Question

2. Consider the following 3 semiannual bonds with par $1,000:

Bond A: 5-year bond with coupon rate 6%

Bond B: 10-year bond with coupon rate 6%

Bond C: 10-year bond with coupon rate 10%

Step 1: (1.5 points)
Calculate the prices of Bond A, Bond B, and Bond C based on the required yield=7%.
Bond A =
Bond B =
Bond C =

Step 2: (3 points)
For each bond (Bond A, Bond B, or Bond C), conduct a scenario analysis through “Data Table” to report the bond’s price at yields 3.5%, 4%, 4.5%, 5%, 5.5%, 6%, 6.5%, 7%,7.5%, 8%, 8.5%, 9%, 9.5%, and 10%.

Step 3: (1.5 points)
Setting the case at yield 7% as the benchmark (P0 case). Calculate the dollar price change for each bond at each new yield level following the formula:
Dollar Price Change= Pt-P0

Step 4: (1.5 points)
(1) Select a case to verify: For a given term to maturity and initial yield, the higher the coupon rate, the higher the dollar price change.
(2) Select a case to verify: For a given coupon rate and initial yield, the longer the term to maturity, the higher the dollar price change.

Step 5: (2 points)
Setting the case at yield 7% as the benchmark (P0 case). Calculate the relative price change for each bond at each new yield level following the formula:
Relative Price Change= (Pt-P0)/P0

Step 6: (1.5 points)
(1) Select a case to verify: For a given term to maturity and initial yield, the higher the coupon rate, the lower the relative price change.
(2) Select a case to verify: For a given coupon rate and initial yield, the longer the term to maturity, the higher the relative price change.

Answer 1

Price of Bond = Coupon₁ / (1 + YTM)¹ + Coupon₂ / (1 + YTM)² + ...... + (Coupon_n + Face Value) / (1 + YTM)ⁿ

Step 4
1) Compare Bond B and Bond C, both have the same maturity, however, Bond C has a higher Coupon Rate.
We can see that as the yield changes, the Dollar prices of the bond C changes at higher rate as compared to Bond B

2) Compare Bond A and Bond B, both have the same coupon rate, however, Bond B has longer maturity.
We can see that as the yield changes, the dollar prices of Bond B changes at higher rate as compared to that of Bond A

Step 6
1) Compare Bond B and Bond C, both have the same maturity, however, Bond C has a higher Coupon Rate.
We can see that as the yield changes, the relative prices of the bond C changes at lower rate as compared to Bond B.

2) Compare Bond A and Bond B, both have the same coupon rate, however, Bond B has longer maturity.
We can see that as the yield changes, the relative prices of Bond B changes at higher rate as compared to that of Bond A.