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Recently I've been reading about trading strategies which maximise geometric returns.
Gamblers might be familiar with a term that means the same thing, "Kelly criterion".
I won't dig too much into what it is, you can just Google the term to understand more. But suffice it to say that it is a position sizing strategy for betting that is designed to maximise geometric returns and thus terminal wealth.
The equation for calculating your position size using Kelly criterion is:
K% = W - ( ( 1-W ) / R )
Where W is your "Win Ratio", i.e. the historical or backtested number of winning trades as a ratio of total, and where R is your "Expectancy Ratio", i.e. the historical or backtested ratio of average winners to average losers.
Now since I have been working on some trend following stuff recently I thought I would apply this sizing algorithm there.
Let's think about a system which has a W of 0.3 (or 30%) and R of 3, that is to say the system is only wins about 30% of the time but when it wins it wins 3 times as much as it loses when it loses.
So over 10 trades you might have 7 consecutive losers and then 3 winners, would look like this versus static position sizing of 10% of available equity:
For a system with a W of 0.4 and R of 3 where you might have 6 consecutive losses followed by 4 winners:
For a system with a W of 0.3 and R of 4:
Now, obviously the distribution of winners and losers will not really look like this in real life, but it gives you a useful idea. If we shuffle around the winners so they are randomly placed:
You see it can be pretty valuable if your goal is to maximise terminal wealth, are sure your historical stats will hold going forward and can stomach some volatility!
Gamblers might be familiar with a term that means the same thing, "Kelly criterion".
I won't dig too much into what it is, you can just Google the term to understand more. But suffice it to say that it is a position sizing strategy for betting that is designed to maximise geometric returns and thus terminal wealth.
The equation for calculating your position size using Kelly criterion is:
K% = W - ( ( 1-W ) / R )
Where W is your "Win Ratio", i.e. the historical or backtested number of winning trades as a ratio of total, and where R is your "Expectancy Ratio", i.e. the historical or backtested ratio of average winners to average losers.
Now since I have been working on some trend following stuff recently I thought I would apply this sizing algorithm there.
Let's think about a system which has a W of 0.3 (or 30%) and R of 3, that is to say the system is only wins about 30% of the time but when it wins it wins 3 times as much as it loses when it loses.
So over 10 trades you might have 7 consecutive losers and then 3 winners, would look like this versus static position sizing of 10% of available equity:
For a system with a W of 0.4 and R of 3 where you might have 6 consecutive losses followed by 4 winners:
For a system with a W of 0.3 and R of 4:
Now, obviously the distribution of winners and losers will not really look like this in real life, but it gives you a useful idea. If we shuffle around the winners so they are randomly placed:
You see it can be pretty valuable if your goal is to maximise terminal wealth, are sure your historical stats will hold going forward and can stomach some volatility!