# Duration of portfolio with pay fixed position

Five-Year Pay-Fixed Swap Overlay
In this example, the manager enters into a pay-fixed swap overlay with a notional principal equal to one-half of the size of the total bond portfolio. We will focus solely on first-order effects of yield changes on price (ignoring coupon income and swap carry) to determine the active and index portfolio impact. As the pay-fixed swap is a “short” duration position, it is a negative contribution to portfolio duration and therefore subtracted from rather than added to the portfolio. Recall the \$100 million “index” portfolio has a modified duration of 5.299, or (1.994 + 4.88 + 9.023)/3. If the manager enters a \$50 million notional 5-year pay-fixed swap with an assumed modified duration of 4.32, the portfolio’s modified duration falls to 3.139, or [(5.299 × 100) − (4.32 × 50)]/100.

Why was the duration calculated like this? You are long 100mn, and short 50mn due to the pay fixed. So, wouldn´t you calculate it as: 5,299 x 100/(100-50) + 4,32 x (-50)/(100-50)? And then the result would be 6,27, which would actually mean a higher duration. Which I know is wrong, duration drops if you enter a pay fixed swap. I just don´t get how they calculated the duration of 3.139.

Yes you are right. I am also facing the same issue. Your method is correct w.r.t. weighted average duration but cannot understand why it’s increasing the new duration

The value of the portfolio doesn’t change by adding the swap, any more than it would change by adding a futures position.