Using equity premium survey data to estimate future wealth

We present the first systematic methods for combining different experts' responses to equity premium surveys. These techniques are based on the observation that the survey data are approximately gamma distributed. This distribution has convenient analytical properties that enable us to address three important problems that investment managers must face. First, we construct probability density functions for the future values of equity index tracker funds. Second, we calculate unbiased and minimum least square error estimators of the future value of these funds. Third, we derive optimal asset allocation weights between equities and the risk-free asset for risk-averse investors. Our analysis allows for both herding and biasedness in expert responses. We show that, unless investors are highly uncertain about expert biases or forecasts are very highly correlated, many investment decisions can be based solely on the mean of the survey data minus any expected bias. We also make recommendations for the design of future equity premium surveys.