Question 1 1) Find and state the generalized central limit theorem applicable to so-called stable distributions with infinite variances. 2) How does this differ from the CLTs that we saw in lecture? 3) Suppose that were going to construct a portfolio that well hold for a few years, i.e., hundreds of days. There are several assets available for investment, and their respective daily returns all follow different (infinite-variance) stable distributions (for simplicity, assume that all future returns are independent of all past returns). What are the implications for portfolio optimization? Why would portfolio optimization be more complicated? [Hint: Read a little bit about the properties of stable distributions.]

Question 2 Note: You are expected to use some sort of computational software to answer this question. MATLAB and Python are good options. Excel is also acceptable, but discouraged on general principle. Two securities, A and B, have normally distributed returns with following parameters: !~(0.01,2) "~(0.02,5) = 0.3 1. Plot the feasible mean-standard deviation [, ] combinations assuming that the two securities are the only risky investment assets available and short-selling is not allowed. 2. Plot the feasible mean-standard deviation [, ] combinations assuming that the two securities are the only risky investment assets available and short-selling is allowed. 3. Show on a graph (standard deviation on the x-axis and mean on the y-axis) the portfolios that belong to the mean-variance efficient set. Question 3 Prove a 3-fund theorem. [Hint: this question should take you about 30 seconds if you do it correctly.]