Question 1

Assume that you have a risky portfolio consisting of only two assets; a portfolio of risky debt (D) and a portfolio of risky equity (E). Prove that the maximization of the Sharpe Ratio for this portfolio results in an optimal weight of debt of wD

Review Session 1 Question 1 Assume that you have a risky portfolio consisting of only two assets; a portfolio of risky debt (D) and a portfolio of risky equity (E). Prove that the maximization of the Sharpe Ratio for this portfolio results in an optimal weight [E(rD)_rf]Glza[E(rE)rf]PDE'D'E f debt wa = [E(rD)rf]o+[E(rE)rdozn-Dian)-rf+E(rE)rf]pDEaDoE . [20 points] Question 2 You have a risky portfolio of debt that has an expected return of 6% and a standard deviation of returns of 14%. You also have a risky portfolio of equity that has an expected return of 15% and a standard deviation of returns of 26%. The correlation between the two is 0.35 and the risk-free rate is 2.5%. a. What are the weights of debt and equity in the optimal risky portfolio? [5 points] b. What is the slope ofthe capital allocation line that passes through this optimal portfolio? [3 points] Question 3 You are considering buying a TransCanada Pipelines Ltd. bond. The bonds mature in 4 years, make semiannual coupon payments and have a coupon rate of 5.60%. The current yield to maturity on these TransCanada bonds is 4.30%. a. What is the modified duration of these TransCanada bonds? [4 points] b. What is the convexity associated with the TransCanada bond prices? [4 points] c. Use the duration and convexity for the TransCanada bonds to determine the price change associated with a 150 bps decline in yields? [3 points] d. Assume that you will buy 1,000 TransCanada bonds and combine them with your existing holding of Bombardier Inc. bonds, of which you have 1,500. These bonds mature in 6 years, make annual coupon payments, have a coupon rate of 7.45% and are currently priced to yield 8.65%. What is the resulting sensitivity of your bond portfolio to large changes in interest rates {i.e., show the values of duration and convexity in the equation g = D*Ard + iConvexity(Ard)2}? [6 points] Question 4 Monthly series V122544: Government of Canada benchmark bond yields - long-term DO\" A V122544 201701 2.45 V122553: Real return bond - long term Date ' \"22553 2017-01 0.70 a. Using the yields on Government of Canada bonds presented above, what is the anticipated long-term annual inflation rate? [6 points] b. If your marginal tax rate is 45%, what is your before- and after-tax real return from investing in Government of Canada bonds? [6 points] Monthly series V122544: Government of Canada benchmark bond yields - long-term Date A wusu 2016-01 2.05 V122553: Real return bond - long term Date ' \"22553 201601 068 Compare the nominal and real rates for January 2016 (above) with those forJanuary 2017 (the first table in Question 5) and explain what happened to interest rates and inflation expectations year-overyear. [8 points]