Bootstrap Methods for Robust Portfolio Allocation and Leverage
Summary
This article uses bootstrap resampling to examine uncertainty in portfolio statistics and allocation decisions. Resampling observed returns with replacement creates alternative histories and a distribution of estimates, rather than a single point estimate. The author contrasts this empirical approach with formula-based estimates and simulations drawn from an assumed distribution. A key caveat is that resampling individual days destroys autocorrelation; strategies that rely on serial patterns may need block or longer-period resampling instead.
The examples consider a bond and equity portfolio, comparing Kelly-style leverage with mean-variance allocation and joint optimisation of weights and leverage. The article evaluates distributions of outcomes and visualises how performance changes across parameter choices. It argues for selecting a point in a broad, relatively stable high-performing region rather than trusting the apparent maximum. Illustrative results include an allocation and leverage region under specified assumptions, but the author explicitly says these are not universal recommendations. Future returns, volatility, correlations, and the suitability of leverage remain uncertain, and the examples depend on the chosen inputs and historical higher-order return characteristics.
Key ideas
- Bootstrap resampling represents parameter uncertainty by generating many alternative samples from observed returns.
- Resampling individual observations may fail to preserve the time dependence needed to evaluate some strategies.
- Kelly and mean-variance approaches optimise different portfolio objectives and can imply different allocations or leverage.
- Joint optimisation should be assessed across a region of outcomes, not only at its highest estimated point.
- Leverage and allocation conclusions depend on assumptions about future returns, volatility, and correlations.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.