An Algorithm to Calculate the Return Distribution of Portfolios with Option Positions

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Abstract
The use of options in altering the return distribution of stock portfolios has found increasing interest among investment managers. The potential of options in forming portfolio return distributions that are more consistent with investor preferences has been well developed, but determining the actual effect of options on portfolio returns remains a complex and unsolved problem. The purpose of this paper is to describe an algorithm for determining the return distribution that will result when option positions are taken on stocks in a portfolio. The distribution is determined for a finite time horizon, and does not rely on the assumption of continuous portfolio revisions. Simulation tests on the algorithm are also discussed. The algorithm is then used to illustrate the effect that several simple and well-known options strategies will have on portfolio return characteristics. This algorithm will be of practical value, giving a technique for generating and analyzing the expanded opportunity set that exists by using options in portfolio management.