Suppose that a two-factor model, where the factors are the market return (Factor 1) and the growth rate of industrial production (Factor 2), correctly describes the return generating processes of all assets and the corresponding two-factor APT correctly prices three well- diversified portfolios, A, B, and C.

a. What are i) the risk premiums of the two factors and ii) the risk-free rate? (4 marks)

b. Another well-diversified portfolio D has sensitivities 1 to factor 1 and 0.5 to factor 2, respectively. What is the APT-consistent expected return on Portfolio D? (2 marks)

c. Suppose that Portfolio D’s expected return is 12%. Given your answers above, design an arbitrage strategy involving Portfolios A, B, C, and D. (Hint: an arbitrage strategy requires no initial investment, has no risk and yet generates a positive return.) (4 marks) (Total for Question: 10 marks)

You just bought a newly issued bond which has a face value of $1,000 and pays its coupon once annually. Its coupon rate is 6%, maturity is 20 years and the yield to maturity for the bond is currently 8%.

a. Do you expect the bond price to change in the future when the yield stays at 8%? Why or why not? Explain. (No calculation is necessary to answer this part of the question.) (2 marks)

b. Calculate what the bond price would be in one year if its yield to maturity stays at 8%. (2 marks)

c. Suppose that one year after you bought the bond, the yield to maturity of the bond declines to 7%. Find the (before-tax) total dollar return (dollar returns from the coupon payment and capital gains) for the one-year investment period. (2 marks)

d. When the ordinary income tax rate is higher than the capital gains tax rate, tax authorities typically tax anticipated price appreciations from bonds at the ordinary income rate in order to prevent tax aversion with discount bonds.

Suppose that from the total dollar return in part c), the coupon payment and the difference between the hypothetical anticipated price with the same yield to maturity in part b) and the purchase price are taxed at the ordinary income tax rate, 40%. The rest of the dollar return in part c) is considered capital gains (due to unanticipated change in yield-to-maturity from 8% to 7%) and taxed at 30%. In other words, coupon payments and the anticipated price appreciation are taxed at the higher ordinary income tax rate and the rest at the lower capital gains rate. Using your answers in part b) and c), calculate the after-tax holding period (percentage) return over one year if the yield to maturity is 7% at the end of the year. (5 marks)

e. (Unrelated to Parts b-d) Find the realized compound yield before taxes for a two-year holding period, assuming that i) the investor, who bought the newly issued bond at the 8% yield to maturity, will sell the bond in two years after the purchase, ii) the bond’s yield-to-maturity is 7% at the end of the second year when it is sold, and iii) the coupon at the end of the first year is reinvested for one year at a 4% interest rate. Ignore taxes. (3 marks) (Total for Question: 14 marks)

Consider a 529 (college savings) plan that will pay $20,000 once a year for a 4-year period (4 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 8 years (at the end of year 8).

a. What is the duration of the pension obligation? The current interest rate is 8% per year for all maturities. (3 marks)

b. To generate the scheduled payments, the fund would like to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bond now? What should be the total face value (not current market value) of each zero-coupon bond held? (3 marks)

c. Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 8% p.a.to 7% p.a. Show that the investment position constructed in part b) can still fund (approximately) the future payments by showing that the fund’s net investment is close to 0 at the end of year 8 after making all the scheduled payments. Assume that interest rates will remain at 7% p.a. Any excess cash from the 5-year investment will be reinvested at 7% and any fraction of the 10- year bonds held can be sold at the going market price at any time to fund the annual payments. (6 marks) (Total for Question: 12 marks)

The current yield curve for default-free zero-coupon bonds is as follows:

All bonds considered in this question have a face value of $1,000. Assume that the pure expectations hypothesis of the term structure holds.

a. If market expectations are accurate, what are the expected yields to maturity on 1- and 2-year zero coupon bonds next year? (3 marks)

b. If you purchase a 3-year zero-coupon bond now, what is the expected total rate of return over the next year assuming that you will sell the bond at the expected price (price that matches the expected yield in part a))? Ignore taxes. (3 marks)

c. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually? (3 marks)

d. If you purchase the coupon bond at the price you calculated in part c), what would your total expected rate of return over the next year be (coupon plus price change)? Ignore taxes. (3 marks) (Total for Question: 12 marks)

You observe the market prices of European options written on a non-dividend paying stock expiring in one month.

a. Suppose you write a call option with X = $35 and buy a call with X = $45. Graph the profit/loss of the individual call positions and the combined option portfolio as a function of the stock price at the expiry. Also indicate at what stock price you will just break even on the graph. (6 marks)

b. Now suppose you further buy a put option with X = $35 and write a put option with X = $45 in addition to the call option positions in part a) – i.e., now your portfolio consists of short call and long put with X = 35 and long call and short put at X = 45. Graph the payoff of the individual option positions and the combined option portfolio as a function of the stock price at the expiry. (3 marks)

c. In light of your answer in part b) above, what should be the one-month risk-free rate to rule out any arbitrage.

Hint: The arbitrage-free one-month risk-free rate should be the same:

Rf = (risk-free cash flow in one month) / (initial cost of the risk-free investment)

for any risk-free investment generating a constant cash flow in one month. (3 marks) (Total for Question: 12 marks)

a. Consider a one-year futures contract for 1 share of a dividend paying stock. The current stock price is $60 and the risk-free interest rate is 8% p.a. It is also known that the stock will pay a $2 dividend at the end of year 1. The current settlement price for the futures contract is $62. Set up a strategy for an arbitrage profit. What are the initial and terminal cash flows from the strategy? Assume that investors can short-sell or buy the stock on margin and that they can borrow and lend at the risk- free rate. There are no margin requirements, transactions costs, or taxes. (5 marks)

b. Consider a stock that pays no dividends on which a futures contract, a call option and a put option trade. The maturity date for all three contracts is T, the exercise price of the put and the call are both X, and the futures price is F. Show that if X = F, then the call price equals the put price assuming that spot-futures parity and put- call parity conditions hold. Assume that interest is continuously compounded (i.e., use the spot-futures parity with continuously compounded interest). (5 marks) (Total for Question: 10 marks)