Question 1 - Suppose that the Capital Asset Pricing Model (CAPM) holds. The market portfolio has an expected return of 10% and standard deviation 15%. The risk-free rate is 4%. Stock A has a beta of 1.4 and standard deviation 30%.
a. What is the expected return of stock A?
b. What fraction of the risk of stock A is systematic?
C. Let P be the optimal portfolio of some investor. If the standard deviation of P is 8%, what is the expected return of P?
Question 2 - Stock XYZ trades for $26, has current earnings of $6, current dividends of $2, and a beta of 1.2. The risk free rate is 6% and the market risk premium is 5%.
a. What is XYZ's plow-back ratio?
b. Using the Gordon Growth Model, what growth rate is implied by the current valuation of XYZ?
c. Your own analysis shows that XYZ's actual growth rate wail be 6%. Based on this you buy XYZ today. If news comes out tomorrow and the rest of the market comes to agree with your analysis, what will be your holding period return {HPR) between today and tomorrow?
Question 3: A two-year annual-pay 50% coupon bond has face value $100 and 5% yield to maturity.
a. What is the price of the coupon bond?
b. What is the duration of the coupon bond?
c. The current yield on one-year zero-coupon bonds is 1% and investors expect that next year the yield on one-year zero-coupon bonds will be 7%. What is the no-arbitrage one-year forward rate? (Do not round to the percentage, i.e. write 1.23%, not 1%).
Question 4: Suppose that the Expectation Hypothesis holds. The yield on one-year zero-coupon bonds is 2% and the yield on two-year zero-coupon bonds is 6%.
a. What do investors expect the yield erg one-year zero-coupon bonds to be one year from now? (Do not round to the percentage, i.e., write 1.23%, not 1%).
b. What is the expected holding period return to buying a two-year zero-coupon bond arid selling it after one year?
Question 5: The assets of Bank of America (BofA) consist of mortgage-backed securities that are worth $100 billion and have duration of 12 years. The value of BofA's liabilities is also $100 billion. The interest rate is 5% at all maturities.
a. If BofA wants to minimize its exposure to interest rate risk by adjusting the composition of its liabilities, what fractions should be one-year zero-coupon bonds and 20-year zero-coupon bonds?
b. Suppose instead that BofA's liabilities are ail one-year zero-coupon bonds. If the interest rate increases by 0.1% (a small amount), what will be BofA's new net worth (assets minus liabilities) approximately?
c. Assuming BofA's liabilities have hither convexity than its assets, will its actual net worth alter the interest rate increase be higher or lower than the approximation in (b)?
Question 6: Stock XYZ trades for $100 and pays no dividends. Next year, with probability 95% it will rise to $110, and with probability 5% it will fall to $70. The interest rate is 5% with annual compounding. A one-year European put option on XYZ has strike price $101.
a. What is the no arbitrage price of the put?
b. If the put were American, would you exercise it today (Yes/No/Depends)?
Question 7: Stock XYZ trades for $100 and pays no dividends. Its volatility is 48%. The Interest rate is 6% continuously compounded. Consider a European call option on XYZ with strike price $101 and six months to expiration.
a. What is the adjusted intrinsic value of the call option?
b. If the assumptions behind the Black-Scholes-Merton formula hold, what must be the price of the call option? (You may use the table)
|
D
|
N(d)
|
|
-0.40
|
0.345
|
|
-0.38
|
0.352
|
|
-0.36
|
0.359
|
|
-0.34
|
0.367
|
|
-0.32
|
0.374
|
|
-0.30
|
0.382
|
|
-0.28
|
0.390
|
|
-0.26
|
0.397
|
|
-0.24
|
0.405
|
|
-0.22
|
0.413
|
|
-0.20
|
0.421
|
|
-0.18
|
0.429
|
|
-0.16
|
0.436
|
|
-0.14
|
0.444
|
|
-0.12
|
0.452
|
|
-0.10
|
0.460
|
|
-0.08
|
0.468
|
|
-0.06
|
0.476
|
|
-0.04
|
0.484
|
|
-0.02
|
0.492
|
|
0.00
|
0.500
|
|
0.02
|
0.508
|
|
0.04
|
0.516
|
|
0.06
|
0.524
|
|
0.08
|
0.532
|
|
0.10
|
0.540
|
|
0.12
|
0.548
|
|
0.14
|
0.556
|
|
0.16
|
0.564
|
|
0.18
|
0.571
|
|
0.20
|
0.579
|
|
0.22
|
0.587
|
|
0.24
|
0.595
|
|
0.26
|
0.603
|
|
0.28
|
0.610
|
|
0.30
|
0.618
|
|
0.32
|
0.626
|
|
0.34
|
0.633
|
|
0.36
|
0.641
|
|
0.38
|
0.648
|
|
0.40
|
0.655
|
c. You wrote (sold short) 100 call options. How many shares of XYZ do you need to buy or sell to hedge your position (indicate whether you buy or sell)?
Question 8: The current price of stock XYZ is $210, and the interest rate is 5% with annual compounding. XYZ does not pay dividends.
a. What is the no-arbitrage price of one-year futures on XYZ?
b. If it costs $20 to buy a one-year at-the-money straddle on XYZ, what is the no-arbitrage price of a one-year at-the-money call option? Assume all options are European.
c. Suppose that the one-year at-the-money call has delta of 0.6. How many one-year futures do you need to buy or sell to hedge one short call (indicate whether you buy or sell)?