## duration

sessiljoseph
Good Student
Posts: 22
Joined: Sat Apr 26, 2014 7:29 am

### duration

A bond portfolio manager makes the following two statements:
I. "We hedged our bond position (B), which has a duration of 6.5 years, with the hedge portfolio (H), which also has a duration of 6.5 years. Therefore, if interest rates increase by 20 basis points, the percentage decrease in the value of (B) will be equal to the percentage increase in the value of (H)."
II. "We have a short position in a portfolio of plain-vanilla [ie., no embedded options] coupon-bearing bonds, with portfolio duration of 5.0 years. Therefore, if yields increase by 20 basis points, our gain will likely be less than 1.0%, but if yields decrease by 20 basis points, our loss will likely be greater than 1.0%"
Which of the above statement(s) is (are) true?
a) Neither is true
b) I. only
c) II. only
d) Both I. and II. are true
can u please explain this question

edupristine
Finance Junkie
Posts: 946
Joined: Wed Apr 09, 2014 6:28 am

### duration

Only II is correct, The statement is correct because for short positions loss will be greater than gain due to convexity effect.
Statement I is incorrect because it is not necessary that the percentage decrease in the value of B will be equal to the percentage increase in the value of H, As we don't have the factors of measurement.