UNIVERSITY OF TORONTO Faculty of Arts and Science and Rotman School of Management. Final Examinations, December 2016

Transcription

1 UNIVERSITY OF TORONTO Faculty of Arts and Science and Rotman School of Management Final Examinations, December 2016 RSM 332H1F Capital Market Theory Duration: 2 hours Aids Allowed: Silent electronic calculator and one 1-sided crib sheet 2 Name: Student Number: Circle the section that you are registered in: Burke Corhay (Thu. 9 11a.m.) Corhay (Thu. 11a.m. 1p.m.) Corhay (Thu. 2 4p.m.) Kan (Mon. 11a.m. 1p.m.) Kan (Mon. 2p.m. 4p.m.) Kan (Tue.) Geoffrey (Mon.) Geoffrey (Thu.) Wang Instructions 1. Write your answers on this examination paper. 2. Answer five out of six questions. Each question is worth 20 points. 3. Do not answer all six questions! In the table below, cross out the question that you choose not to answer. Question Marks Total 1

2 1. (a) You just signed a 10-year lease agreement for a business property. The monthly rent for the first year is $2,000/month, with the first month s rent due today. Starting from the second year onward, the monthly rent will be increased by 10%/year (i.e., the monthly rent for the second year will be $2,200, the monthly rent for the third year will be $2,000(1.1) 2 = $2,420, and so on). Assuming the annually compounded interest rate is 8%/year, what is the present value of the 120 monthly rental payments. (10 marks) Consider the following excerpt for parts (b) and (c) Powerball s $900 million bait and switch, Chris Isidore and Ahiza Garcia (CNNMoney, January 9, 2016) What happens when you win the lottery? The likelihood of someone winning $900 million in the Powerball lottery tonight is very slim. And that s not just because the odds of winning are 292 million to one. It s because the jackpot is actually only $558 million (before taxes) if the winner decides to take a lump sum payment. And almost all winners opt for the lump sum. Lotteries always advertise the larger amount, presumably to avoid confusion. But the jackpot would really only be $900 million if the winner opts for a 29-year payout. The longer-term payout is a larger sum because it includes the interest that accumulates from the prize money that is invested over the 29-year period. But out of the 102 Powerball winners in the last seven years, only one chose the larger, but deferred, jackpot. That was Vinh Nguyen, who bought a winning Powerball ticket in September 2014 in San Mateo, Calif., and took the $228 million annuity prize. Another big advantage of the annuity versus the lump sum besides the fact that you ll collect millions of dollars more is that you can t blow all the winnings as fast. Unfortunately, there are lots of stories about lottery winners who blow through their winnings only to end up paupers just a few years later. One of them was Andrew Jack Whittaker of West Virginia, who took a $170 million lump sum in But after that he was robbed often, including one time when he had a brief case full of cash stolen from him at a strip club. Today he s nearly 70 years old and still has to work, and says he wishes he had taken the annuity payments. (b) Suppose the interest rate is 3.7%/year, annually compounded. What is the present value of the 30 annual payments (with a total amount of $900 million), over a 29-year period, assuming the first annual payment will be paid immediately. (5 marks) (c) The Internal Revenue Service (IRS) taxes lottery income at a rate of 39.6%. However, IRS only withholds 28% from the winner s cheque, and the additional 11.6% will be paid when the tax return is filed, say a year later. Suppose you win the jackpot 2

3 and take the 30 annual payments over 29-year option, Assuming that you will receive the first payment immediately, what is the present value of your after-tax winning, assuming the same interest rate of 3.7%/year for part (b). (5 marks) 2. Suppose you observe the following market prices for risk-free bonds Bond Maturity Coupon rate Price T-bill 1 Year 0% $97.5 Canada Bond 3 Years 2.25% $88.53 Canada bond 3 Years 5.25% $96.57 Assume all coupon bonds have annual coupon payments. (a) Use this information to price the following risk-free bonds (with face value 100) 3 year zero-coupon bond. 2 year 5.25% Canada Bond. 3 year 7.25% Canada Bond. (7 marks) (b) Find out the 1-year, 2-year and 3-year spot rates. (6 marks) (c) Without doing any calculations, explain why the yield-to-maturity for the two 3- year Canada bonds given in the table above are different. Explain which one of these two bonds have a higher yield-to-maturity. Is the 3-year bond with higher yield-tomaturity a better investment than the 3-year bond that has a lower yield-to-maturity? Explain your answer. (7 marks) 3. Assume the following information on three different stocks Expected Standard Correlations of Returns Return Deviation Stock A Stock B Stock C Stock A Stock B Stock C The risk-free rate is 2%. There are two portfolios p and q. Portfolio p has 60% in stock A, 20% in stock B, and 20% in stock C. Portfolio q has 20% in stock A, 20% in stock B, and 60% in stock C. (a) Compute the expected return and standard deviation of the two portfolios. (6 marks) (b) Compute the correlation between the returns on the two portfolios. (3 marks) (c) Compute the Sharpe ratio of portfolios p and q. If one of these two portfolios were the tangency portfolio, which portfolio would be the tangency portfolio and why? (4 marks) 3

