1. There are only two securities (A and B, no risk free asset) in the market. The correlation between returns of A and B is -0.4. Expected returns and standard deviations are as follows: Expected Return Standard Deviation of Returns Stock A Stock B 20% 15% 20% 25% 1.1. 1.2. 1.3. 1.4. 1.5. Would anyone be interested in investing in B? If so, why? What is the expected return and standard deviation of a portfolio that invests 60% in A and 40% in B? Suppose your client wants to form a portfolio out of these securities with the lowest standard deviation. Solve for the portfolio weights analytically. What is the expected return and standard deviation of your portfolio? Now introduce a riskless asset, and the risk free rate is 4%. Now, fixing the standard deviation at a constant level, solve for the portfolio (of the 3 assets) that gives you maximal return. This gives you the tangent portfolio. Now, using the results in (d), what is the optimal portfolio if your client wants a return of (i) 10%, (ii) 20%? What is the ratio between wealth invested in A and B in each case? 2. Recall that risk premium is the excess return of the asset, ri, over the risk-free rate, rf. Sharpe ratio for a given asset, si, is defined as risk premium on a portfolio, or security, per unit of that asset's risk, i. Mathematically, the definition writes: S = ri-rf Consider a portfolio of two assets with weights w and w2, such that w1 + W2 =1. Is the Sharpe ratio of the portfolio equal to the weighted average of the Sharpe ratios of individual assets? Explain. 3. Consider the following eight portfolio investments: Asset 1 Asset 2 Asset 3 Asset 4 Asset 5 Asset 6 Asset 7 Asset 8 Expected Return 12% 8% 6% 3% 2% 5% 21% 0% Variance of 25% 15% 12% 0% 3% 10% 50% 8% Returns 3.1. Which of the assets seem to be efficient and which look like inefficient? Explain. 3.2. How would you compute the betas of assets 2 or 3, if necessary?