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Volume 12/Number 4, Summer 2010 Research Papers Optimal portfolio choice using the maximum Sharpe ratio Ross A. Maller
School of Finance & Applied Statistics and Centre for Financial Mathematics, Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia; email: Ross.Maller@anu.edu.au Robert B. Durand
University of Western Australia, M250 Nedlands, Western Australia 6009, Australia; email: Robert.Durand@uwa.edu.au Hediah Jafarpour
Department of Mathematics and Statistics, Faculty of Sciences, Islamic Azad University – Shiraz Branch, Shiraz, Fars, Iran; email: hedieh.jafarpour@gmail.com This paper analyzes the properties and performance of daily realized futures hedge ratios. Using five-minute data from the Spanish IBEX 35 equity spot and futures market, realized variances, covariances and hedge ratios are constructed. The realized variances and covariances exhibit long memory dependency that is consistent with extant research on other markets, while the realized hedge ratios do not exhibit this property. To measure performance, we compared a hedged portfolio based on the realized hedge ratio with hedged portfolios constructed using a constant regression-based hedge ratio, a time-varying rolling regression hedge ratio and a time-varying bivariate generalized autoregressive conditional heteroscedasticity (GARCH) hedge ratio. Our results suggest that, solely in terms of minimizing portfolio variance, the static regression, rolling regression and GARCH-based methods perform better, ie, they yield smaller portfolio variances; however, this often comes at the expense of negative mean values. In contrast, if performance measurement takes into account both mean and variance by using the Sharpe ratio, then the portfolio based on the realized hedge ratio is almost unanimously favored. Furthermore, as the realized hedge ratio is simple in construction and does not involve estimating a large number of parameters, this method could be of interest to the finance industry, although its volatile nature may limit its usefulness.
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