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.