Optimizing a Portfolio of Equities, Equity Futures and Equity European Options by Minimizing Value-at-Risk - A Simulated Annealing Framework

Student Name: Ajay Raina

Value-at-Risk, defined as a given quantile of a portfolio of loss, was minimized to obtain optimal allocation of a unit capital into different elements of the portfolio. The considered portfolio included equities, equity futures, and European options on the equities, which made the return and thus loss non-linear, requiring numerical techniques for optimization. The loss distribution for a given composition of a portfolio was computed using monte-carlo simulation, while the optimization of this composition was performed using simulated annealing, with the iterative step involving generation of random vectors from a Dirichlet distribution with a mean at the current step and variance controlled by another parameter determined by near-optimality of the solution.