Question

A 30-year maturity bond making annual coupon payments with a coupon rate of 7% has duration of 15.16 years and convexity of 315.56. The bond currently sells at a yield to maturity of 5%.

   

a.	Find the price of the bond if its yield to maturity falls to 4% or rises to 6%. (Round your answers to 2 decimal places. Omit the "$" sign in your response.)

   

Yield to maturity of 4%	$
Yield to maturity of 6%	$

  

b.	What prices for the bond at these new yields would be predicted by the duration rule and the duration-with-convexity rule? (Round your answers to 2 decimal places. Omit the "$" sign in your response.)

  

	Duration Rule	Duration-with- convexity Rule
YTM falls to 4%	$	$
YTM increases to 6%	$	$

   

c.	What is the percentage error for each rule? (Negative answers should be indicated by a minus sign. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

   

	Duration Rule	Duration-with- convexity Rule
Percent error for 4% YTM	%	%
Percent error for 6% YTM	%	%

        

Answer 1

Price (5%)	$1,307.45
Price (4%)	$1,518.76
Price (6%)	$1,137.65
	Duration	Convexity
Price (4%)	$ 1,505.66	$ 1,526.29
Price (6%)	$ 1,109.24	$ 1,129.87
% Error (4%)	-0.86%	0.50%
% Error (6%)	-2.50%	-0.68%

Bond Price can be calculated using PV function on a calculator

N = 30, PMT = 7% x 1000 = 70, FV = 1000, I/Y = 5% => Compute PV = $1,307.45 is the current bond price

Change I/Y to 4% and 6% to compute actual price.

Using duration rule,

% Change in bond price = - Duration x Change in Yield

Using convexity rule,

% Change in bond price = - Duration x Change in Yield + 0.5 x Convexity x Change in yield^2

Percent error = Price using duration or convexity rule / Actual Price - 1