Question 1 Pricing zeros and carry trade

In Year 20XZ, the six-month zero-coupon bond price is $99.5025, the 10- year zero coupon bond1 price is $64.0817.

1. What are the six-month and 10-year spot rates?

2. What will happen to the bond prices if the six-month and 10-year rates are 1.5% and 5%, respectively?

3. What will happen to the bond prices if the six-month and 10-year rates are 0.5% and 4%, respectively?

4. from the results of Questions Q.1.1-Q.1.3, we conclude that bonds' prices with different maturities react differently to the same interest rate change. In what way?

5. Using the interest rates computed in Questions Q.1.1, construct the following "carry trade":

Borrow $1Billion at the six-month rate for six months and use the money to buy the 10-year bond. Six months later, the 10-year bond you bought becomes a 9 12 -year bond. Sell the 9 12 -year bond and use the proceeds to repay the loan.

1 Note that a 10-year treasury bill does not exist in practice. The 10-year zero-coupon bond could be a STRIP 1

• Calculate the 9 12 -year bond price, assuming that the 9 12 -year spot rate six-month later is the same as the 10-year spot rate computed in Questions Q.1.1;
• How much profit did the carry trade strategy make?
• Under what interest rate movement will this strategy lose money in six months?