THE ALTERNATIVE SHARPE RATIO Bernard Lee and Youngju Lee
INTRODUCTION
Lee and Lee apply the tools of portfolio optimization to the problem of selecting a portfolio of hedge funds, i.e., building a fund of funds (“FoF”). Their approach provides an important supplement to the qualitative work of FoF managers in the assessment of individual portfolio managers for possible inclusion in their portfolio of funds.
Their quantitative approach is guided by very practical issues. First, they recognize that elegant mathematical models, while interesting in the abstract, need to be balanced against the need for ease of implementation and interpretation.
Second, they recognize that actual return characteristics of hedge funds, more specifically the negative skewness and excess kurtosis observed empirically, raise questions about the applicability of standard Markowitz meanvariance portfolio optimization.
An added benefit of their approach is the development of an alternative performance ratio that is robust to the departures from normality that lessen the usefulness of the Sharpe Ratio.
Sharpe has argued for some time that the appropriate way to measure the desirability of an asset is by it’s impact on the portfolio’s Sharpe Ratio, not by its stand alone Sharpe Ratio (See, http://www.stanford.edu/~wfsharpe/art/sr/sr.htm).
Lee and Lee extend this idea to show that the optimal fund of funds portfolio is found by choosing the particular allocations to various funds, such that each individual candidate fund’s Alternative Sharpe Ratio (“ASR”), measured by its contribution to the FoF’s risk, is equal to the FoF’s ASR (in some cases with an added adjustment factor).
Lee and Lee describe a very practical approach to implementing this optimization in a way that recognizes that there is little value to being overly precise, if in practice investors are unlikely to allocate their assets in very tiny bits, maybe no smaller than one percent or onehalf of one percent. They are able to illustrate with hedge fund index data that their method can yield better cumulative returns and be more sensitive to exposure to drawdowns accompanying extreme market events, such as the Liquidity Crisis of 1998.
return to top
BIBLIOGRAPHY
 Cornish, E. A., and R. A. Fisher, 1937, “Moments and Cumulants in the Specification of Distributions,” Extrait de la Revue de l’Institute International de Statistique 4, 114, reprinted in FISHER, R. A., 1950, Contributions to Mathematical Statistics (New York: Wiley).
 Fernholz, E. R., 2002, Stochastic Portfolio Theory (SpringerVerlag).
view at Amazon.com
 Fung, W., and D. A. Hsieh, 1999, “Is MeanVariance Analysis Applicable to Hedge Funds,” Economics Letters 62, 5358.
http://www.GloriaMundi.org/picsresources/rbfh.pdf
 Jaschke, S., 2001, “The CornishFisher Expansion in the Context of DeltaGammaNormal Approximations,” Working Paper, WeierstrassInstitut für Angewandte Analysis and Stochastik, March.
http://www.jaschkenet.de/papers/CoFi.pdf
 Karatzas, I., and S. Shreve, 1991, Brownian Motion and Stochastic Calculus (2 ed.), (Springer).
view at Amazon.com
 Karatzas, I., and S. Shreve, 1998, Methods of Mathematical Finance, (Springer).
view at Amazon.com
 Markowitz, H. M., 1999, “The Early History of Portfolio Theory: 16001960,” Financial Analyst Journal 55(4), 516.
 Mina, J. and A. Ulmer, 1999, “DeltaGamma Four Ways,” Technical Paper, RiskMetrics Group, August 1999.
http://www.GloriaMundi.org/picsresources/jmau.pdf
return to top
ERRATA AND OTHER MATERIAL
 Other research by Bernard Lee:
Lee, B., 2004, "How to Construct Hedge Fund Portfolios and Structured Products Using a Robust Quantitative Framework", presentation notes.
download (pdf 212K)
return to top
