Modern Portfolio Theory with VaR Objective Functions

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 are used like a utility function for the investor. This paper develops closed form solutions for the investor’s ideal portfolio weights, volatility, and expected returns where the VaR limit binds.

Keywords: modern portfolio theory, MPT, Value at Risk, VaR

JEL Classification: G11