How Efficient is Efficient Frontier?

Student Name: Chakshu Deep Raina

For finding the optimal allocation of assets in a portfolio, which maximizes expected return but minimizes the risk, measured in terms of return volatility or variance, the most popular or standard method employed in practice is Markowitz's mean-variace efficient frontier (MVEF), which essentially formulates and solves the problem as a qudratic programming problem. However the inputs to this quadratic programming porblem, like the mean returns, variances and covariances of the reurns of individual securities being considered in the portfolio, are obtained after collecting observations on the return series of the securities. That is these input parameters are estimated from data, and are thus subject to sampling fluctuation. This statistical issue of the resulting MVEF has largely been ignored in the literature. In this project a bootstrap based modification has been proposed and implemented to obtain better (bias reduced) point estimate and ponit-wise confidence band of the MVEF. Both parametric (under the multivariate Normality assumption about the return of the series) and standard non-parametric booststrap techniques have been carried out. Simulation study shows that the proposed method is very efficient and beats the few ad-hoc techniques that have so far been proposed in the literature for this problem.