Reading 25 CFAI #13 (effect of repos on duration)

Sheila Ibahn, a portfolio manager is reviewing the performance of a fixed income portfolio and expects a downward parallel shift in the yield curve. Therefore, she recommends increasing interest rate risk across the portfolio. She says,

“We could lever the portfolio by entering into either an overnight or 2-year term repurchase agreement and use the repo funds to purchase additional bonds that have the same duration as the current portfolio.”

Question 13 asks, "the levered portfolio would have: A) the same duration if either the overnight repo or the 2-year repo is used; 2) a longer duration if the overnight repo is used instead of the 2-year term repo; C) a shorter duration if the overnight repo is used.

The correct answer is B. I’m having trouble wrapping my head around how the repo term in the use of leverage affects portfolio duration. Can anyone clarfiy? Thanks

repo provides leverage.

and leverage affects the duration.

and a longer term repo has a bigger duration than a shorter term repo. And since this repo duration is subtracted - the combined portfolio with the longer term repo will have a shorter duration than the one with the shorter term repo.

Dp = (Di x I - Db x B) / E

where Dp = duration of levered portfolio

Di = duration of invested fund

I = invested funds

Db = duration of borrowed funds (which is repo in this case)

B = Borrowed funds & E = equity

So Duration of levered portfolio is indirectly proportional to duration of borrowed funds

this is why i love AF. Thanks!