Duration of levered portfolio

G

Gersonides

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
Is a levered portfolio’s total duration equal to the duration of the equity component? I am familiar with the De = (DaA - DlL) / E to derive equity duration, but the 2012 Question 7 involves a question about the portfolios duration. I took that to mean a weighted average of the duration of the equity funds and borrowed funds.
 
It is the
total duration (Debt + Equity) - Duration (Debt) / (Equity)
In this case the 300M in the 1st part of the answer needed to be used
[(500 * 8.5) - (300)(0.8) ] / 200 = 20.05
 
The duration of a levered portfolio is the weighted average duration of the equity and liability components.
 
cebrach wrote:
The duration of a levered portfolio is the weighted average duration of the equity and liability components.
Click to expand...
This is exactly what I thought; and using this method, I arrived at 3.88:
(.4)(8.5)+(0.6)(.8) = 3.88
Further, when I use the (DaA-DLL)/E = De, I get the same answer if I solve for Da, which is what I thought the question “Determine the duration of the leveraged portfolio” is asking:
8.50 = Da(500) - (.8)(300) / 200
solve for Da ====> Da = 3.88
So what am I missing here?
 
cebrach wrote:
It doesn’t sound like you are missing anything.
Click to expand...
But the guideline answer, just as what cpk123 cited above, solves for De and states that the answer is 20.05:
DE = (DAA – DLL)/E
= [8.50 × (200,000,000 + 300,000,000) – 0.8 × 300,000,000] / 200,000,000
= 20.05.
 
I got 3.88 as my answer as well. Maybe this question could have been worded “Determine the duration of the equity in the leveraged portfolio”.
 
I am not sure where you are getting this statement from…
The duration of a levered portfolio is the weighted average duration of the equity and liability components. – NOT TRUE.
That is NOT TRUE.
The duration of liability (leverage) deducts (just like the interest you pay on the leveraged portion) from the duration of the portfolio always.
They state that in no uncertain terms in the book / reading as well.
And by now you would have realized - when they talk of Portfolio + Leverage together - The portfolio means the equity portion, always.
 
[1(8.5) - 0.6 (0.8)] / 0.4 = 20.05
You borrowed 60% of portfolio which has a duration of 8.5 with 40% of equity
 
Hi guys, now I also get confused with this… now that I see Gersonides answer, I would also have solved for Da in the equation as the question asks for the duration of the levered portfolio. However if we do this, then we would end up with a duration of 3.88 lower than 8.5 (meaning that the duration of the levered portfolio is way lower than the equity duration… but it doesn’t sound right to me)
 
I still think the question is worded poorly.
Not sure if the method to finding duration of a leveraged portfolio is the same as an unleveraged portfolio. In the 2014 AM Exam, there is a question to find the duration of the portfolio when bonds of a developing nation’s bonds are added.
It gives:
DURp = (Weight of Alphastan bonds x Adjusted Alphastan bond duration) + (Weight of UK bonds x new UK bond duration)

Anyone have any ideas?
 
cpk123 wrote:
I am not sure where you are getting this statement from…
The duration of a levered portfolio is the weighted average duration of the equity and liability components. – NOT TRUE.
That is NOT TRUE.
The duration of liability (leverage) deducts (just like the interest you pay on the leveraged portion) from the duration of the portfolio always.
They state that in no uncertain terms in the book / reading as well.
And by now you would have realized - when they talk of Portfolio + Leverage together - The portfolio means the equity portion, always.
Click to expand...
How is this not true? You literally just typed what was stated in bold in your next response.
Duration of assets/portfolio = Weight of Loan*Duration of loan + Weight of Equity * Duration of Equity.
You move that around to solve for Duration of Equity and it’s what you wrote:
Duration of assets/port - (weight of loan * duration of loan) all divided by Weight of Equity = Duration of Equity
 
verse214 wrote:
cpk123 wrote:
I am not sure where you are getting this statement from…
The duration of a levered portfolio is the weighted average duration of the equity and liability components. – NOT TRUE.
That is NOT TRUE.
The duration of liability (leverage) deducts (just like the interest you pay on the leveraged portion) from the duration of the portfolio always.
They state that in no uncertain terms in the book / reading as well.
And by now you would have realized - when they talk of Portfolio + Leverage together - The portfolio means the equity portion, always.
Click to expand...
How is this not true? You literally just typed what was stated in bold in your next response.
Duration of assets/portfolio = Weight of Loan*Duration of loan + Weight of Equity * Duration of Equity.
You move that around to solve for Duration of Equity and it’s what you wrote:
Duration of assets/port - (weight of loan * duration of loan) all divided by Weight of Equity = Duration of Equity
Click to expand...
You’re mixing up portfolio with levered portfolio, the latter which is equity.
 
they asked for leveraged portfolio’s duration.
Leveraged portfolio is poor wording. It can mean:
1. The portfolio that is leveraged meaning the De.
2. or the portfolio once it is levered or Da.
i see how others made the mistake. flip of a coin on this one.
 
You must log in or register to reply here.
Back
Top