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 ?

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

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

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

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).

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.