Learning Objectives: Calculate and interpret the impact of different compounding frequencies on a bond’s value. Define spot rate and compute discount factors given spot rates. Describe a swap transaction and explain how a swap market defines par rates.
Questions:
24.12.1. Given an annual nominal interest rate of 7% compounded semi-annually, you need to calculate the equivalent quarterly compounded rate. Which of the following is the correct answer?
a. 6.9398%
b. 7.0306%
c. 7.0000%
d. 14.7523%
24.12.2. Monument Fund purchased a continuously compounding bond for USD 100 million today and is expected to receive USD 120 million in three years. What would be the three-year spot rate when compounded semi-annually, and how does it compare to annual compounding.
a. Semi-annual discount rate 0.8310, continuous discount rate 0.8286
b. Semi-annual discount rate 0.8286, continuous discount rate 0.8310
c. Semi-annual discount rate 0.8333, continuous discount rate 0.8286
d. Semi-annual discount rate 0.8286, continuous discount rate 0.8333
24.12.3. Party A and Party B enter a five-year swap with a notional principal of USD 100 million. Party A pays a fixed annual rate of 4%, while Party B pays a quarterly-adjusted floating rate based on three-month SOFR. Initially, the three-month SOFR is 3%. The payments are recalculated quarterly based on the notional principal.
What does the initial payment exchange between Party A and Party B illustrate about the nature of swap agreements and par rates?
a. Party B pays Party A USD 0.75 million, reflecting a 3% SOFR, while Party A pays USD 1.0 million based on the fixed rate, resulting in a net payment of USD 0.25 million to Party A.
b. Party A pays Party B USD 0.75 million, while Party B pays USD 1.0 million, incorrectly describing the payment flow.
c. Party B’s payment suggests a disparity, indicating that fixed-rate bonds are valued higher than floating-rate bonds.
d. Both parties pay USD 1.0 million each quarter, incorrectly stating that no adjustments are made for SOFR, indicating a misunderstanding of par rates.
Answers here:
Questions:
24.12.1. Given an annual nominal interest rate of 7% compounded semi-annually, you need to calculate the equivalent quarterly compounded rate. Which of the following is the correct answer?
a. 6.9398%
b. 7.0306%
c. 7.0000%
d. 14.7523%
24.12.2. Monument Fund purchased a continuously compounding bond for USD 100 million today and is expected to receive USD 120 million in three years. What would be the three-year spot rate when compounded semi-annually, and how does it compare to annual compounding.
a. Semi-annual discount rate 0.8310, continuous discount rate 0.8286
b. Semi-annual discount rate 0.8286, continuous discount rate 0.8310
c. Semi-annual discount rate 0.8333, continuous discount rate 0.8286
d. Semi-annual discount rate 0.8286, continuous discount rate 0.8333
24.12.3. Party A and Party B enter a five-year swap with a notional principal of USD 100 million. Party A pays a fixed annual rate of 4%, while Party B pays a quarterly-adjusted floating rate based on three-month SOFR. Initially, the three-month SOFR is 3%. The payments are recalculated quarterly based on the notional principal.
What does the initial payment exchange between Party A and Party B illustrate about the nature of swap agreements and par rates?
a. Party B pays Party A USD 0.75 million, reflecting a 3% SOFR, while Party A pays USD 1.0 million based on the fixed rate, resulting in a net payment of USD 0.25 million to Party A.
b. Party A pays Party B USD 0.75 million, while Party B pays USD 1.0 million, incorrectly describing the payment flow.
c. Party B’s payment suggests a disparity, indicating that fixed-rate bonds are valued higher than floating-rate bonds.
d. Both parties pay USD 1.0 million each quarter, incorrectly stating that no adjustments are made for SOFR, indicating a misunderstanding of par rates.
Answers here:
