Option-implied preferences adjustments, density forecasts, and the equity risk premium

The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two lognormals and several alternative risk adjustments: the power, exponential and habit inspired based stochastic discount factors. Moreover, by allowing additional flexibility in the shape of the stochastic discount factor, two other ad hoc time varying risk aversion adjustments are also employed. Our results show that, between October 1996 and March 2000, we can reject the hypothesis that the risk neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at four and eight week horizons. When forecasting through risk adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. Somehow surprisingly, all risk adjusted densities generate similar forecasting statistics. Finally, from October 1996 to December 2004, the ex ante risk premium perceived by investors and that are embedded in option prices is between 12 and 18 percent higher than the premium required to compensate the same investors for the realised volatility in stock market returns.