Duration of leveraged portfolio

CFA Level III Fixed Income
#1

Given duration of bond portfolio is 8.5 , duration of borrowed​ fund is 0.8, Question ask to find duration of leveraged portfolio. De = (Da*A - Dl*L ) / E The duration of bond portfolio of 8.5, is it Da asset duration or De equity duration ?

#2

It’s similarly worded in the CFAI book. Da = 8.5

#3

Thanks. Why is duration of leveraged portfolio same as duration of equity?

#4

Duration of Leveraged Portfolio = Duration of Equity after you lever the portfolio. It is the same thing.

#5

The only part of the portfolio that is YOURS is the part that is the Equity Portion. You may add X amount of debt - that changes the equity Duration - and how much did that change by is what you are seeing.

(Similar to: you had $100 in the bank. You borrowed $20. You pay interest on the $20 - and the interest coverage or other such ratios are calculated wrt the original $100 not with respect to $120).

#6

Thank you cp, i sort of understand it. The duration of portfolio will not changed when you add debt, only the duration of leveraged portfolio changes.