# Duration of leveraged portfolio

Given \$100 million fixed income portfolio, use additional borrowed money to buy extra \$25 million bonds, for 1% change in interest rate, 5,125,000 is the portfolio change in value. What is the duration of the leveraged portfolio?

5.125 …

because they always ask for duration of the “equity” (100 Million) of the portfolio.

the formula to calculate duration of leveraged portfolio is:

( D(A)*A - D(L)*L ) / Equity

or

Total dollar duration / Equity x 100

why do we use (5,125,000/100,000,000) x 100 to get 5.125? How do we know 5,125,000 is the total dollar duration?

What is Change in Value of Portfolio = Value of Portfolio * Duration Of Portfolio * -1

What is Dollar Duration of Portfolio = (Value of Portfolio * Duration of Portfolio)/100 – the /100 here is to make this Dollar Duration per 1% change in Rate. (Duration of A Basis Point)…

Except for the -1 factor above - both are the same, as can be seen…

And here this number 5125000 is the value for a 1% change in Rate… hence you do not need to do the /100 part …

Thank you.