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

Abstract

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. The model estimates a parametric form for the Market Price of Risk, the Sharpe Ratio, of the S&P 500 Index. In addition to short- and long-term riskfree rates of interest, the model's empirical estimation makes use of two forward-looking measures: The economy's growth rate estimate; and the option market's (priced) implied volatility on the S&P 500 Index. The model accounts for past rates of return by modeling and estimating the impact of an assumed increasing relative risk aversion, which gives rise to an increased willingness to invest in risky assets as the realized rate of return for the recent past is "high".

Keywords: Risk Premium, Time-Series, Growth-Rates, S&P 500, VIX Index

JEL Classification: G10, g12