Question 1  [24 points]

Consider an economy with two dates (t=0,1) and two states. The following two assets are traded: Asset A has a payoff of xA=(2,6)  and asset B has a payoff of xB=(1,7) at t=1.

(a)       Suppose the prices of asset A and B at t=0 are pA=2 and pB=3, respectively. Is there an

arbitrage? If so, find a profitable trading strategy.   [6p]

Now suppose pA=2 and pB=2.2 for questions (b) to (d).

(b)       A call option on asset A with exercise price E=3 is traded. What is the price of this option at t=0?  [4p]

(c)       Consider a portfolio consisting of two units or asset A and four units of asset B. What is the payoff of this portfolio at t=1? And what is the price of this portfolio at t=0? [4p]

An investment firm is offering options on the above portfolio.

Option I is a call option on the portfolio with exercise price E=20. (I.e. if you buy this option at t=0, you can buy one unit of the portfolio for the price 20 at t=1)

Option II is aput option on the portfolio with exercise price E=20.

(d)       Which option has the higher price at t=0?   [6p]

(e)       Draw the payoff (at t=1) of the following portfolio of options on a stock

Sell a call with exercise price E=10

Buy a call with exercise price E=20

Buy a call with exercise price E=30

Sell a call with exercise price E=40

as a function of the underlying stock price at t=1.  [4p]

Question 2  [10 points]

Consider a 10% two year corporate bond. This bond pays a coupon of $10 at t=1 and pays

back $110 at t=2. The default spread for an AAA rated bond is 0.25% and a BB rated bond is 9%. Suppose the risk free rate is constant at 1%.

(a)       Suppose the bond has an AAA rating. What is the market price of the bond at t=0? [3p]

(b)       Suppose the bond has a BB rating. Do investors buy the bond for $100 at t=0?   [3p]

Suppose the central bank changes the interest rate. Please comment on the following statements. (You can use a numerical example to illustrate your answer.)

(c)       The price of the AAA rated bond goes up, if the central bank increases the risk free interest rate.  [2p]

(d)       If the yield curve is not constant but increasing, the price of the BB rated bond goes up ceteris paribus.  [2p]

Question 3  [12 points]

Consider an economy with three states which occur with probability (0.3, 0.3, 0.4). Suppose a firm has a project which generates the state dependent cash flows (100, 300, 200) at t=1. The  investment costs are $180 at t=0. The market portfolio generates the payoff (100, 200, 300) and has an expected return of 10%. The risk free rate is 1%. Suppose the CAPM holds.

(a)       What is the beta of this project? [4p]

(b)       Explain whether the firm should conduct the project.  [4p]

(c)       Please comment on the following statement. “ Suppose the CAPM holds. The firm can either invest in project A or B. The firm should conduct project A if it has a higher expected return than project B.” Is this statement true?   [4p]