Foster-Hart Optimal Portfolios

34 Pages Posted: 26 Mar 2016 Last revised: 26 Apr 2023

See all articles by Abhinav Anand

Abhinav Anand

Indian Institute of Management Bangalore

Tiantian Li

State University of New York (SUNY) - Department of Applied Mathematics and Statistics

Tetsuo Kurosaki

Bank of Japan

Young Shin Kim

College of Business, Stony Brook University

Date Written: March 1, 2016

Abstract

We reinvestigate the classic portfolio optimization problem where the notion of portfolio risk is captured by the “Foster-Hart risk” — a new, bankruptcy-proof, reserve based measure of risk, extremely sensitive to left tail events (Foster and Hart, 2009). To include financial market frictions induced by market microstructure, we employ a general, ex-ante transaction cost function with fixed, linear and quadratic penalty terms in the objective function. We represent the US equity market by the Dow Jones Industrial Average (DJIA) index and study the performance of the Foster-Hart optimal DJIA portfolio. In order to capture the skewed and leptokurtotic nature of real life stock returns, we model the returns of the DJIA constituents as an ARMA-GARCH process with multivariate “normal tempered stable” innovations. We demonstrate that the Foster-Hart optimal portfolio’s performance is superior to those obtained under several techniques currently in use in academia and industry.

Keywords: ARMA-GARCH model, normal tempered stable distribution, Foster-Hart risk, value-at-risk (VaR), average value-at-risk (AVaR), reward-risk ratio

JEL Classification: C13, C22, C61, C52, G11

Suggested Citation

Anand, Abhinav and Li, Tiantian and Kurosaki, Tetsuo and Kim, Young Shin, Foster-Hart Optimal Portfolios (March 1, 2016). Journal of Banking and Finance, Vol. 68, 2016, Available at SSRN: https://ssrn.com/abstract=2753620 or http://dx.doi.org/10.2139/ssrn.2753620

Abhinav Anand (Contact Author)

Indian Institute of Management Bangalore ( email )

Bannerghatta Road
Bangalore, 560 076
India

Tiantian Li

State University of New York (SUNY) - Department of Applied Mathematics and Statistics ( email )

Stony Brook University
Stony Brook, NY 11794
United States

Tetsuo Kurosaki

Bank of Japan ( email )

2-1-1 Nihonbashi-Hongokucho,Chuo-ku
Tokyo
Japan

Young Shin Kim

College of Business, Stony Brook University ( email )

312 Harriman Hall
100 John S. Toll Drive
Stony Brook, NY 11794
United States
6316327171 (Phone)

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