But how much is it actually used in trading?
In theory, Kelly is optimal--if you knew the exact probability density function of your returns, it would give you the right leverage to take.
In practice, you're always playing with risks, some you're factoring into your models, some you're choosing not to because they're intractable, some you're not even aware of until they occur. The most basic premise--today's returns will be a function of hypotheses that I've derived from looking at past observations--is an approximation at best.
This mismatch between model and reality can lead to expensive lessons learned when using the full Kelly model, so often traders will "half-kelly" or something like that, to incorporate the basic idea of risk scaling proposed by the Kelly model but with more safety margin.
It's optimal for one utility function (log of future $), but that doesn't make it necessarily optimal for everything, right?
If we’re close to an investment goal, like saving a house downpayment or retiring, the calculus is quite different. Even outside that, loss aversion is a real thing and we’re likely happier trading some upside for being able to sleep at night.
And to be clear, half-Kelly, quarter-Kelly, eighty-percent-Kelly and any other linear combination between wallet and full Kelly are actually still the only strategies that are growth optimal -- given the particular safety margin each corresponds to.
Page 27: Vince(vi) and independently Thorpv(ii) provide a solution that satisfies the Kelly Criterion for the continuous finance case, often quoted in the financial community to the effect that “f should equal the expected excess return of the strategy divided by the expected variance of the excess return:”
f = (m-r) / s^2
so it's Sharpe with variance instead of standard deviation in the denominator, correct?
An intuitive way to think about this is that Sharpe depends on the specific horizon you're using. E.g. annualized Sharpe will be sqrt(252) larger than daily Sharpe. It would not make sense to change the Kelly criterion based on a substitution of variables. In contrast variance, like returns, scales linearly with time horizon. Therefore the variance ratio is invariant to the time horizon.
Edward Thorpe and Ralph Vince both conclude that the Kelly Criterion in the continuous case is excess returns divided by variance, which is pretty close to the Sharpe Ratio, correct?
Asking to understand better, not to be combative. Your comment made it seem like that formula is way off.
I precalc my stoplosses + stopgains then use a simulation to get the win/loss probabilities on training data.
What I observed is the kelly formula really prefers the tiny stoplosses, so when you sort your predictions by kelly score it will pick the ones with tiny stoplosses.
What happened to me in the live test is the tiny stoplosses triggered, when a stopgain would have triggered later.
I know someone is going to say "thats a problem with your stoplosses+stopgains OOS performance" and they are right, but OOS stoploss+stopgain calculation isn't trivial for me to calculate :\
Moreover you can find the same result with a simple grid search over bet sizes, obviating the need to estimate any parameters of the outcome distribution.
It would be more useful in professional gambling where outcome distributions are more knowable.