Question 1: Trading on the Level of Interest Rates

Suppose that you are given the following zero-curve (interest rates are annual, but com-

pounded semi-annually):

t	0.5	1	1.5	2	2.5	3	3.5	4
r	0.02	0.021	0.023	0.025	0.03	0.035	0.04	0.041

1. Calculate the value of a 4-year Treasury bond with a 10% coupon rate, coupons paid

semi-annually, and a face value of $100.

2. Calculate the modi_ed duration and convexity of the bond in (1). You can use the

approximation formulas from class. What is the approximate percentage change in

the bond price if the zero-curve shifts up by one percentage point (i.e. r2;0:5 = 0:03,

r2;1 = 0:031, etc.)?

3. Because you believe that the zero-curve will shift upward and decrease the bond price,

you decide to use a reverse repo trade to short the bond. Let's suppose that a repo

dealer quotes you a special repo rate of 2% and you borrow 100 units of the Treasury

bond (which you then sell on the market as part of your reverse repo transaction).

(a) Draw a picture of the initial transactions in the repo trade.

(b) If the zero-curve shifts up by one percentage point, what is the value of the

Treasury bond in part 1?

(c) What is your net payo_ to unwinding the repo trade tomorrow? Recall that you

need to buy the bond and sell it to the repo dealer at the prespeci_ed price.

Assume that the price tomorrow is the price that you calculated in (b).