Assignment 3: Rates and Interest Rate Sensitivity
Section 1: Duration and bond characteristics
The textbook (Bodie, Kane, & Marcus, 2021) gives you a number of rules regarding duration and bond characteristics. These questions ask you to verify each rule and train you in calculating interest rates, duration, and interest rate sensitivity.
Rule 1: The duration of a zero-coupon bond equals its time to maturity.
1.1. Explain rule 1 using an example. (1 point)
Rule 2: Holding maturity constant, a bond's duration is lower when the coupon rate is higher.
2.1. Calculate the duration of a 3-year coupon-bond with face value $100 and coupon rate 3% selling at par. (2 points)
2.2. Calculate the duration of a 3-year coupon-bond with face value $100 and coupon rate 4% selling at par. (2 points)
2.3. Can you now explain why rule 2 holds? (1 point)
Rule 3: Holding the coupon rate constant, a bond's duration generally increases with its time to maturity. Duration always increases with maturity for bonds selling at par or at a premium to par.
3.1. Calculate the duration of a 4-year coupon-bond with face value $100 and coupon rate 3% selling at par. (2 points)
3.2. Can you explain the second part of rule 3? (1 point)
Rule 4: Holding other factors constant, the duration of a coupon bond is higher when the bond's yield to maturity is lower.
4.1. Calculate the duration of a 3-year coupon-bond with face value $100 and coupon 3% selling at $95. (2 points)
4.2. Explain rule 4. (1 point)
Section 2: The limits of duration
Duration is only an approximation for small changes in interest rates.
1.1. Using the duration you calculated for the 3-year 3% coupon-bond selling at par in question 2.1., what is the interest rate sensitivity of this bond to a 2 percentage point change (2%) in interest rates? (2 points)
1.2. Calculate the present value of the 3-year 3% coupon-bond using a yield to maturity of 5%. (1 point)
1.3. Compare the decrease in price (from par to the present value you calculated) to the interest rate sensitivity you calculated. Are they exactly equal? (1 point.)
Section 3: Application to recent data
Explain 4 graphs in the ECB's latest Monetary policy transmission brief. (8 points).
