Question

1. Assume that all discount rates are 4% per year, and semi-annually compounded.

You are given the following semi-annual coupon bond.

· Settledate: 1-Jan-2019

· Maturity date: 1-Jan-2024

· Annual coupon rate: 6%

· Coupons paid semi-annually

· Yield to maturity: 4%

· Par value: $1000

Time to maturity: T=5 years

- Calculate the bond price using (y + Delta_y) as the bond's yield to maturity. Round to six digits after the decimal

- Calculate the bond price using (y - Delta_y) as the bond's yield to maturity. Round to six digits after the decimal.

- Calculate the modified duration using the formula above.

-What does the modified duration mean? Assume that the modified duration on Question 1.5 was 4.
In that case, if interest rates increase by 1 percentage point, then the bond price...

A) changes by approximately -4%

B) changes by approximately +4%

C) changes by approximately -0.25%

D) changes by approximately +0.25%

E) changes by approximately -1%

F) changes by approximately +1%

Answer 1

Modified Duration measures the percentage change in bond price for a 1 percentage-point change in yield.

	Annual Coupon Rate	6%
	Yield	4%
	Settlement date	01-01-2019
	Maturity date	01-01-2024
	Payment frequency	2
	Par Value	1000
	Time to Maturity	5
1	Modified Duration	4.34
2	Original Bond price, P	1089.825850
3	% Change in YTM	0.50%
	% Change in bond price	-2.17%
	New bond price	1066.194444
4	% Change in YTM	-0.50%
	% Change in bond price	2.17%
	New bond price	1113.457256
5	Given, Modified Duration	4
	Increase in Interest rate	1%
	Change in bond price	-4%
		Option (A)