Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?

We show in any economy trading options, with investors having mean-variance preferences, that there are arbitrage opportunities resulting from negative prices for out of the money call options. The theoretical implication of this inconsistency is that mean-variance analysis is vacuous. The practical implications of this inconsistency are investigated by developing an option pricing model for a CAPM type economy. It is observed that negative call prices begin to appear at strikes that are two standard deviations out of the money. Such out-of-the money options often trade. For near money options, the CAPM option pricing model is shown to permit estimation of the mean return on the underlying asset, its volatility and the length of the planning horizon. The model is estimated on S&P 500 futures options data covering the period January 1992–September 1994. It is found that the mean rate of return though positive, is poorly identified. The estimates for the volatility are stable and average 11%, while those for the planning horizon average 0.95. The hypothesis that the planning horizon is a year can not be rejected. The one parameter Black–Scholes model also marginally outperforms the three parameter CAPM model with average percentage errors being respectively, 3.74% and 4.5%. This out performance of the Black–Scholes model is taken as evidence consistent with the mean-variance analysis being vacuous in a practical sense as well.