Question 1:

A hedge fund expects that proposed elimination of the personal taxation on dividends will be enacted and that this tax reform will benefit particularly stocks paying high dividends. The hedge fund ranks the 500 stocks in the S&P 500 index according to their dividend yield. The 250 stocks with the highest dividend yields are included in the highdividend portfolio and the 250 stocks with the lowest dividend yields are included in the low-dividend portfolio. The high-dividend portfolio has a beta of 0.7 and the lowdividend portfolio has a beta of 1.3. The risk-free interest rate is 2% and the expected return on the S&P 500 index is 7%. The hedge fund has currently $10 million available to invest in this strategy.

(a) Suppose that the hedge fund decides to go long $50 million in the high-dividend

portfolio and to go short $40 million in the low-dividend portfolio. What is the beta andthe expected return of the hedge fund according to the CAPM?

(b) Hedge funds often want to eliminate all systematic risk by pursuing ?market-neutral? strategies. Which positions in the two portfolios can the hedge fund enter into with a net investment of $10 million without incurring any systematic risk? Please give the dollar values of the long and short positions in the high- and the low-dividend portfolios. (Hint: A market-neutral portfolio has a beta of zero.)

(c) Under what conditions can the hedge fund expect to make abnormal profits from the transaction in (b)?

Question 2:

You are currently 100% invested in the S&P500. You are evaluating two trading

strategies. You have historical data on the returns to these strategies and the S&P500. After analyzing the data you come up with the following estimated quantities (?1? refers to the first strategy, ?2? refers to the second strategy, rf is the risk-free rate and S&P refers to the S&P500):

E(r1) = 15% ?1 = 0.50 ?1, S&P = 0.35

E(r2) = 6% ?2 = 0.30 ?2, S&P = 0.25 ?1, 2 = 0.4

E(rS&P ) = 12% ?S&P = 0.15

rf = 5%

Answer the following:

(a) Let?s examine how the CAPM performs when using the S&P500 as a proxy for the market portfolio. What are the alphas and betas of the two strategies?

(b) Recall that you are currently holding the S&P500. Describe in words how you would adjust your portfolio in response to the alphas calculated in part (a)?

(c) Find a combination of the two strategies that would make you react to market risk the way S&P 500 does. What is the expected return to this portfolio? What is the alpha of this portfolio? What is the idiosyncratic risk of the portfolio?

Question 3:

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 4:

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 5:

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 2019? 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 6:

This question requires data collection. You can find all numbers on finance.yahoo.com.

The questions concern Microsoft (ticker: MSFT).

(a) What are the current price and the current price-earnings ratio?

(b) What is the current plowback ratio?

(c) What is the growth rate of earnings for the next 5 years according to the analysts?

Hint: look for annual growth rates under ?analyst estimates?

(d) What is the beta of MSFT? Hint: look for ?key statistics?. If the risk-free rate (Rf) is

1% and the market risk premium E[RM ?Rf ] is 11%, what is the required rate of return on MSFT according to the CAPM?

(e) Assume that Microsoft will have earnings and dividends that will grow at the analysts forecasted rate forever after; i.e., the Gordon growth model (GGM) applies. What is the price-earnings ratio that the GGM predicts for Microsoft?

Question 1: A hedge fund expects that proposed elimination of the personal taxation on dividends will be enacted and that this tax reform will benefit particularly stocks paying high dividends. The hedge fund ranks the 500 stocks in the S&P 500 index according to their dividend yield. The 250 stocks with the highest dividend yields are included in the highdividend portfolio and the 250 stocks with the lowest dividend yields are included in the low-dividend portfolio. The high-dividend portfolio has a beta of 0.7 and the lowdividend portfolio has a beta of 1.3. The risk-free interest rate is 2% and the expected return on the S&P 500 index is 7%. The hedge fund has currently $10 million available to invest in this strategy. (a) Suppose that the hedge fund decides to go long $50 million in the high-dividend portfolio and to go short $40 million in the low-dividend portfolio. What is the beta andthe expected return of the hedge fund according to the CAPM? (b) Hedge funds often want to eliminate all systematic risk by pursuing \"market-neutral\" strategies. Which positions in the two portfolios can the hedge fund enter into with a net investment of $10 million without incurring any systematic risk? Please give the dollar values of the long and short positions in the high- and the low-dividend portfolios. (Hint: A market-neutral portfolio has a beta of zero.) (c) Under what conditions can the hedge fund expect to make abnormal profits from the transaction in (b)? Question 2: You are currently 100% invested in the S&P500. You are evaluating two trading strategies. You have historical data on the returns to these strategies and the S&P500. After analyzing the data you come up with the following estimated quantities (\"1\" refers to the first strategy, \"2\" refers to the second strategy, rf is the risk-free rate and S&P refers to the S&P500): E(r1) = 15% 1 = 0.50 1, S&P = 0.35 E(r2) = 6% 2 = 0.30 2, S&P = 0.25 1, 2 = 0.4 E(rS&P ) = 12% S&P = 0.15 rf = 5% Answer the following: (a) Let's examine how the CAPM performs when using the S&P500 as a proxy for the market portfolio. What are the alphas and betas of the two strategies? (b) Recall that you are currently holding the S&P500. Describe in words how you would adjust your portfolio in response to the alphas calculated in part (a)? (c) Find a combination of the two strategies that would make you react to market risk the way S&P 500 does. What is the expected return to this portfolio? What is the alpha of this portfolio? What is the idiosyncratic risk of the portfolio? Question 3: 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 4: 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 5: 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 2019? 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 6: This question requires data collection. You can find all numbers on finance.yahoo.com. The questions concern Microsoft (ticker: MSFT). (a) What are the current price and the current price-earnings ratio? (b) What is the current plowback ratio? (c) What is the growth rate of earnings for the next 5 years according to the analysts? Hint: look for annual growth rates under \"analyst estimates\" (d) What is the beta of MSFT? Hint: look for \"key statistics\". If the risk-free rate (Rf) is 1% and the market risk premium E[RM Rf ] is 11%, what is the required rate of return on MSFT according to the CAPM? (e) Assume that Microsoft will have earnings and dividends that will grow at the analysts forecasted rate forever after; i.e., the Gordon growth model (GGM) applies. What is the price-earnings ratio that the GGM predicts for Microsoft