Assume that the true and unknown return R* of a stock (the return that should contain all information about a firm’s fundamentals) is independently and identically distributed over time, with standard deviation σ. Assume further that the observed return Rt is a combination of last period’s true return and this period’s true return:
Rt = a Rt-1* + (1-a) Rt*.
Think of 0<a<1 as underreaction and a<0 as overreaction by investors to information.
a. Derive formulas for the variance and the autocorrelation of observed returns.
b. Evaluate the autocorrelation obtained above for a = 1/3 and a = -1/3 and
compare. What conclusions can we draw?