Question

Three investors invest in the same 10-year 8% annual coupon bond. They bought the bond at the same price ($85.503075 for a par value of $100) and at the same time. A is a buy-and-hold investor (hold till maturity), B will sell the bond after four years, and C will sell the bond after seven years.

1. What is the yield to maturity of this bond?
2. For each of these three investors, find the total cash flow (in dollar amount) at the time of maturity (for A) and at the time of sale (for B and C).
3. After the bond is purchased by the three investors and before the first coupon is received, interest rate go up to 11.4%. What happens to the realized yield of these investors?
4. The Macaulay duration of this bond is: 7.0029 years. The difference between the Macaulay duration of a bond and the investment horizon is called the duration gap. For each of these three investors, find their respective duration gap.
5. Combine answers from ABCD, what are the relations between duration gap, interest rate risk, and reinvestment risk?

Answer 1

(A)

	Bond
Settlement date	30-Mar-20
Maturity date	30-Mar-30
Coupon	8%
Price	85.50308
Redemption	100
Frequency	1
Yield	10.40%
	=YIELD(B2,B3,B4,B5,B6,1)

Yield to maturity is 10.4%

(B)

Cash flow for A = coupon + face value = 8%*100 +100 = 8 + 100 = 108

When B sell the bond, the bond will have remaining maturity of 6 years

	Bond
Settlement date	30-Mar-24
Maturity date	30-Mar-30
Coupon	8%
Yield	10.40%
Redemption	100
Frequency	1
Price	89.66877
	=PRICE(B2,B3,B4,B5,B6,1)

B cash flow = 89.66877

When C sell the bond, the bond will have a remaining maturity of 3 years

	Bond
Settlement date	30-Mar-27
Maturity date	30-Mar-30
Coupon	8%
Yield	10.40%
Redemption	100
Frequency	1
Price	94.07334
	=PRICE(B2,B3,B4,B5,B6,1)

C cash flow = 94.07334

(C) After the bond is purchased and before the first coupon is received, which means the time to maturity remains is 9 years & yield becomes 11.4%

	Bond
Settlement date	30-Mar-21
Maturity date	30-Mar-30
Coupon	8%
Yield	11.40%
Redemption	100
Frequency	1
Price	81.46319
	=PRICE(B2,B3,B4,B5,B6,1)

In such a case, the price of the bond becomes 81.46319 while they had purchased it at 85.503075