Question

Bond A is a $1,000, 6% quarterly coupon bond with 5 years to maturity.

(a) If you bought Bond A today at a yield (APR) of 8%, what is your purchase price? Is this a

premium or discount bond? Why?

(b) One year later, Bond A's YTM (APR) has gone down to 6% and you sell it immediately after

receiving the coupon.

(i) What is the current yield?

(ii) What is the capital gains yield?

(iii) What is the one-year total rate of return (in APR) if the coupons are reinvested at 2%

per quarter during the holding period?

(iv) Can Bond A’s one-year total rate of return be determined correctly by simply adding up

the current yield and the capital gains yield? Explain your answer without calculations.

(c) Consider two other bonds: Bond B and Bond C.

Bond B: A $1,000, 7% quarterly coupon bond with 4 years to maturity

Bond C: A $1,000 zero coupon bond with 2 years to maturity

(i) Without calculation, briefly explain which bond in the following pairs has higher

interest rate risk.

1) Bond A vs. Bond B

2) Bond B vs. Bond C

(ii) Suppose you are holding a bond portfolio made up of Bonds A and B for long-term

investment purpose. If you are predicting the general interest rate to decrease in the next

year (i.e., the coming quarters), what should you do to your portfolio to maximize your

return?

Answer 1

1.
=6%*1000/8%*(1-1/1.02^20)+1000/1.02^20
=918.24283
Discount bond as price is less than par of 1000

2.
As coupon rate is equal to ytm, price is equal to par=1000
current yield=6%

3.
capital gains yield=1000/918.24283-1=8.904%

4.
=(6%*1000/8%*(1.02^4-1)+1000)/(918.24283)-1
=15.637%

5.
No as reinvestment rate is not the same as purchase yield

Formulas used above:
1.
=Present value of coupons+Present value of par
=coupon rate*par value/yield*(1-1/(1+yield/4)^(4*t))+Par value/(1+yield/4)^(4*t)

2.
=Coupon rate

3.
=Price now/Price one year ago-1

4.
=(Future value of coupons+Price one year later)/Purchase Price-1

1.
Lower the coupon rate higher the interest rate risk
Higher the maturity higher the interest rate risk
Between Bond A and Bond B, Bond A has higher interest rate risk

Between Bond B and Bond C, it is difficult to say without calculations but Bond B will have higher interest rate risk probably because of maturity effect dominating coupon effect

2.
If rates decrease, we should hold higher duration bonds

hence sell bond B and buy from the amount Bond A