Question

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?

Please show how to do it and use excel if possible. thank you

Answer 1

SOLUTION:-

a.

Annual coupon rate	8%
Yield	10%
Settlement date	4/10/2020
Muturity date	4/10/2024
Payment frequency	1

MDURATION function in excel

3.237903803

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) + convexity * (change in yield)^2)

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

= -2.388%

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

d. Percentage error = = 0.001203%

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