 # Reading 30 Question 14 - Fixed Income

The answer to this question is that duration of sample leveraged portfolio = total dollar duration / investor’s equity x 100. Can anyone tell me where this is coming from? I am drawing a complete blank on this. Thanks

5125000/100m

Thanks i see that but why isn’t the whole portfolio value of 125MM used instead of 100MM equity?

Good question. I don’t know. I think they should add 25m as it was leveraged portfolio.

Question is asking the duration of the levered portfolio i.e. dollar duration of the net portfolio which is = dollar duration of the portfolio/equity*100. The numerator duration is net of liability which is zero duration for overnight funding. And the denominator is also net portfolio value which is equity and is \$100M and not \$125M. I hope this helps

Thanks for that bills. I read the CFAI text again to get a better understanding and it looks like that for this and for leveraged return calculation, the terms used “portfolio” / “equity” can be confusing. I used this formula: Dollar duration formula is = duration x portfolio value x 0.01 Here we have dollar duration = 5125000 = duration x 125mm x 0.01 duration = 5125000/(125mm x 0.01) = 4.1 I am guessing, leveraged means equity and not total portfolio and I should have used 100mm instead of 125mm.

I Believe the formula is (Value of Portfolio*Duration of Portfolio- Value of Debt*Duration of Debt)/Amount of Equity in portfolio. Where the term equity is referred to as valuoe your own money in the portfolio. The duration of a leveraged portfolio is greater than the duration of unleveraged portfolio.

I have the exact same problem, why isn’t the answer 4.1? The duration of the leveraged portfolio is not given.

levered position has exactly the same nature as using futures --> you use borrowed money to buy a position to change your beta/duration. The resulting beta/duration must be calculated on your original position/equity, not on the TOTAL borrowed/levered position, since it measures the effect on market/interest change on your position because of the leverage.

Now I know where this Q comes from…Don’t get confused when you are asked to calculate the duration of equity. Thanks to elcfa, again.