Question

Both Bond Sam and Bond Dave have 6.5 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?

Answer 1

when bonds are priced at par value Coupon rate = YTM

1 - when interest rates raise by 2% :

New YTM = 6.5% + 2% =8.5%

Usng financial calculator price of the bond can be calculated

Bond Sam:

Number of periods (N) = 3*2 = 6

YTM (I/Y) = 8.50% / 2 = 4.25%

Coupon(PMT) = 1000 * 6.5% / 2 = 32.5

[N = 6 ; I/Y = 4.25% ; PV = ? PMT = 32.5 ; FV = 1000] compute for PV

Bond Price(PV) = 948

% change = (948 - 1000) / 1000 = 5.20% (Negative)

Bond Dave :

[N = 40 ; I/Y = 4.25% ; PV = ? PMT = 32.5 ; FV = 1000] compute for PV

price = 809.23

% change = (809.23 - 1000) / 1000 = 19.08% (Negative)

2 - if interest rate fall by 2%:

new YTM = 6.5% - 2% = 4.5% (2.25% per semi annual)

Bond Sam :

[N = 6 ; I/Y = 2.25% ; PV = ? PMT = 32.5 ; FV = 1000] compute for PV

Price = 1055.54

% change = (1055.54 - 1000) / 1000

= 5.55%

Bond Dave :

[N = 40 ; I/Y = 2.25% ; PV = ? PMT = 32.5 ; FV = 1000] compute for PV

Price = 1,444.44

% change = (1444.44 - 1000) / 1000 = 44.44%

Graph :

Bond Sam :

Bond Dave:

More the Maturity period  More the Interest rate Risk of the bond