Sample size and Markowitz diversification

A lthough more than a quarter of a cen18 2 r r E tury has passed since Markowitz presented his concept of diversification and an algorithm for selecting assets within a mathematical optimization framework [21], the implementation of his approach still seems to have been retarded by the volume of data needed and the computational effort required.’ Therefore, this study investigates the effect of sample size on the efficient frontier in order to assess the marginal benefit of working with larger and larger efficient sets. The results suggest that, on the basis of a single index model to develop informational inputs for common stocks, the marginal benefit of increased sample size is slight beyond a couple of hundred securities. Markowitz’s full covariance model requires expected returns, standard deviations of returns, and expected covariances between all asset returns as data inputs. A quadratic programming algorithm is then applied to the data to identify efficient portfolios. In order to reduce the computational and data requirements, a number of modifications have been proposed