Over the course of many years, the Gallup survey asks individual investors about their beliefs about the stock market over the next twelve months. We will indicate this future return over the next 12 months as Rt, t+ 12. The survey was conducted at the beginning of each month, call it t. We can take the average of the forecasts across surveyed subjects and call it the consensus expectation from these subjects of the return from time t to time t + 12, Expt[Rt,t + 12]. (1) Two common criticisms of survey data on expected returns are that (a) they are noisy and thus meaningless and (b) people do not mean what they say. Can you make one suggestion on how we can tell whether survey expectations reasonably reflects the expectations of the subjects? (2) In a world consistent with rational models, how should Exp+[Rt,t + 12] predict Rt,t + 12? Briefly explain. (3) You run a regression as follows: Rt,t + 12 = a + Expt[Rt,t + 12] + &t where your left-hand side variable is Rt,t + 12 and your right-hand side variable is Expt[Rt,t + 12] Rt,t + 12 is what actually happened over the 12 months after the survey. You find a coefficient on Expt[Rt,t + 12] of -7.485 with a t-statistic of -4.864. Is this consistent with the rational model of the world you discussed in part (1)? Briefly explain. Your explanation should include attributes of both of these two numbers. (4) To explore this further you run the regression of the forecast of returns on the returns that occurred over the year prior to the survey, Rt 13, t1. This is a regression of expectations of future returns on past returns: Exp:[Rt,t + 12] = a + R+ 13,t 1 + & You find a coefficient of 91.227 with a t-statistic of 8.811. Describe a behavioral concept that is consistent with the regression results. Your explanation should include attributes of both of these two numbers.