Modern Portfolio Theory with VaR Objective Functions

Wilson, Linus

doi:10.2139/ssrn.2516022

Modern Portfolio Theory with VaR Objective Functions

23 Pages Posted: 30 Oct 2014

See all articles by Linus Wilson

Linus Wilson

University of Louisiana at Lafayette - College of Business Administration

Date Written: October 28, 2014

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

Suggested Citation: Suggested Citation

Wilson, Linus, Modern Portfolio Theory with VaR Objective Functions (October 28, 2014). Available at SSRN: https://ssrn.com/abstract=2516022 or http://dx.doi.org/10.2139/ssrn.2516022