The Sortino ratio and the generalized Pareto distribution:
an application to asset allocation
Geoffrey Booth – Michigan State University
John Paul Broussard – Rutgers University

Extreme events in finance

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Problem with the measure of risk in traditional asset allocation model

Asset allocation decisions are generally made within traditional modern portfolio theory (MPT) construction techniques. One creates portfolios that benefit from diversification within a mean-variance setting. What happens, though, in a situation where variance does not accurately capture the risks associated with losses beyond a comfortable level? Extreme value techniques provide valuable probabilities of large losses, and hence, assist the portfolio construction decision using the Sortino ratio.

Use of extreme value techniques

Our effort incorporates extreme value techniques, and the Sortino Ratio portfolio performance measure, to consider how large losses above a defined amount to impact the benefit vs cost analysis of an asset allocation decision. Using Real Estate Investment Trusts (REITs) as a proxy for the real estate asset class, we find that the old rule-of-thumb indicating 3% to 5% exposure to real estate may not be as out of line as recently thought. Using our approach provides benefit to the asset allocation decision-maker who wishes to better understand the impact large losses have on an overall portfolio.

Why is this analysis important?

Mean-variance portfolio optimization provides a useful structure for making asset allocation decisions. When returns are extreme, though, the traditional approach may not provide the outcome desired. Our analysis illustrates how one can adjust the traditional approach to better incorporate large losses and their can effect on an overall portfolio of assets.

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Geoffrey Booth, Michigan State University

Geoffrey Booth

Michigan State University

John Paul Broussard, Rutgers University

John Paul Broussard

Rutgers University