Question

(excel) Consider a 8% coupon bond making annual coupon payments with 4 years until maturity and a yield to maturity of 10%.

1. What is the modified duration of this bond?

2. If the market yield increases by 75 basis points, what is the actual percentage change in the bond’s price? [Actual, not approximation]

3. Given that this bond’s convexity is 14.13, what price would you predict using the duration-with-convexity approximation for this bond at this new yield?

4. What is the percentage error?

Answer 1

a.

Annual coupon rate	8%		MDURATION function in excel
Yield	10%		3.237903803
Settlement date	4/10/2020
Maturity date	4/10/2024
Payment frequency	1

b.

Annual coupon rate	8%
Old Yield	10%
Settlement date	4/10/2020
Maturity date	4/10/2024
Payment frequency	1
Redemption value	100
New yield	10.75%

Using function PRICE in excel
Bond Price at old yield = 10%	Bond Price at new yield = 10.75%
93.66026911	91.42253393

Percentage change in bond price => (91.4225-93.6602)*100/91.4225 = -2.4476% (decrease)

c. Change in bond price = Duration effect + convexity effect

= (- Modified duration * change in yield) + (0.5* convexity* (change in yield)^2)

= (-3.2379*0.0075)+(0.5*14.13*0.0075*0.0075)

= -0.02388

=-2.388%

New price using convexity-duration = 93.6602*(100-2.388)/100 = 91.4236

d. Percentage error = = 0.001203%