A Simple Model for Time-Varying Expected Returns on the S&P 500 Index

James S. Doran, Ehud I. Ronn and Robert S. Goldberg

Volume 7, Number 2, Second Quarter 2009

This paper presents a parsimonious, implementable model for the estimation of the short and long-term expected rates of return on the S&P 500 stock market Index. Sufficient statistics for the expected return on the S&P 500 Index consist of the risk-free rate of interest, the option market’s (priced) implied volatility on the S&P 500 Index, and a measure of the economy’s wealth level.

The short- and long-term risk-free rates of interest reflect the impact of the level and slope of the risk-free term structure. The implied volatility captures a forward-looking measure of uncertainty. Utility-function assumed decreasing relative risk aversion gives rise to an increased willingness to invest in risky assets when current wealth level is “high”. The model’s empirical parameters are estimated using Livingston/Philadelphia Fed growth rates substituted into a dividend-discount model.