Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has six years to maturity, whereas Bond Dave has 19 years to maturity. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave?

Answer 1

assume Par Value = 1000

Price = 1000

Coupon = 7%

Coupon = Coupon rate * Par Value/2 = 7% * 1000/2 = 35

For Sam Maturity = 6 years

Price = summation Coupont/(1+YTM/2)2t + Par Value/(1+YTM/2)2t

1000 = 35/(1+YTM/2)2t + 1000/(1+YTM/2)2t

YTM = 7%

For Dave Maturity = 19 years

Price = Coupont/(1+YTM/2)2t + Par Value/(1+YTM/2)2t

1000 = 35/(1+YTM/2)2t + 1000/(1+YTM/2)2t

YTM = 7%

If YTM increases by 2% so new YTM =9%

For Sam Maturity = 6 years

Price = Coupont/(1+YTM/2)2t + Par Value/(1+YTM/2)2t

Price = 35/(1+(9%/2)2t + 1000/(1+9%/2)2t

Price = 908.81

Percentage change in price of Sam bond = 908.81 -1000/1000 = -9.12%

For Dave Maturity = 19 years

Price = Coupont/(1+YTM/2)2t + Par Value/(1+YTM/2)2t

Price = 35/(1+9%/2)2t + 1000/(1+9%/2)2t

Price = 819.50

Percentage change in price of Dave bond = (819.50-1000)/1000 = -18.05%

If YTM decreases by 2% so new YTM =5%

For Sam Maturity = 6 years

Price = Coupont/(1+YTM/2)2t + Par Value/(1+YTM/2)2t

Price = 35/(1+(5%/2)2t + 1000/(1+5%/2)2t

Price = 1102.58

Percentage change in price of Sam bond = (1102.58 -1000)/1000 = 10.26%

For Dave Maturity = 19 years

Price = Coupont/(1+YTM/2)2t + Par Value/(1+YTM/2)2t

Price = 35/(1+5%/2)2t + 1000/(1+5%/2)2t

Price = 1243.49

Percentage change in price of Dave bond = (1243.49-1000)/1000 = 24.35%