This article says that while this is often quoted, it’s only true for an even-money bet where you lose everything. Which is a shame because this would have been a fairly easy heuristic.
In particular, for a single asset, the formula becomes
f∗=μ−rσ2
Where μ is the drift, r is the risk-free rate, and σ is the volatility. This is the better heuristic, and is perhaps the formula I should have included in the first place.
But in practice, we don’t know our payoff distribution. Note that the drift is not simply the observed returns. It’s what’s left over when you subtract out the stationary noise. Which part of the return is the drift and which part is the noise? We don’t know! And we don’t really want the past drift and volatility, but the future drift and vol for the bet we’re about to make. These are not constants. The past can help us estimate the future, but it’s very uncertain.
Furthermore, this is only for a single asset. If you apply this formula to each asset in a portfolio, and they’re at all positively correlated, this will tend to overallocate.
Don’t Bet the Farm. If you’re going to use it as a heuristic, then due to these uncertainties, it’s probably best to think of this as an upper bound, rather than an exact target.
This article says that while this is often quoted, it’s only true for an even-money bet where you lose everything. Which is a shame because this would have been a fairly easy heuristic.
In particular, for a single asset, the formula becomes
f∗=μ−rσ2
Where μ is the drift, r is the risk-free rate, and σ is the volatility. This is the better heuristic, and is perhaps the formula I should have included in the first place.
But in practice, we don’t know our payoff distribution. Note that the drift is not simply the observed returns. It’s what’s left over when you subtract out the stationary noise. Which part of the return is the drift and which part is the noise? We don’t know! And we don’t really want the past drift and volatility, but the future drift and vol for the bet we’re about to make. These are not constants. The past can help us estimate the future, but it’s very uncertain.
Furthermore, this is only for a single asset. If you apply this formula to each asset in a portfolio, and they’re at all positively correlated, this will tend to overallocate.
Don’t Bet the Farm. If you’re going to use it as a heuristic, then due to these uncertainties, it’s probably best to think of this as an upper bound, rather than an exact target.
Right. Sorry if that wasn’t clear. The Wikipedia article I linked to right below the formula explains other cases.