Indications of Risk: Standard Deviation of Returns or VaR of Terminal Wealth?

Abstract

Investors with long time horizons are more concerned with the dispersion of their terminal wealth than with within-period volatility of asset returns. The risk of terminal wealth will indicate whether the liquidated value of the portfolio will be sufficient to finance liabilities. In this paper we apply three different strategies to construct portfolios using the historical returns of five asset classes and report their performance over several time horizons. These three investment strategies are: mean-variance optimized portfolios, Roy’s safety first rule, and Value at Risk, VaR to minimize the impact of downsize risk when selecting portfolios. The distributions of terminal wealth generated from these portfolios are used to compare these investment strategies.