3. (15 points) Suppose an investor invests $100 in a stock that in each period can…

3. (15 points) Suppose an investor invests $100 in a stock that in each period can either double or half with equal probability. The returns in each period are uncorrelated a. Calculate the variance of the investors’ dollar position after one period. b. Calculate the variance of the investor’s dollar position after holding the stock for two periods c. Suppose there are two independent stocks: each stock can either double or half with equal probability. Assume the investor invests 850 in one stock and 850 in another stock. Calculate the variance of the investors’ dollar position after one period. c. Why the variances in (b) and (c) are different?