Question 2 and Question 5 from the uploaded file.

FFM BPES Winter Semester 2015 Marcin Kacperczyk Homework 3 Due Tuesday 03/24 (any time during the day) Hard copy only. One copy per group Question 1: Suppose that there are two securities RAIN and SUN. RAIN pays $100 if there is any rain during the next world cup soccer final. SUN pays $100 if there is no rain. Suppose that the world cup soccer final is 1 year from today, and suppose that RAIN is trading at a price of $23 and SUN is trading at a price of $70. (a) If you buy 1 share of RAIN and 1 share of SUN, what is your payoff after 1 year depending on the weather? (b) What does the No-Arbitrage Condition imply about the price of a 1-year zero-coupon bond? (Assume no trading costs.) (c) Suppose that a 1-year zero-coupon bond is trading at $90. Show how you would set up a transaction to earn a riskless arbitrage profit. (Assume no trading costs.) (d) Suppose that trading zero-coupon bonds is costless, but trading RAIN and SUN each cost $2 per $100 face value. Can you still make an arbitrage profit? Question 2: Consider a market in which currently two assets are traded: (1) A stock, currently selling for $40, which is expected to increase in value by 40% or decrease in value by 20% every year. (2) A zero-coupon risk-free bond with one year maturity that costs $100 and offers 2% annually compounded interest. Suppose the financial institutions are considering the sale of the third asset with maturity of one year whose value at maturity equals max(S-40, 0)? S is the value of the stock at the time the asset matures and max(x, y) equals the greater of the two values x and y. a) What should be the fair price of this asset today? b) Suppose the price of this asset today equals $4. Is there anything you could do to make arbitrage money and implement your \"Bora-Bora dreams\"? Show formally the arbitrage strategy. Question 3: Explain why the following statements are true/false/uncertain. a. Holding all else constant, a firm will have a higher P/E if its beta is higher. b. P/E will tend to be higher when ROE is higher (assuming plowback is positive). c. P/E will tend to be higher when the plowback ratio is higher. 1 Question 4: Yippie is a recent startup and is currently not paying any dividends. The earnings at the end of 2015 are expected to be $4 a share and analysts predict that Yippie's earnings will grow at an annual rate of 30% for the next three years (until 2018). The return of new investments of Yippie is expected to be 10% indefinitely starting in 2019. Yippie is expected to start paying annual dividends in 2019 and these dividends will be equal to 60% of the earnings. Assume that all earnings accrue at the end of the year and that the dividends are also paid once at the end of the year. Yippie has a beta of 1.5, the market return is 7%, and the risk-free rate is 2%. a. What is the intrinsic value of Yippie's stock at the end of April 2015 using the dividend discount model? b. Should Yippie increase or decrease its dividend payout ratio starting in 2018? Briefly discuss the reasons. c. The main competitor of Yippie has a stock price of $25 and expected earnings of $1 per share in 2015. What is the intrinsic value of Yippie's stock using the price-earnings multiplier method? Question 5: Long-Term Capital Management was a prominent hedge fund of Greenwich, Conn, whose partners included two Nobel Prize winners. In September 1998, a cash infusion of $3.5 billion from a consortium of commercial banks and investment firms rescued this hedge fund with the support from the Federal Reserve Bank of New York. Among the many strategies employed by the firm was one in which Treasury Bonds were shorted and the proceeds of these sales were used to purchase higher yielding (and higher risk) mortgage-backed or corporate debt securities. The strategy - known as playing a credit spread - generates huge profits as long as bond yields remain stable. But since the stock market began plunging in July of 1998, investors fled for cover in the quality of liquid U.S. government securities and required higher risk premia on all risky assets. This question analyzes the risk of this investment strategy in a highly stylized example. Suppose in September 1997, the fund was invested in the following two positions: A long position of 1,000,000 less liquid fixed-income securities (LLS) (such as off-the-run Treasury securities, mortgage-backed securities, corporate bonds, etc.) maturing in 5 years with an annual interest payment of 7.5% (each bond has a face value of $100,000). A short position of 950,000 Treasury securities (TS) maturing in 5 years with an annual interest payment of 6.5% (each bond has a face value of $100,000). The table summarizes the yield curve of zero-coupon bonds in September 1997 and September 1998: 2 Maturity 1 Year 2 Years 3 Years 4 Years 5 Years September 1997 TS LLS 5.50% 6.50% 5.75% 6.75% 6.00% 7.00% 6.25% 7.25% 6.50% 7.50% September 1998 TS LLS 4.50% 7.50% 4.75% 7.75% 5.00% 8.00% 5.25% 8.25% 5.50% 8.50% a. What are the market values of the two bonds in September 1997? What is the equity value of the hedge fund? Questions b and c look at the situation in September 1998 under two possible scenarios. In the first scenario the yield curve does not change and in the second scenario the yield spread increases. Assume that the hedge fund does not adjust its positions between September 1997 and September 1998. Thus, the fund still holds in 1998 the bonds it purchased or short-sold in 1997. Assume that the bonds just paid a coupon payment in early September 1998 and that they have now a remaining maturity of 4 years. b. Suppose that the yield curve does not change and is the same in September 1998 as it was in September 1997. For example, in September 1998, a Treasury bond with a maturity of one year has a yield of 5.5%. What are the current market values of the two bonds? How high are the net interest receipts of the fund? What is the value of the fund? c. Actually, the yield curve changed considerably between September 1997 and 1998, as shown in the Table above. For example, in September 1998, a Treasury bond with a maturity of one year had a yield of 4.5%, while less-liquid securities yielded 7.5%. What are the current market values of the two bonds? How high are the net interest receipts of the fund? What is the value of the fund? 3