Question

An investor buys 6% semi-annual coupon paying bond with six years to maturity and $1000 par value at $906.15.The bond has a YTM of 8%. For all the calculations ,keep four digits after the decimal place

b)Calculate the bond's modified duration

c)If the interest rate increases by 20 basis points, what is the approximate value of the bond by using modified duration?

d)What is the real value of the bond after the change (using the bond pricing formula )?

Answer 1

Modified Duration = 9.756 years and Increase in Interest Rate = 20 basis points

% Change in Bond Price = - Modified Duration x change in interest rate = - 9.756 x 0.002 = - 0.01951 or - 1.951 %

New Bond Price = Original Bond Price x % Change in Bond Price = (1-0.01951) x 906.15 = $ 888.47

If the actual bond price formula is used, then Coupon Rate = 6 % per annum payable semi-annually, New YTM = 8-0.2 = 7.8 % per annum or (7.8/2) = 3.9 % per half-year and Par Value = $ 1000, Tenure = 6 years or 12 half-years

Semi-Annual Coupon = 0.06 x 0.5 x 1000 = $ 30

Therefore, New Bond Price = 30 x (1/0.039) x [1-{1/(1.039)^(12)}] + 1000 / (1.039)^(12) = $ 915.042