Optimization Analysis of Risk/Return of Large Equity Portfolios, Applying Option Strategies

Abstract

This is a study of the risk/return characteristics of large equity portfolios, consisting of different option contracts. In times when there is nervousness present in the financial market, and the future prospects of the market are highly uncertain, the importance of appropriate mathematical models is emphasized by traders. Tools to implement option strategies in different markets will be investigated, in order to minimize the risk and maximize the return of the portfolios. Using various options and statistical simulation methods, the risk/return characteristics of options will be studied. Monte Carlo simulation is used, in order to obtain a thorough understanding of the risk/return characteristics of various option strategies, applied on different indices. As the strategies investigated are meant to be applied by traders, the daily changes in portfolio value are the basis from which the risk of the strategies is estimated. There are various methods of estimating the risk available. In order to examine the risk characteristics, the probability of extreme outcomes is of interest. The Value-at-Risk and the expected shortfall are to be analyzed, when examining the risk of the strategies evaluated. Analyzing the properties of the expected return of the portfolios, the tails of the densities of the portfolio values, for the different strategies and indices, will be of interest.