The schweser text says that “Just as the leverage increases the portfolio return variability, it also increases the duration, given that the duration of borrowed funds is typically less than the duration of invested funds”
I don’t understand the second part of the sentence- "…given that the duration of borrowed funds is typically less than the duration of invested funds". Can someone explain why this is given?
Well, you’re short duration on the borrowed funds. So we know the simple relationship (assuming no leverage for simplicity), when rates fall, bond prices rise as a function of duration.
Now introduce leverage, where you are short duration. When rates fall, and you are short duration, the value of your short position (AS FAR AS YOU’RE CONCERNED), the value of your borrowed funds rises, making you owe more money (like, increased negative value in your portfolio).
Assume there is a potential investment with duration 1. And you borrow funds to make that investment, but the duration of the funds you borrow is 1. So, actually, it’s a perfectly hedged combination. If rates fall, the investment rises in value, but your obligation also rises by the same amount. What if the duration of your borrowed funds was greater than 1? Then your obligation would rise by MORE than your investment, so the levered portion of the portfolio would actually be net short duration , and the levered portion of the portfolio value would actually be positively correlated with rates.
Just write down a couple of examples and do the math.
Go back to Level I and remember what affects duration:
Longer maturity, longer duration.
Higher coupon, shorter duration.
Higher YTM, shorter duration.
So, if you borrow short-term and invest long-term, the duration of your borrowed funds would be shorter than the duration of your invested funds. If you borrow at a higher interest rate than you invest (stupid, in my opinion, but not uncommon, I suspect), the duration of your borrowed funds will be shorter than the duration of your invested funds (even if the maturities are equal).