Question

Sarah just used $96.83 purchased a Treasury bond. Assume that the yield rate for this bond is j₂ =3.68% p.a. and the duration of this bond is 3.62 years. Without actually calculating the new price for this bond, use the bond price and the duration value to estimate (use the price sensitivity formula) the change in price of this bond that would result from an increase in yield rate (j₂) of 18 basis points. Round your answer to four decimal places.

Answer 1

Bond Price = $96.83

Yield Rate = 3.68%

Macaulay Duration = 3.62

Modified Duration = Macaulay Duration /(1+yield/n)

Where n is the number of compounding per year

For treasury bonds coupon is paid semi-annually and hence, n = 2

Modified Duration = 3.62/(1+3.68%/2) = 3.62/ 1.0184 = 3.5546

Change in yield rate = 18 basis points = 0.18%

% Change in bond price = - Modified Duration * Change in yield

= -3.5546*0.18% = -0.6398%

Change in bond price = Bond price * % change in bond price = 96.83 * -0.6398% = -0.6195

Hence the bond price will reduce by $0.6195