Question

New South Wales Treasury has issued $1,000 face value, 3 - y e a r bonds that pay semi-annual
coupons at a rate of 10 per cent and 4-year bonds that pay semi-annual coupons at a rate of 16 per
cent. The market interest rates decreased sharply just after the issue and the current market rate for
similar bonds is 9.2 per cent.
a. What would be the bond’s current market values (prices)?
b. Calculate the duration for the bonds.
c. If the market condition is expected to be volatile and if you are a risk-averse investor,
what bond should you include in your portfolio?

Answer 1

Sub question (a):

Current Market Price of the bond is the present value of cash flows involved, discounted at the current market interest rates. Market interest rate is given as 9.2%.

Bond -1.

Face value (redemption amount): $1,000     Tenure: 3 years Coupon rate: 10% (yearly)

Coupon payment frequency: semiannual.

Cash flows involve

(1) interest payment semiannually for 6 half years as follows:

$1,000*(10/2*100)= $50 each and

(2) Redemption of principal $1,000 at the end of 3 years.

Market value of bond 1 is arrived at $1,020.56

Detailed Working as follows:

Bond -2.

Face value (redemption amount): $1,000     Tenure: 4 years Coupon rate: 16% (yearly)

Coupon payment frequency: semiannual.

Cash flows involve

(1) interest payment semiannually for 6 half years as follows:

$1,000*(16/2*100)= $80 each and

(2) Redemption of principal $1,000 at the end of 4 years.

Market value of Bond 2= $525.52 + 697.82 = $ 1,223.35   Details as follows:

Sub question (b): Duration of Bonds are as follows:

Bond 1 is 5.337292 half years or  2.668646 years

Bond 2 is 6.395274 half years or 3.197637 years.

Detailed working as above along with calculation of market value.

Sub question (c)

Duration measures sensitivity of bond price to change in interest rates. As per bond dynamics, whenever the yield expectation increases, bond price decreases and vice versa so that the price is adjusted to generate the expected yield, due to market forces. Generally, higher the duration, higher the sensitivity of price to changes in interest rates, upward or downwards. Hence, between the two given cases, for a risk averse investor, Bond 1 is preferable due to lower Duration.