# Duration

Can someone explain why would the duration on a levered portfolio be longer when a 1day repo is used instead of a 2-year repo?

Also, when a duration (D) is calculated for a levered portfolio (Dollar duration=0.01*D*Value) andf or example, 100 is equity, 25 is borrowed and 125 is total invested. Why do we use 100 and not 125 for Value to get the portfolio duration? If we have the dollar duration for the entire 125 and D for the total portfolio is required, it would make sense that 25 borrowed also affects the sensitivity.

Thank you

To be clear we are referring to practice problems 13 and 14 in Reading 23 (CFAI book no. 4).

As regards to your second question the borrowed \$25m indeed affects the sensitivity and is reflected in the DD.

The \$5.125m results from the algebraic sum of a certain DD coming from the asset (\$125m) plus the DD coming from the \$25m liability (these dd will have opposite sign). DD asset + (-) DD liability = 5.125m

What we are doing is this:

DD asset + (-) DD liability / (Asset - Liab.) *.01

As to the first question, the same general reasoning applies. The liability is associated with a negative duration and the negative duration resulting from a 2-yrs repo is greater than the duration associated to an overnight repo.

Hence computing the total duration

D asset + (-) D liability

the higher overall duration is associated with the overnight repo.

Good luck, Carlo