A test of historical and shrinkage estimates of expected returns in international portfolio selection : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Finance at Massey
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A number of researchers have chosen internationally diversified portfolios using the Mean-Variance approach to portfolio selection. Typically, the estimates of expected returns, variances and covariances are taken from historical data. Recently this approach has come under criticism due to the poor performance of these portfolios out of the sample period. A suggested improvement is to use "shrinkage" estimators to improve the estimates, particularly for expected returns. This statistical adjustment leads to less emphasis being placed on increasing expected return and more on risk reduction. The researchers to test shrinkage estimates internationally have had conflicting results, possibly due to the methodology used. Jorion (1985) found support for shrinkage estimators outperforming historical estimates, with short sales unconstrained. A single period model with a five year sample was used. Grauer and Hakansson use a multi-period model, with short sales restricted. The sample period is eight years in this instance, and the opposite result is obtained. This study tests both types of mean estimate in a single period model, with short sales restricted. The difference in out of sample performance is insignificant with both four and eight year samples. Additionally, a naive strategy of weighting the portfolio equally between countries, thereby ignoring the historical data, outperforms the other methods. Thus, the use of four year sample periods appears to be of no use. With the eight year sample the performance of all methods is remarkably similar, with a portfolio chosen to minimise variance having the best performance, although only slightly. The use of historical data, whether or not shrinkage estimates are used, has proved to be of very little benefit in this study.
Investments, Statistical methods