The Two-Parameter Long-Horizon Value-at-Risk

20 Pages Posted: 16 Apr 2010  

Guy Kaplanski

Bar-Ilan University - Graduate School of Business Administration

Haim Levy

Hebrew University of Jerusalem - Jerusalem School of Business Administration; Fordham University

Multiple version iconThere are 2 versions of this paper

Date Written: April 1, 2010

Abstract

Value-at-Risk (VaR) has become a standard measure for risk management and regulation. In the case of a two-parameter distribution, a common method among practitioners is first to calculate the daily VaR and then to apply it to a longer investment horizon by using the Square Root Rule (SRR). We show that the SRR is theoretically incorrect and propose a correct measure. The error from employing the SRR is positive for short horizons, inducing an overestimation of the true VaR, and negative for longer horizons, inducing underestimation of the true VaR. This error is relatively small for conservative portfolios and for short horizons. However, for risky portfolios and for long horizons – where accurate VaR is most important – the underestimation error is both substantial and systematic.

Keywords: Risk Analysis, Risk Management, Value-at-Risk, Basel Regulations, Square Root Rule

JEL Classification: C10, C13, C46

Suggested Citation

Kaplanski, Guy and Levy, Haim, The Two-Parameter Long-Horizon Value-at-Risk (April 1, 2010). Frontiers in Finance and Economics, Vol. 7, No. 1, pp. 1-20, 2010. Available at SSRN: https://ssrn.com/abstract=1590773

Guy Kaplanski (Contact Author)

Bar-Ilan University - Graduate School of Business Administration ( email )

Ramat Gan
Israel

Haim Levy

Hebrew University of Jerusalem - Jerusalem School of Business Administration ( email )

Mount Scopus
Jerusalem, 91905
Israel

HOME PAGE: http://pluto.huji.ac.il/~mshlevy/

Fordham University ( email )

140 West 62nd Street
New York, NY 10023
United States

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