Is Mean-Variance Analysis Vacuous: Or was Beta Still Born? |
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Authors: | Jarrow Robert A; Madan Dilip B |
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Institution: | Johnson School of Management, Cornell University and Kamakura Corporation
University of Maryland |
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Abstract: | We show in any economy trading options, with investors havingmean-variance preferences, that there are arbitrage opportunitiesresulting from negative prices for out of the money call options.The theoretical implication of this inconsistency is that mean-varianceanalysis is vacuous. The practical implications of this inconsistencyare investigated by developing an option pricing model for aCAPM type economy. It is observed that negative call pricesbegin to appear at strikes that are two standard deviationsout of the money. Such out-of-the money options often trade.For near money options, the CAPM option pricing model is shownto 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 coveringthe period January 1992September 1994. It is found thatthe 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 hypothesisthat the planning horizon is a year can not be rejected. Theone parameter BlackScholes model also marginally outperformsthe three parameter CAPM model with average percentage errorsbeing respectively, 3.74% and 4.5%. This out performance ofthe BlackScholes model is taken as evidence consistentwith the mean-variance analysis being vacuous in a practicalsense as well. |
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