Options and market information: a mean-variance portfolio approach

Abstract

The major objective of this study was to extend the mean-variance portfolio model to incorporate option markets. Previous attempts in the literature have been only partially successful and this is due to an improper specification of the mean vector and variance-covariance matrix of returns. An option introduces special problems in modeling because of its truncated return structure. Conventional mean-variance analysis has not been developed to handle this problem. This study uses a statistical theorem, based upon the definition of a conditional moment, to arrive at a mean vector and variance-covariance matrix of returns for the portfolio containing options;Using the modified portfolio model, several interesting observations were made regarding the informational role of option markets. The determination of the optimal portfolio position was found to be related to the interaction of information incorporation into the speculative and hedging components of the option and futures demand equations. When an individual investor had information only regarding the variance of prices, the straddle position was used to capitalize upon this information;Heterogeneous expectations, among traders, regarding the future spot price variance was found to be a possible justification of speculative trading in commodity options. These information differentials were sufficient to make the option market informationally inefficient in the Grossman-Stiglitz sense. However, information regarding the future spot price mean was found to be a more significant factor in influencing the value-added to an investor's portfolio;The equilibrium option price was found to be a weighted average of each of each investor's subjective valuation of the option, plus some extraneous terms representing the subjective valuations of the futures and a component representing the net hedging pressure upon the market. The introduction of an option market was found to significantly increase the volume of futures trading but had little impact other variables. An examination of the importance of factors influencing the bias of the equilibrium option price from an unweighted average of each investor's subjective value provided inconclusive results.