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1. Portfolio Theory and CAPM a. [5 marks] The risk-free rate is 1 percent, the expected return on the market portfolio is 15 percent, and the expected return of a stock is 12 percent. What is its beta? b. [5 marks] Suppose there is a 10 percent chance of a recession next year. For the two stocks below, calculate the expected return, variance, and covariance. What is the minimum variance portfolio formed of these two stocks? c. [5 marks] Explain how you can construct a portfolio from the two stocks in part (b) above with a standard deviation of 15%. What are the expected return and variance of this portfolio? What are the losses if there is a recession, and what are your gains otherwise? d. [5 marks] Your portfolio manager offers you the following risky portfolios: Which portfolios are dominated? If you can also borrow at the risk free rate of 6%, and you would like a portfolio with a standard deviation of 5%, what is the optimal combination of risk-free assets and risky portfolios above? e. [5 marks] Among the set of risky portfolios in problem (d), identify the optimal portfolio for different ranges of risk-free rates 2 Essay Questions. Keep your answers short and precise (i.e. around five sentences). a. [5 marks] Is the price of a put option higher or lower when the strike price increases (and the maturity stays the same)? Why? b. [5 marks] Can tests of market efficiency by means of abnormal returns conclusively reject the notion of efficiency? Explain your answer. c. [5 marks] Do stock prices following a random walk imply that markets are irrational? Why or why not? d. [5 marks] Suppose you knew in January that the stock market would drop massively due to the pandemic. How could you protect your investments or profit from this knowledge? e. [5 marks] Give an example of an option embedded in a business decision, and the associated costs and payoffs 3 Stock valuation a. [5 marks] Company A currently pays an annual dividend of £10, but the dividend is expected to decline by 5% each year. If the market capitalization rate is 10%, what is the current price of the stock? b. [5 marks] Company B is forecast to pay dividends of £20, £25, and £30 in the next three years. The stock’s price is currently £100, and its expected return is 15%. What is the price expected to be in three years? c. [5 marks] Company C currently pays no dividends, but is expected to start paying a constant annual dividend of £4 starting in year six in perpetuity. Company D is expected to pay a dividend of £6 for 5 years and nothing thereafter. If the stocks trade at the same price, and the market capitalization rate is the same for both firms, what is the current market capitalization rate? d. [5 marks] Company D is growing rapidly. It has book equity of £100 and an ROE of 45 percent. It will not pay any dividends for 2 years. In year 4, its ROE will fall to 10 percent. If the cost of equity capital is 12 percent, what is the maximum share price the company can achieve, and what are the plowback ratios in years 3 and 4 (and onwards) necessary to implement this? e. [5 marks] Company E is stable and profitable, generating annual dividends per share of £8 in perpetuity, and currently trading at £100. It is considering changing its business into a growth venture that would generate earnings per share of £10, with an ROE of 25 percent, and increase its stock price to £200. The market capitalization rate of the firm remains constant. What are the implied market capitalization rate, plowback ratio of the growth company, growth rate and present value of the growth opportunity? 4 Discounting cash flows and bonds a. [5 marks] The term structure of interest rates is currently: 1YR 2YR 3YR 2.0% 1.2% 1.1% Calculate the prices of a one-year zero coupon bond, a two-year bond with a 0.7 percent coupon rate, and a three-year bond with a 1.11 percent coupon rate. The face values of all three bonds is £100 and coupon bonds pay one coupon per year. b. [5 marks] A bond with a face value of £100 pays an annual coupon of 8% for 4 years and its yield to maturity is 6%. The coupon payment is once per year. What is the market price of the bond? c. [5 marks] Suppose you want to retire at 60. You want to have a nice retirement lifestyle, which you expect will require you to spend £50,000 per year, for 40 years in retirement. Suppose there is no inflation, and the annual rate of return on funds invested is 3 percent. How much do you need to have saved by the time you retire? Assume you withdraw your first 50,000 on your 60th birthday (and each birthday thereafter). If you just turned 24, and you already spend £50,000 per year, what annual salary do you need to earn to meet your retirement goal? Assume no salary growth. d. [5 marks] An insurance company has three liabilities of £8 million, £8 million, and £24 million due in one, two, and six years, respectively. The company has £35 million in cash. Interest rates are currently at 4 percent, and the term structure is flat. What is the company's net worth, and what happens to the firm's net worth if interest rates decrease by 1 percent? How can the company hedge against the interest rate risk using one-year and four-year zero-coupon bonds? Assume the face value of these zero-coupon bonds is £10. e. [5 marks] Consider three bonds with prices and cash flows in years 1, 2 and 3 as indicated: Bond Price C1 C2 C3 A 4 1 2 3 B 7 0 5 6 C 18 9 10 0 What is the no-arbitrage price of a one-year zero coupon bond with a face value of £100?