Question

3. Ah Cheung is the portfolio manager for large pension fund and is considering investing $100 million to purchase the following 3 choices of HSMC Ltd issued bonds:

HSMC Bond A matures in 5 years and pays a 9%p.a. coupon on a $1,000 face value bond).

HSMC Bond B matures in 10 years, pays an 8%p.a. coupon yield and is being offered at PAR.

HSMC Bond C is a zero-coupon bond but will pay the face amount of $1,000 per bond at maturity in 10 years.

Note: All HSMC bonds pay coupon semi-annually and have market prices that imply a YTM of 8%p.a. Each of the 3 bonds is based on a $1,000 face value (par value) to be repayable at maturity.

(A) Without performing any calculations, can you roughly guess the price of the 3 bonds compared to PAR? (Hint: Observe the relationship between coupon and coupon.)

(B) Calculate each bond price?

(C) In the following table, it is the prices of the three bonds at 5% & 11% yield (YTM) comparing to their valuations when the required yield (YTM) was 8%p.a.:

YTM	HSMC Bond A	HSMC Bond B	HSMC Bond C
5%	$1,175.04	$$1,233.84	$610.27
11%	$$924.62	$$820.74	$342.73

Explain why each of these bonds has a different degree of sensitivity to a +/- 3% change in required yield (YTM). Give your reasoning in terms of volatility based on maturity and coupon effect.

(D) Calculate the duration of HSMC Bond A, B, C?

(E) As an alternative, Ah Cheung has been invited to invest $1 million in a 10-year bond of a second firm, HKU. HKU bonds are similar in risk to “HSMC Bond B”: they both pay 8%p.a. coupon for 10 years, but HKU bonds pay coupon annually, not semi-annually as in the case of HSMC. The HKU bonds are priced 99% (or $990 per $1,000 face value).

What yield to maturity (YTM) is implied by the HKU bond? Compare this yield to the 8%p.a. of the HSMC semi-annual coupon bond (Bond B) above. In which bond should Ah Cheung invest?

Answer 1

Answer A:

In bond A, since coupon rate is higher than YTM (discount rate), so the bond price will be higher than face value.

In bond B, since the coupon rate is equal to YTM (discount rate), so the bond price will be equal to face value of the bond.

In bond C, since the bond is a zero coupon bond i.e. doesn’t pay any interim payments, so the bond’s price will be much lower than the face value.

Answer B:

Bond A price = 1,040.6, Bond B price = 1,000, Bond C price = 463.2

Answer C:

we can see from the above table that the change in price of a bond is lowest for a higher coupon and lower maturity period bond for an increase yield because bond returns original cost faster ( due to higher income) and also matures early (here only 5 years compared to bond B & C - 10 years).

In case of bond B & bond C, bond B's price change is lower because it pays at least some amount every year but in zero coupon bond there is no interim payments. so bond C is more sensitive to +-x% change in YTM.

We measure this sensitivity with the term called Duration. The higher the bond's duration, the greater its sensitivity to changes in YTM and vice versa.