MGMT 511 Sample Exam
SAMPLE FINAL EXAMINATION
1) Assume that the coupon rate for a ten year Treasury bond is 4.00% for the first five years, and then steps up to 5.80% for the last five years. Assuming that the yield to maturity is 5.25%, solve for the price of the bond.
2) Assume that par rates are as given below,
T = 0.50 4.75%
T = 1.00 5.00%
T = 1.50 5.24%
T = 2.00 5.46%
Solve for the spot curve out to two years at semiannual intervals. At what rates could you lock in a six-month and a one year loan one year from now?
3) Assume that D (0.5) = 0.95, D (1.0) = 0.91, D (1.5) = 0.85, and D (2.0) = 0.8.
Show how you would hedge a $100 notional position in a one-year par bond with an 18-month par bond. Compute the convexities of both bonds and identify any convexity risks in the hedge. What are the advantages and disadvantages of your hedging approach?
4) As in problem 3, assume that D (0.5) = 0.95, D (1.0) = 0.91, D (1.5) = 0.85, and D (2.0) = 0.8. You are considering issuing a 2 year, semi-annual fixed coupon bond to finance a project. The fixed coupon on this bond would equal the par rate, plus 126 basis points. As an alternative, you could issue a 2 year floating rate note where you pay 6 month Libor plus 125 basis points on a semi-annual
A/360 basis, and then swap into fixed (swaps are normally based on 3 month
Libor with quarterly cash flows, but let’s assume semi-annual payments to keep this simple). Compare the costs of the two alternatives and identify which is the better financing vehicle for you.
5) The current short-term rate r equals 5.00%. Using the Merton interest rate model with α = 0.01, and σ = 0.02, solve for the 3 × 6 FRA rate (the three month rate, three months forward).
6) Let X be the average short-term rate over the next year (time zero to time one). There is a 20% chance X will be 5%, a 30% chance X will be 7%, a 20% chance X will be 9%, and a 30% chance X will be 15%. Solve for the price of a chooser option on the average interest rate where
1) Assume that the coupon rate for a ten year Treasury bond is 4.00% for the first five years, and then steps up to 5.80% for the last five years. Assuming that the yield to maturity is 5.25%, solve for the price of the bond.
2) Assume that par rates are as given below,
T = 0.50 4.75%
T = 1.00 5.00%
T = 1.50 5.24%
T = 2.00 5.46%
Solve for the spot curve out to two years at semiannual intervals. At what rates could you lock in a six-month and a one year loan one year from now?
3) Assume that D (0.5) = 0.95, D (1.0) = 0.91, D (1.5) = 0.85, and D (2.0) = 0.8.
Show how you would hedge a $100 notional position in a one-year par bond with an 18-month par bond. Compute the convexities of both bonds and identify any convexity risks in the hedge. What are the advantages and disadvantages of your hedging approach?
4) As in problem 3, assume that D (0.5) = 0.95, D (1.0) = 0.91, D (1.5) = 0.85, and D (2.0) = 0.8. You are considering issuing a 2 year, semi-annual fixed coupon bond to finance a project. The fixed coupon on this bond would equal the par rate, plus 126 basis points. As an alternative, you could issue a 2 year floating rate note where you pay 6 month Libor plus 125 basis points on a semi-annual
A/360 basis, and then swap into fixed (swaps are normally based on 3 month
Libor with quarterly cash flows, but let’s assume semi-annual payments to keep this simple). Compare the costs of the two alternatives and identify which is the better financing vehicle for you.
5) The current short-term rate r equals 5.00%. Using the Merton interest rate model with α = 0.01, and σ = 0.02, solve for the 3 × 6 FRA rate (the three month rate, three months forward).
6) Let X be the average short-term rate over the next year (time zero to time one). There is a 20% chance X will be 5%, a 30% chance X will be 7%, a 20% chance X will be 9%, and a 30% chance X will be 15%. Solve for the price of a chooser option on the average interest rate where