Question

1. A bond has a $1,000 par value, 4% coupon paid annually, 3.5% YTM, 15 years to maturity, and a modified duration of 7.4. Use the interest rate risk estimation formula to estimate interest rate risk for this bond in response to a 50 basis point decrease in its yield to maturity.

2. A bond has a $1,000 par value, 6% coupon paid annually, 6.25% YTM, 12 years to maturity, and a modified duration of 5. Estimate the price change for this bond if its yield to maturity increases by 25 basis points.

Answer 1

(1) Bond Par Value = $ 1000, Coupon Rate = 4 % payable annually, YTM = 3.5 % and Time to Maturity = 15 years

Annual Coupon Rate = 0.04 x 1000 = $ 40

Therefore, Bond Price = 40 x (1/0.035) x [1-{1/(1.035)^(15)}] + 1000 / (1.035)^(15) = $ 1057.587

Modified Duration = 7.4 and Change in YTM = - 50 basis points

Interest Rate Risk = % Change in Price(owing to given change in YTM) = - Modified Duration x (Change in YTM) = - 7.4 x (-0.005) = 0.037 or 3.7 %

(2) Bond Par Value = $ 1000, Coupon Rate = 6 % payable annually, YTM = 6.25 % and Time to Maturity = 12 years

Annual Coupon Rate = 0.06 x 1000 = $ 60

Therefore, Bond Price = 60 x (1/0.0625) x [1-{1/(1.0625)^(12)}] + 1000 / (1.0625)^(12) = $ 979.3247

Modified Duration = 5 and Change in YTM = + 25 basis points

Interest Rate Risk = % Change in Price(owing to given change in YTM) = - Modified Duration x (Change in YTM) = - 5 x (0.0025) = - 0.0125 or - 1.25 %

New Bond Price = 979.3247 x (1-0.0125) = $ 967.0831