 3
then expectancy is = 3*50%-(1-50%)*1=1.5-0.5=1
Negative expectancy shows that if you are following that process you will lose the money.
So higher the positive expectancy better it is to generate a
good return on your investment.
From the above table, we can see that only a % win rate is
not that important for a profitable investment process or trading. Even though
with a 90%-win rate we losing the money.
Generally, people focus on % win rate as it satisfies human
emotion but actually for the profitable investment or trading, a combination of
average P/L ratio and % Win rate both are important.
A high % win rate means you have to beat the market quite
a lot of times. For another case let's say your winning rate is just 50%, which
is quite achievable (Even though if you just toss the coin the probability of a
win is 50%. So, it is quite possible to find a 40%-50% win rate). Once you made
the system that has around a 50% win rate and average P/L ratio of 3 then you have
just find the edge and now you have to just follow and repeat your setup so
basic math works in favor of you and you will generate a good return.
When you are doing back-testing of your strategy your focus
should be on the pay-off ratio and not on % win rate. If you are in the top right-most
area of the expectancy curve then even if the market conditions are changing
compared to the back-testing period when the strategy goes live you still have a good margin on safety on your designed system.
To get a good payoff ratio you need to do the research and
make your edge and you just need to exploit it.
In all my strategies my major focus is on the payoff ratio
and for the long-only 10 stocks strategies %win rate is around 50% but the
payoff ratio is around 2.5 and around 65% of the time these strategies are in
the market but for the index long-short strategy win rate is only around 40%
but and payoff ratio is around 2.5 but this system is in the market maximum
time, which generates additional alpha.
Once you have a decent %win rate and good payoff ratio for your system then you just need to stay in the market maximum possible time so that math works in favor of you.
