Effect of Leverage on Duration

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PJStyles

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From the Schweser Notes:
“Just as leverage increases the portfolio return variability, it also increases the duration, given that duration of borrowed funds is typically less than duration of invested funds.”
I don’t get this… Isn’t the duration on borrowed funds HIGHER than duration of invested funds because of it’s increased return variability?
 
borrowing makes sense only if the rate on the liability is less than the rate on the asset.
 
I get that… You should only borrow if the rate of return on the asset/investment is higher than the rate on the loan but how does that result in a higher duration for invested funds as opposed to borrowed funds?
Material clearly states that return variability rises with leverage. As a result, duration of borrowed assets should in theory be higher. Maybe I’m just not getting it…
 
the formula to calculate duration using leverage is
D(A)*A - D(L)*L / Equity
D(A) - Duration of assets
A - Assets
D(L) - Duration of Liability
L - Liability
E - Equity = Assets - Liability
Just wanted to check if I remember :)
 
Yes…leverage certainly increases duration. The part I don’t get is where it states:
“…given that duration of borrowed funds is typically LESS than duration of invested funds”
How is that possible?
 
Its the Overall portfolio’s duration that increases…not the individual bonds. Also the duration of borrowed funds is typically LESS because you borrow on a short term basis, say 90 days which migth have a duration less than .25.
 
Ahhh… okay that makes sense.. “borrowing is usually short-term in nature”… got it! The rest I understand… Thanks for clearing this up… Many you guys are ready for this exam!!! I’m getting nervous now… lol
 
Leverage increases the portfolio duration because the variability of returns rise with the use of leverage. Increased return variability = Increased Duration (price sensitivity of the bond to changes in rates). At least that’s my understanding.
PJStyles
 
If I am a fixed income hedge fund, buying typical corporate and mortgage bonds etc, I am probably investing in lots of 30yr and 10yr bonds, so my average asset duration is almost certainly >5.0. As someone explained earlier, financing for fixed income leverage is typically in the repo markets or other short term borrowings with duration of less than a quarter of a year.
So does duration increase or decrease relative to an unlevered portfolio? To answer the question, figure out if the part of the levered portfolio which is different from the unlevered portfolio has a positive duration or a negative duration. A positive duration would suggest that portfolio value increases if rates (i.e. discount rates) decline. A negative duration suggests the opposite.
The levered part of the portfolio is the part where I borrow on an overnight basis, or a 90 day basis, or whatever. I then use the proceeds to buy 10yr and 30yr bonds. If rates (i.e. discount rates) decline, it has a much greater effect on the present value of my 30yr cashflows than on the present value of my overnight or 90 day cashflows. Ergo, leverage increases duration.
 
thanks newsmaker…
can i follow up…..so i focus on the fact that i have increased my exposure to 10 or 30 yr position. however, i dont ignore the duration impact of borrowed funds, they do reduce duration, just but the impact is so negligible. (do we include liabilities - i forgot)
correct?
 
I finally got it. With leverage, we long the total assets I with duration Di, short the borrowed funds B with duration Db, therefore portfolio assets E’s duration Dp should be
[Di*I - Db*B]/E
Rearrange it we get Dp = [(Di-Db)*B + Di*E]/E since B+E=I
Now as bigwilly said, Di > Db, therefore Dp > Di. So if without leverage you usually invest to a target duration of Di, now with leverage if you invest the borrowed funds the same way, portfolio duration will increase to a level higher than Di.
 
“i dont ignore the duration impact of borrowed funds, they do reduce duration, just but the impact is so negligible. ”
Well I donn’t know about negligible, but the impact is certainly smaller than the impact of the new assets. Yes, you do include the liability side of the equation.
 
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