Suppose that you are given the following zero-curve (interest rates are annual, but compounded 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 modified duration and convexity of the bond in (1). What is the approximate percentage change in the bond price if the zero-curve shifts up by one percent

(i.e. dy = 1% or r_2,0.5 = 0.03, r_2,1 = 0.031, etc.) using the modified duration and convexity you just calculated?

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 percent, what is the value of the Treasury bond?

(c)    What is your net payoff to unwinding the repo trade tomorrow? Recall that you need to buy the bond and sell it to the repo dealer at the prespecified price. Assume that the price tomorrow is the price that you calculated?