Bayesian Updating of Strategy Sharpe Ratios for Allocation

Summary

The document considers allocating capital across multiple strategies based on their recent performance. It proposes using each strategy’s Sharpe ratio over a recent window as an estimate of future performance, while recognizing that short samples can produce noisy estimates that differ from long-run performance.

It suggests bootstrapping windows from each strategy’s historical returns to form a prior distribution, then updating that prior with the latest window’s Sharpe ratio. The author raises a question about how to perform this update, noting uncertainty about conjugate priors for a t-distributed likelihood. The document does not provide an answer, a tested allocation procedure, or evidence that recent Sharpe ratios predict future results. It is therefore a problem statement about Bayesian estimation and strategy selection, rather than a validated method.

Key ideas

• Recent strategy performance could be used to guide capital allocation.
• Short-window Sharpe ratios may be noisy estimates of long-run performance.
• Bootstrapped historical windows are proposed as a way to construct strategy-specific prior distributions.
• The document asks how to update such a prior with a recent Sharpe observation and gives no solution.

Tags

# Bayesian strategy selection


# Bayesian strategy selection












I have N strategies/signals that I would like to allocate to. I want to estimate an estimate of future performance based off of recent realized performance (momentum of strategies per se - e.g. strategies that performed well recently will get higher allocation and vice versa).

Now, despite having shortcomings let's use the test statistic as the Sharpe ratio. One way to do this would just be to take the Sharpe ratios of each N strategy over the past D days and use those as our estimate of the forward expected returns. This is flawed, however, as for short enough windows, the sample Sharpe can be very different from a long run Sharpe.

So, I would like to use some type of Bayesian updating. We know that Sharpe ratios are just scaled T-distributions (scaled by sqrt(n), where n is the sample size). I was thinking that I could bootstrap samples of D days from my entire signal performance history to get some sort of prior distribution for the Sharpe ratio for each strategy. This should be distributed T. However, I don't see a conjugate prior distribution for a T likelihood, so I'm unsure how to update my prior distribution for the Sharpe ratio with the most recent Sharpe ratio observation (most recent D days)

Has anyone done something similar?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.