Using leverage to extend portfolio duration
For example, a portfolio with 10 million market value and a duration of 6 has PVBP = 6000.
(10 million *6)/10000=6000
To increase the effective portfolio duration to 7, how does a manager use leverage to purchase similar bonds with a duration matching the portfolio duration of 6?
Answer from curriculum:
To increase the effective portfolio duration to 7, we need to add 1000 PVBP. (10 million*7)/10000=7000
Required additional PVBP: 1000
divided by duration of bonds to be purchased: 6
equals additional market value of bonds to be purchased: 1.67 million
My question is: After purchasing the new bonds, the market value of the portfolio becomes 11.67 million. The new PVBP becomes 7000. According to the equation: market value*duration*1bp=PVBP (11.67m*duration*1bp=7000), the new portfolio duration does not equal to 7.
I do not think we can simply add 1000 PVBP to the portfolio in order to change the duration from 6 to 7. We have to consider the change of market value.