Optimal Investment and Asymmetric Risk for a Large Portfolio: A Large Deviations Approach

Posted: 4 Sep 2008

See all articles by John Knight

John Knight

University of Western Ontario, Faculty of Social Science, Deparment of Economics (Deceased)

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics

Ba M. Chu

Carleton University

Date Written: September 3, 2008

Abstract

In reality, hedge funds staffs more often than not face the problem of optimal asset allocation for large portfolios of investable stocks. In this study, we propose a new method based on the large deviations theory to select an optimal investment for a large portfolio such that the risk, which is defined as the probability that the portfolio return underperforms an investable benchmark, is minimal. As a particular case, we examine the effect of two types of asymmetric dependence; 1) asymmetry in a portfolio return distribution, and 2) asymmetric dependence between asset returns, on the optimal portfolio invested in two risky assets. Furthermore, since our analysis is based on a parametric framework, this allows us to formulate a close-form relationship between the measures of correlation and the optimal portfolio. Finally, we calibrate our method with equity data, namely S&P 500 and Bangkok SET. The empirical evidence confirms that there is a significant impact of asymmetric dependence on optimal portfolio and risk.

Keywords: Optimal portfolio, The Edgeworth expansion, Asymmetric Risk, Large deviations, Asymmetric Gamma distribution, Nonlinear correlations, Value at Risk

JEL Classification: C4, D8, G11

Suggested Citation

Knight, John L. and Satchell, Stephen E. and Chu, Ba M., Optimal Investment and Asymmetric Risk for a Large Portfolio: A Large Deviations Approach (September 3, 2008). Available at SSRN: https://ssrn.com/abstract=1262611

John L. Knight

University of Western Ontario, Faculty of Social Science, Deparment of Economics (Deceased)

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom
44 (0)1223 335213 (Phone)
44 (0)1223 335475 (Fax)

HOME PAGE: http://www.econ.cam.ac.uk/faculty/satchell/index.h

Ba M. Chu (Contact Author)

Carleton University ( email )

Department of Economics
Ottawa, Ontario K1S 5B6
Canada

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