Question

Both Bond Sam and Bond Dave have 10 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 4 percent, what is the percentage change in the price of Bond Sam?

    

	If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave?

    

	If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Sam be then?

    

	If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Dave be then?

Answer 1

1.
Let par value =1000
Coupon = 1000*10%/2 = 50
Since Price of Bond = Par Value so YTM = 10%
Half yearly rate = 10%/2 = 5%

Maturity of Sam's Bond =3
Number of years = 3*2 =6
If interest increase in 4% = YTM+4% = 10%+4% = 14%
Half Yearly Interest rate 14%/2 =7%
Bond Price = PV of coupons + PV of Par value = 50*(1-(1+7%)^-6)/7% + 1000/(1+7%)⁶ = 904.67

Percentage change in price of Bond Sam= (904.67 -1000)/1000 = -9.53%

Maturity of Sam's Bond =20
Number of years = 20*2 =40
If interest increase in 4% = YTM+4% = 10%+4% = 14%
Half Yearly Interest rate 14%/2 =7%
Bond Price = PV of coupons + PV of Par value = 50*(1-(1+7%)^-40)/7% + 1000/(1+7%)⁴⁰ = 733.37

Percentage change in price of Bond Dave = (733.37 -1000)/1000 = -26.67%

2. Maturity of Sam's Bond =3
Number of years = 3*2 =6
If interest decrease in 4% = YTM-4% = 10%-4% = 6%
Half Yearly Interest rate 6%/2 =3%
Bond Price = PV of coupons + PV of Par value = 50*(1-(1+3%)^-6)/3% + 1000/(1+3%)⁶ = 1108.34

Percentage change in price of Bond Sam= (1108.34 -1000)/1000 = 10.83%

Maturity of Sam's Bond =20
Number of years = 20*2 =40
If interest decrease in 4% = YTM-4% = 10%-4% = 6%
Half Yearly Interest rate 6%/2 =3%  
Bond Price = PV of coupons + PV of Par value = 50*(1-(1+3%)^-40)/7% + 1000/(1+3%)⁴⁰ = 1462.30

Percentage change in price of Bond Dave = (1462.30 -1000)/1000 = 46.23%

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