Calculating duration of a leveraged portfolio

[johntavv]

CFAI readin 23, practice problem 14 asks for the duration of the sample leveraged portfolio given the following info:
If we use funds from a $25m overnight repo to purchase bonds in addition to the current $100m portfolio, the levered portfolio’s change in value for a 1% change in interest rates would equal $5,125,000 while giving you the portfolio duration you require.
The answer has duration of the portfolio = (Total Dollar Duration / Investor’s equity in the original portfolio) x 100
= (5,125,000 / 100,000,000) x 100.
Where do they get this formula from, i can’t seem to find it?

 

[cpk123]

Amount Invested * Duration * 0.01 = Dollar Duration
It is just the simple Dollar Duration formula - and that formula stares at me from the top of Pg 110 on the 2014 books.
100M * Duration * 0.01 = 5.125M
So Duration = 5.125 / 100 * 100 = 5.125

 

[johntavv]

Got it thanks