4 (d) You create a new portfolio with a target expected return of 11% using portfolio p and the risk-free asset. What are the weights on portfolio p and the risk-free asset for this new portfolio, and what is the standard deviation of this new portfolio? (3 marks) (e) You create a new portfolio with a target portfolio standard deviation of 15%, using portfolio q and the risk-free asset. What are the portfolio weights on portfolio q and the risk-free asset for this new portfolio, and what is the expected return of this new portfolio? (Note: There should be two solutions, report the one with higher expected return). (4 marks) 4. Your parents are nearing retirement age. They have asked you, a University of Toronto commerce student, for help making a difficult financial planning decision. For the past ten years your parents have had two different financial advisors, A and B, each managing independent portfolios. Your parents are happy with the services they offer but now want the convenience of having all their investment capital with the same advisor. They have asked you to select the best advisor out of A and B. You plan to use the Capital Asset Pricing Model as the base of your analysis. You have gathered whatever information you could find in your parents financial records and compiled it in the following chart. Historical Data Standard Correlation Average Return Beta Deviation with market 5 yr 10 yr 5 yr 10 yr 5 yr 10 yr 5 yr 10 yr Advisor A 16.0% 12.0% Advisor B % % Market Proxy M % % Market Risk Premium - 9.0% (a) You see that advisor A has produced a Jensen s alpha of zero over the past five years. Explain in two sentences or less what this means about advisor A s performance. Based on this information about advisor A, determine what the average return of market proxy M has been over the past five years. (4 marks) (b) What is the five year historical market beta for financial advisor B. (4 marks) (c) Using 10 year historical data calculate the risk adjusted performance of advisor A and advisor B. Has one manager been outperforming the other, and if so, in what way and by how much? (8 marks) (d) List two potential downfalls of giving your parents financial advice based on the CAPM. Answers should not be longer than a two or three simple sentences or bullet points. (4 marks) 4

5 5. Suppose that a two-factor APT holds, and returns on stocks A, B, C, D follow the factor structure: R A = F 1 0.4F 2, R B = F 1 1.0F 2, R C = F F 2, R D = F 1 0.2F 2, where firm specific errors are assumed away for simplicity. Like in a standard framework, the two factors are demeaned (i.e., E[F 1 ] = E[F 2 ] = 0). (a) Consider a portfolio p with the weights: 20% on stock A, 10% on stock B, 40% on stock C, and 30% on stock D. Calculate the expected return on p, the sensitivity of the portfolio to factor 1 (β p1 ), and the sensitivity of the portfolio to factor 2 (β p2 ). (4 marks) (b) A portfolio q is called a Factor 1 portfolio if the sensitivity of the portfolio to factor 1 is one and the sensitivity to factor 2 is zero, i.e., β q1 = 1 and β q2 = 0. Find the weights of such a portfolio. If the solution is not unique, show that all Factor 1 portfolios have the same expected return. (5 marks) (c) According to the APT, the expected return on any asset i must be: µ i = λ 0 + β i1 λ 1 + β i2 λ 2, where β i1 and β i2 are the sensitivities of the asset i to factor 1 and factor 2, respectively. Calculate the values of λ 0, λ 1, and λ 2. (3 marks) (d) Suppose that the sensitivities of another stock, E, to factors 1 and 2 are 0.5 and 0.3 (i.e., β E1 = 0.5 and β E2 = 0.3). If the expected return on stock E is 0.12, show that there is an arbitrage opportunity such that one can construct a strategy with a non-zero expected profit but no systematic risk (i.e., the sensitivities of the strategy to both factor 1 and factor 2 are 0). (8 marks) 6. (a) Identify which form of market efficiency (if any) is violated in the following statements. Justify your answer (maximum 2 sentences). (i) Recent research in finance has found that more profitable firms (as measured by gross profits-to-assets) earn significantly higher abnormal returns than unprofitable firms. (2 marks) (ii) Investing in a strategy that takes a long position in a portfolio of high-tech firms and short pharmaceutical companies consistently generates an annual return of 12%. (2 marks) (iii) A double top and bottom occurs when the price of a stock has twice tried to move above a certain price level without success. Research shows that after two unsuccessful attempts at pushing the price higher, abnormal returns are significantly negative. (2 marks) 5

6 (iv) Boeing just secured an important contract with Air Canada. On the day the news was out, the stock price of Boeing generated a statistically significant abnormal return of 3%. (2 marks) (v) Mutual Fund A consistently generated positive Jensen s alphas over the past five years. Other funds using the same trading strategy were not able to generate positive abnormal returns. After some investigation, it was found that Mutual Fund A managers were using insider tips to help them pick stocks. [2 marks] (b) It is 9:59am, and you are sitting at your trading desk. Today Apple, is expected to make an important announcement. You collected the following information on Apple: the required rate of return is 10% per annum, the expected dividend in a year is $8 per share and is expected to grow at a rate of 3% per year thereafter. Assuming that the Gordon growth formula is the appropriate model to price securities and that analysts make correct forecasts, (i) What is the current price of a share of Apple? (3 marks) (ii) At 10:00am, the CEO of Apple, Tim Cook, announces the launch of a new product line: the idrone. Analysts are excited about the potential of this new line of products and update their forecasts. The dividend a year from now is expected to be cut by 25% to finance the R&D of the idrones. Thereafter, the sales of idrones are expected to grow dividend by 5% per year. Compute P A, the post-announcement price of a share of Apple? What is the realized return on the announcement? (5 marks) (iii) Assume that no additional news are released that day concerning Apple. Following the announcement, the stock price slowly increases and reaches P A at 12:00pm. Thereafter, the price stays at P A until stock markets close. Which form of market efficiency (if any) is violated? Justify your answer (maximum 2 sentences). (2 marks) 6