Using Bootstrap Methods for Asset Allocation Estimates

Summary

The document asks whether bootstrap estimates of returns, variances, and correlations should be used to construct an efficient frontier from two stocks’ historical returns. The response clarifies that bootstrapping is primarily a way to estimate the sampling variability of an estimator when a direct formula is unavailable. In portfolio analysis, it could therefore help assess uncertainty around estimated returns or covariances; it is not presented as a preferred replacement for estimating those inputs or as an allocation method by itself.

The answer distinguishes two data settings. Under an independent, identically distributed Gaussian assumption, it says closed-form results are available. When returns are not Gaussian or may be serially dependent, ordinary bootstrap methods become difficult to apply appropriately, and specialized approaches for dependent series require care. The document points to a technical reference on bootstrap methods for non-independent data but gives no resampling procedure, simulation, or portfolio comparison. It does not establish that bootstrapping will improve an efficient frontier, especially when the historical sample has autocorrelation or other dependence.

Key ideas

• Bootstrapping can estimate the sampling uncertainty of return or covariance estimators.
• It is a tool for quantifying estimator variability, rather than an asset-allocation rule by itself.
• Under an iid Gaussian assumption, the response notes that closed-form results are available.
• Serial dependence makes bootstrap methods more difficult and calls for methods suited to non-iid data.
• The document offers no empirical test of bootstrap-based efficient frontiers.

Tags

# bootstrap asset allocation


# bootstrap asset allocation












I want to ask if the bootstrap method for asset allocation is preferable. For instance, suppose that we have data for the past returns for two stocks. Is it wise to generate the efficient frontierby estimating the correlations, the returns and the variances via the bootstrap method?

## Answer by lehalle (score 1, accepted)

https://quant.stackexchange.com/a/18077

I am not sure you have the same definition of bootstrap than myself: bootstrap is mainly a way to estimate the variance of estimators when you do not have a closed form formula to obtain it directly (thanks to Efron's theorem). It means if you want the variance of your estimator of returns or covariance, you could use bootstrapping.

Bad news:

- if you believe your data are iid and Gaussian, you have a closed form formula,

- if you don't, and especially if you believe in autocorrelations in retruns, bootstrap is the very difficult.

The best reference for bootstrapping non iid series is Giné, E. (1997). Lectures on some aspects of the bootstrap. In E. Giné, G. R. Grimmett, L. S. Coste, and P. Bernard (Eds.), Ecole d'été de Probabilités de Saint-Flour, XXVI, Volume 1665 of Lecture Notes in Math, pp. 37-152. Springer Verlag.

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