# duration and market value risk question

To reduce duration, we should enter into a pay fixed receive floating swap… also if duration reduces market value risk reduces.

Then why does market value risk increase when a firm swicthes from floating rate debt to fixed rate using pay fixed receive floating swap?

If you’re paying fixed and receiving floating, you’re net short duration _ on the swap _.

Whether that increases or decreases your market value risk depends on the rest of your portfolio. If you’re net long duration on the rest of your portfolio (more than 50% of the net swap dollar duration), it reduces your market value risk. If you’re net short duration on the rest of your portfolio (or zero, or positive, but less than 50% of the net swap dollar duration), it increases your market value risk.

thanks S2000, could you explain what happnes in the other case i.e on adding a net long duration swap

Suppose that you’re given this information:

• Portfolio value: £10 million
• Portfolio duration: 3 years

The portfolio dollar (pound?) duration is £10 million × 3 years = 30 million pound-years.

If you enter into a pay fixed, receive floating plain vanilla interest rate swap with a notional amount of £5 million and a net duration of -5 years, then the dollar duration of the swap is £5 million × -5 years = -25 million pound-years, so you have reduced your market value risk to 30 million pound-years – 25 million pound-years = 5 million pound-years.

If you enter into a pay fixed, receive floating plain vanilla interest rate swap with a notional amount of £15 million and a net duration of -3 years, then the dollar duration of the swap is £15 million × -3 years = -45 million pound-years, so you have reduced your market value risk to 30 million pound-years – 45 million pound-years = -15 million pound-years. The market risk is in the opposite direction from your original, but in magnitude it’s smaller.

Suppose instead that you’re given this information:

• Portfolio value: £15 million
• Portfolio duration: -1 years

The portfolio pound duration is £15 million × -1 years = -15 million pound-years.

If you enter into a pay floating, receive fixed plain vanilla interest rate swap with a notional amount of £5 million and a net duration of 5 years, then the dollar duration of the swap is £5 million × 5 years = 45 million pound-years, so you have increased your market value risk to -15 million pound-years + 45 million pound-years = 30 million pound-years. The market risk is in the opposite direction, and its magnitude is greater.

If you enter into a pay floating, receive fixed plain vanilla interest rate swap with a notional amount of £5 million and a net duration of 2 years, then the dollar duration of the swap is £5 million × 2 years = 10 million pound-years, so you have reduced your market value risk to =15 million pound-years + 10 million pound-years = -5 million pound-years.