# Calculating Duration for Leveraged Bond Positions?

Does anyone know how to do this? I am drawing a blank.

The only thing I’ve seen is: effective duration of leveraged portfolio = duration * leverage Is that correct?

Simplistically, you borrow cash and invest in bonds. What is the sensitivity of this portfolio to interest rates. Shouldnt the net duration be lower than the stand alone bond portfolio?

My thought was since leverage magnifies the returns, it must therefore magnify the impact of changes in sensitivity to interest rates - e.g. higher duration?

Presumably the point of a leveraged bond portfolio is to increase duration (assume we are talking long bonds). You borrow money short-term, and invest in long term bonds. There are two portfolios, one with big positive duration and the other with small negative duration. Add 'em.

JoeyDVivre Wrote: ------------------------------------------------------- > Presumably the point of a leveraged bond portfolio > is to increase duration (assume we are talking > long bonds). You borrow money short-term, and > invest in long term bonds. There are two > portfolios, one with big positive duration and the > other with small negative duration. Add 'em. Joey this will be true for Dollar D only. My answer was just for Duration. I may be completely off though.

That makes sense, thanks!

needhelp Wrote: ------------------------------------------------------- > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > Presumably the point of a leveraged bond > portfolio > > is to increase duration (assume we are talking > > long bonds). You borrow money short-term, and > > invest in long term bonds. There are two > > portfolios, one with big positive duration and > the > > other with small negative duration. Add 'em. > > Joey this will be true for Dollar D only. My > answer was just for Duration. I may be completely > off though. So weighted Add 'em

I think the relevant term is “Equity Duration,” which is the sensitivity of your fund’s equity value (i.e. Total Assets minus Debt ) to interest rate changes. That gets magnified by leverage so that the sensitivity of your fund’s “equity” is much higher. The two relevant parts of the equation are the proportion of equity to debt (which is a magnification factor) and the spread between the bond’s return and the return on bonds you are buying (which is a correction for the fact that you pay interest to get leverage). They teach the formula at L3 but I’ve forgotten it and I’m too lazy/unmotivated to derive it here. It’s not that hard to derive, though. There is a totally different meaning of “Equity Duration” which is the sensitivity of stock prices to interest rates. For a dividend paying stock in a mature company, this should be 1/(dividend yield). Interestingly, equities often have a very long duration, which probably has to do with the fact that stocks - like many people on AF - never mature.

Yeah that’s actually what I had in mind. I wasn’t sure what the correct wording was, obviously. Clearly I haven’t opened my level three books yet…