Bonds

Question 1

The YTM on all bonds and liabilities is 4%. You hold a 3% coupon bond (par value = 1000) with a time to maturity of 2 years. The coupon is paid annually at the end of the year. Convexity is 0. First, explain what duration is. In addition, what´s the difference between duration and modified duration? What does convexity mean?

Answer 1

Duration is a measure of the bond’s interest rate sensitivity.
It relates interest rate changes to price changes.

Modified duration is “ D/(1+y) “ (Macaulay’s duration divided by 1 + yield to maturity).
The difference is that in the D* the percentage price change is proportional to its duration.

Convexity measures the curvature (non-linearity) of the bond’s price-yield curve.

Question 2

!Explain in words what investors mean when they talk about the “duration of a bond”. In addition, include answers to the following questions: (i) What is the difference between duration and modified duration? (ii) What does convexity mean?

Answer 2

Duration measures the bond’s price sensitivity to interest rate changes. It’s an approximate measure of the percentage change in a bond’s price for a 1% change in interest rates.

Modified duration is a refined version of duration that takes into account the bond’s yield. It provides a percentage change in bond price given a change in yield.
MD = D/(1+y)

Convexity is a measure of how a bond’s price changes in response to changes in interest rates. A bond with higher convexity is less affected by interest rate changes than a bond with lower convexity.

Question 3

The yield to maturity on all bonds and liabilities is 4%. You hold a 5% coupon bond (par value = € 1000) with a time to maturity of 2 years. The coupon is paid annually at the end of the year. Assume that the convexity for this bond is 0.

Please give the duration (in years) of the bond.
a. 1.953
b. 1.961
c. 2.000
d. 1.970

Answer 3

a

Question 4

A zero coupon bond’s duration will be equal to…

Answer 4

… it’s maturity

Question 5

A 9-year-old bond has a yield of 15% and a duration of 8.908. If the market yield changes by 70 b.p. what is the percentage change in the bond’s price?

Question 6

To turn bases point to a number you multiply *10^??

Answer 6

-4

Question 7

Explain why modified duration is a better measure than maturity when calculating the bond’s sensitivity to changes in interest rates

Answer 7

Modified duration is a better measure of the bond’s sensitivity to changes in interest rates because Maturity considers only the final cash flow, while Modified Duration includes other factors, such as the size and timing of coupon payments, and the level of interest rates (yield to maturity).

Question 8

Modified duration increases as the coupon …

Answer 8

decreases

Question 9

Modified duration … as maturity decreases

Answer 9

decreases

Question 10

Define convexity and explain how modified duration and convexity are used to approximate the bonds’s percentage change in price, given a change in interest rate.

Answer 10

Convexity measures the curvature of the bond’s price-yield curve.

Such curvature means that the duration rule for bond price change (which is based only on the slope of the curve at the original yield) is only an approximation. Adding a term to account for the convexity of the bond increases the accuracy of the approximation.