Finance

5°

At par, the duration of a 5-year, $1000 Treasury bond with a 10% semiannual coupon equals 4.05 years.

With a yield-to-maturity of 12%, its duration equals 4.01 years.

With a yield-to-maturity of 14%; its duration equals 3.97 years.

We can see that duration decreases as yield-to maturity increases.

6°

a) A Treasury Bond with 10% semiannual coupon is trading at par, what is its duration (a measure of interest rate risk)?

Maturity of 4 years: 3.39 years

Maturity of 3 years: 2.67 years

Maturity of 2years: 1.87 year

b)

Naturally, the duration of a Treasury Bond is lower than its maturity. As the time goes by, a bond duration decreases faster than its maturity and the two are getting closer.

7°

The duration of a 6-year, $10000 CD paying 6% of annual interests equals 5.21 years.

I interests were to be paid semiannually, its duration would be of 5.13 years.

When the relative frequency of interest payments increases, the duration decreases. This can be explained by the fact that investors are able to receive interest payments more quickly and then reinvest them in other financial products.

8°

A consol bond is also said to be ‘perpetual’ in the sense that it pays a fixed coupon to its holder forever. Its duration is computed as follows: 1 + (1/YTM).

YTM = 8% Duration = 13.50 years

YTM = 10% Duration = 11.00 years

YTM = 12% Duration = 9.33 years

As zero-coupon bonds do not generate during their maturity, a consol bond with a YTM of 10% while have a superior duration (11 years).

9°

a) Duration of a bond with a 5-year maturity:

YTM = 9% ; annual coupon = 7% Duration = 4.36 years

YTM = 9% ; annual coupon = 9% Duration = 4.24 years

YTM = 9% ; annual coupon = 11% Duration = 4.14 years

b)

With similar YTMs, the duration of a bond decreases as annual coupons increase.

10°

a) Duration of a bond with a 5-year maturity and a par value of $10000:

YTM = 10% ; annual coupon = 8% Duration = 4.28 years

YTM = 10% ; annual...