Chapter 11: Managing Bond Portfolios

Question 1

What are the six main propositions related to sensitivity in bond prices?

Answer 1

1. Bond prices and yields are inversely related.
2. An inc in a bond’s yield to maturity results in a smaller price change than a dec in yield of equal magnitude.
3. Prices of long-term bonds tends to be more sensitive to interest rate changes than prices of short-term bonds.
4. The sensitivity of bond prices to changes in yields inc at a decr rate as maturity inc.
5. Int rate risk is inversely related to the bond’s coupon rate. Prices of low-coupon bonds are more sensitive to changes in int rate.
6. The sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling.

Question 2

What is Macaulay’s duration?

Answer 2

A measure of the effective maturity of a bond, defined.as the weighted average of the times until each payment, with weights proportional to the PV of the payment.

Question 3

What is the formula for Macaulay’s duration?

Answer 3

w𝘁 = CF₁/(1+y)ᵗ/bond price

Question 4

What is the modified duration?

Answer 4

Macaulay’s duration dividend by 1+yield to maturity. Measures interest rate sensitivity of bond.

Question 5

What is the formula for modified duration?

Answer 5

D*=D/(1+y)

Question 6

What is the formula for the proportional change in a bond’s price as it related to the change in its yield to maturity?

Answer 6

△P/P = -D x [(△(1+y)/(1+y)]
or
△P/P = -D*△y