Constructing portfolios using stable distributions: The case of S&P 500 sectors exchange-traded funds

Abstract

Portfolio construction is an important practical problem in finance. In the traditional approach, introduced by Markowitz, one assumes normally distributed returns and constructs a portfolio with a minimum risk (measured by the standard deviation of portfolio returns) for a specified (and minimally acceptable) return.In practice, returns are not normally distributed and have heavy tails. As a result, the normality assumption severely underestimates risk. It has been long suggested that a more appropriate way is to model returns by using alpha-stable distributions.In this paper, we use elliptical stable distributions for optimal stable portfolio construction. We illustrate this by considering portfolios from S&P 500 sector exchange-traded funds (ETFs).Our main results indicate that stable portfolios are in general comparable with standard Markowitz portfolios. But we discovered a few properties of stable distributions that are promising for optimal portfolio selection problem. Stable risk estimation for next year is much closer to the actual portfolio risk, stable portfolios are more balanced, so they better handle maximum restriction on component weights, and stable portfolios are more resilient to extreme market conditions.Both stable and normal optimal portfolios outperform S&P 500 index and equally-weighted ETF portfolio in most years.We propose an investment strategy that uses both stable and normal distributions for building optimal portfolios. The return of this strategy exceeds the return of the strategies which use only stable or only normal distributions.