Using Swaps to Adjust Duration of a Fixed-Income Portfolio

A fixed income manager enters into a receive floating interest rate swap with notional principal of CHF 18 million, in order to adjust the duration of a CHF 60 million bond portfolio to 5. If the swap's duration is estimated to be 2.5, what is the duration of the bond portfolio?

Correct! The notional principal needed for this adjustment is given by: $$\displaystyle NP = B \left( \frac{MDUR_T - MDUR_B}{MDUR_S} \right) $$ In this case, the following is known: $$\displaystyle 18 = 60 \left( \frac{5 - MDUR_B}{-2.5} \right) $$ The duration of the bond portfolio must be: $$\displaystyle MDUR_B = 5 + 2.5(\frac{18}{60}) = 5.75 $$ It is important to note that the swap duration is negative since the manager decided to receive floating; this must therefore be an adjustment to reduce portfolio duration.

Incorrect. Since the manager has chosen to receive floating, the duration adjustment will be negative, not positive.

Incorrect. Start with the calculation for the duration adjustment, plugging in the known values: $$\displaystyle NP = B \left( \frac{MDUR_T - MDUR_B}{MDUR_S} \right) $$

3.75

5.75

6.25