Finish Q9 with submitting an excelwriter can use template in “eq3” file
2/25/2021 Quiz: Midterm Exam https://courseworks2.columbia.edu/courses/125086/quizzes/88453/take 9/12 f) You would invest 100% of your money at the risk-free rate. 94 ptsQuestion 9 Open Answer Questions Fixed Income (47 Points) Unless stated otherwise, assume that all coupons are paid semi-annually, all yields are compounded semiannually, all par values are $100, and investors can buy/sell any fraction of a bond. Rafael Djokerer is a promising young tennis star who has recently turned professional, securing a $500,000 sponsorship deal with the popular sportswear brand Mike. Rafael has decided to invest the money in low-risk bonds, as he intends to buy an apartment in Monte Carlo in three years’ time. As his financial advisor, you are currently considering two potential fixed-income investment strategies. Strategy 1: Invest for the full three years in three-year US Treasury Notes with a coupon rate of 0%, currently yielding 3% per annum. Strategy 2: Invest for the first year in one-year, zero-coupon US Treasury Bills, currently yielding 1% per annum. Then, after one year, immediately reinvest all proceeds for the remaining two years at the forward rate of 3.5% per annum, which is currently offered by Doytshire Bank. (a) (7 points) Compute the final dollar value of Rafael’s investment after three years, according to each of the two strategies. If there are no transaction costs when buying or selling US government bonds, which strategy would be preferred? What does this imply about the forward rate offered by Doytshire Bank? (b) (7 points) Compute the “no-arbitrage” forward rate implied by the yields on the one-year and three-year Treasuries. SY－Kristine SY－Kristine 2/25/2021 Quiz: Midterm Exam https://courseworks2.columbia.edu/courses/125086/quizzes/88453/take 10/12 (c) (7 points) Using the yields on the two Treasury bonds and the forward rate you found in part (b), construct a portfolio of one-year and three-year Treasuries such that the portfolio’s cash flows are identical to the cash-flows of the forward contract. How many of each bond does this portfolio hold (long or short)? What is its cost today (year 0)? Shortly after you have executed the necessary trades to invest Rafael’s $500,000 in the three-year T-Note, he tells you that he has changed his mind about moving to Monte Carlo in three years. Since all his friends already live there, he now wants to move in one year, and will need access to his savings then. (d) (6 points) Should Rafael expect to earn a return equal to the bond’s 3% annualized yield (taking semi-annual compounding into account) if he sells the T-Note after one year? Why/why not? (e) (6 points) Compute the Macaulay and Modified durations of the three-year T-Note. (f) (7 points) If the yield curve shifts up by 2%, by what percentage would you predict the price of the T-Note to change based on the Modified duration? How would the actual price change compare to this approximation? Explain your answer. After explaining the above to Rafael, he asks if there are any other investments that might offer a higher expected return. You suggest a one-year zero-coupon corporate bond issued by the smartphone manufacturer, Pear. Based on your credit analysis, you estimate that the probability that Pear will default is 5%, and that bondholders will recover only 50% of their investment in the event of a default. (g) (7 points) If the bond is currently trading at a price of $91, compute its yield and expected return. Explain why the two differ. (Assume annual compounding for this question.) Equity (47 Points) Your investment portfolio currently comprises of 50% investment in a broad market ETF (Broad) and 50% in an Emerging Markets ETF (EM). You expect the volatility and expected return of these two ETFs to be as follows: Broad: ?[?] = 5%; ? = 12% EM: ?[?] = 10%; ? = 38% Additionally, the correlation between these two ETFs is ? = 0.4. SY－Kristine SY－Kristine 2/25/2021 Quiz: Midterm Exam https://courseworks2.columbia.edu/courses/125086/quizzes/88453/take 11/12 a) (5 points) Given a risk-free rate of 2.5%, what is the Sharpe Ratio of the two ETFs? b) (6 points) What is the Sharpe Ratio of your current 50-50 portfolio? You first would like to assess whether the current percentage of capital invested in these two ETFs is appropriate. c) (6 points) Could you increase the Sharpe Ratio of your risky portfolio by changing the percentage of your capital that’s invested in the two ETFs? If so, what are the optimal weights? You have taken a questionnaire and found out that your risk-aversion coefficient is ? = 3. Additionally, you can borrow and land at the risk-free rate of 2.5%. d) (6 points) Given this additional information, would you still invest 100% of your capital in the two risky ETFs? If not, how would you optimally allocate your portfolio? Give the optimal weight in all assets that comprise your portfolio. Lately, you have started paying more attention to the stock market, trying to identify undervalued stocks to add to your portfolio. You have set your eyes on HouseWise, an innovative home-appliances manufacturer that you believe has great growth opportunities. The stock is currently trading at $130 per share and has recently paid a dividend of $5 per share. You have assessed HouseWise’s cost of capital to be 9%. Additionally, you believe that for the next 6 years HouseWise will grow at a very high rate of 12%, and it will then keep growing in perpetuity at the lower rate of 4%. You strongly believe in your analysis. e) (6 points) Using the dividend discount model, what is your assessment of HouseWise’s fair value? Do you still think this would be a good investment opportunity? If so why? You expect to sell your HouseWise investment in 1 year and you expect that in that timeframe the price of HouseWise will converge to its fair value. f) (6 points) What is your expected return from that investment? SY－Kristine SY－Kristine 2/25/2021 Quiz: Midterm Exam https://courseworks2.columbia.edu/courses/125086/quizzes/88453/take 12/12 Quiz saved at 11:06pm Upload After further research you assessed that the volatility of HouseWise is 42% and its correlation with Broad and EM is 0.35 and 0.30 respectively. g) (6 points) Given that information, would you add HouseWise to your risky portfolio? If so, explain why and what would be the weights of the assets in the risky portfolio (Broad, EM and HouseWise). h) (6 points) Would this change your optimal allocation between the risky portfolio and the risk-free rate? If so, what would be the final weights in your portfolio. Choose a File Submit Quiz SY－Kristine SY－Kristine My Bookmarks