SOLUTIONS TO THE PORTFOLIO CHOICE PROBLEM WITH VAR OBJECTIVE FUNCTIONS
SOLUTIONS TO THE PORTFOLIO CHOICE PROBLEM WITH VAR OBJECTIVE FUNCTIONS

Summary/Abstract: In the context of modern portfolio theory (MPT), the actual weights of the market portfolio and cash are determined by investor preferences for risk and return. Value at risk (VaR) models specify losses with a percent frequency. VaR models are popular because they are easy to explain and interpret. In the context of MPT, the VaR limits in this study are used like a utility function for the investor. This paper develops closed-form solutions to the multi-asset portfolio choice problem using matrix algebra for the investor’s ideal portfolio weights, volatility, and expected returns where the VaR limit binds. pp. 29–46JEL codes: G11

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