An Application of Maximum Entropy Bootstrapping for Portfolio Construction - Yao, Azriel (Quezon City University of the Philippines, 2023)
ABSTRACT

Investors are faced with task of allocating their finite capital to a variety of investments over their individual investment horizons. Computing the historical return on investment is straightforward, but future returns are not guaranteed. Investors may also need to liquidate the investment earlier than expected. For this reason, risk is taken as the volatility of returns. The problem facing investors is to maximize future returns while minimizing risk.

Modern Portfolio Theory prescribes an asset allocation based on expected returns and expected risks of the assets. It also takes into account the pairwise correlations between different assets. This lowers the expected risk for the portfolio as a whole. Under Modern Portfolio Theory, the asset allocation problem is reduced to one of maximizing the expected return while simultaneously minimizing the risk, for the entire portfolio. This process results in the optimal portfolio. However, this Mean-Variance Optimization model is very sensitive to inputs; relatively small changes in expectations could lead to substantially different asset allocations.

Maximum Entropy Bootstrapping is a method of bootstrapping that aims to retain the shape and the time independence structure of the time series (both the autocorrelation function and partial autocorrelation function), which is particularly important for financial time series. This method was used to simulate multiple scenarios for Mean-Variance Optimization, and the resulting optimal asset allocations were combined.

The result is an asset allocation that performs better out of sample that that which relies only on a single point estimate. Across different levels of risk, the risk-adjusted return on this new portfolio is higher than one that uses only Mean-Variance Optimization. Additionally, the portfolio is less sensitive to changes in inputs.
Keywords: Maximum Entropy Bootstrapping; Financial Time Series; Asset Allocation; Mean Variance Optimization