Question

Unilever has issued bonds that pay annually with the following characteristics:

Coupon	Yield to Maturity	Maturity	Macaulay Duration
3%	3%	30 years	27.92 years

1. Calculate modified duration using the information above.
2. Explain why modified duration is a better measure than maturity when calculating the bond's sensitivity to changes in interest rates.
3. Identify the direction of change in modified duration if:
   1. The coupon of the bond were 2%, not 3%.
   2. The maturity of the bond were 7 years, not 30 years.

Answer 1

Answer:

Question a.

Modified Duration = [Macaulay Duration / (1+YTM)]

Modified Duration = [27.92 / (1+3%)]

Modified Duration = 27.10679612 OR 27.11 years.

Hence the modified duration is 27.11 years,

Question b.

It is because the modified duration is viewed as the better proportion, when figuring a bond's sensitivity to the change in the interest rate as the change in the bond price of a bond is corresponding to the modified duration. Therefore, the higher the duration of bond, the higher is the sensitivity of a bond.

Question c.

As per the relationship of bond pricing, the different things being steady similar to maturity years and the interest rate or the yield to maturity of the bond, the duration of a bond is greater with lesser coupon rate. Hence, the modified duration will tend to rise with decline if the coupon rate decline from 3% to 2%.

According to the relationship of bond pricing, for the most part all bonds are exchanged in the market that have lesser modified duration with a decline in the time to maturity. In this manner, it will be protected to expect that with decline in the time to maturity of the bond from 30 years to 7 years, there will be a decline in the modified duration as well.

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