Comment by kqr
4 years ago
E log X strategies are known for Being very volatile.
However, there are two things that take the scariness out of estimating probabilities for me:
- You're often maximising something that looks like a quadratic function. This means you're aiming at a plateau more than a peak: if you make small errors in either direction it doesn't affect growth that much.
- You always have the safe option of underestimating. The E log X strategy forms an "efficient frontier" (to borrow terminology from MPT) of linear combinations from the risk-free rate to the full Kelly bet (and even past it into leveraged Kelly strategies.) You can always mix in more of the risk-free rate and get lower growth but at higher safety.
These two properties makes the Kelly criterion very forgiving to estimation. (In contrast to MPT style mean--variance estimations, and other less principled strategies.)
I find both mean variance and Kelly to be very poor in practice due to the dependence on the expected return term. Like, if I knew that, I wouldn't be wasting my time with all this math! (half joking)
Kelly does not depend on the expected return -- it depends on the joint distribution of outcomes. That is a big difference!
Accidentally thinking that "E log X" and "log E X" are the same thing is a common mistake, but Jensen's inequality tells us it can be a costly one.
Of course, your general point still stands: if we only knew the joint distribution of outcomes the battle would be over already.