How can the interest-rate risk of the projectedliabilities of a defined benefit pension plan bemeasured?

What will be an ideal response?

Let us ignore all risks other than interest-rate risk for projected liabilities of a defined benefit pension plan. Doing this, we can get a first approximation for measuring the funding gap's exposure to interest-rate risk by considering the dollar duration of the assets and liabilities. That is, the funding gap interest-rate risk (or change in the funding gap due to interest-rate risk)equals the dollar duration of projected liabilities minus the dollar duration of fund assets. In equation form, we have:

Funding gap interest-rate risk = Change in the funding gap due to interest-rate risk =
Dollar duration of projected liabilities − Dollar duration of fund assets

As interest rates change, the relative change in the market value of the assets and liabilitieswill change depending on their respective dollar duration. If the dollar duration of the projectedliabilities exceeds that of the dollar duration of the fund's assets, then a rise in interestwill reduce the funding gap as the liabilities will decline by more than the assets. The risk iswith a decline in interest rates, which will result in an increase in the funding gap. More details are given below in form of an example.

For example, consider the following DB pension plan:

Market value of fund assets = $500 million
Projected value of liabilities = $600 million
Portfolio duration (i.e., duration of fund assets) = 7
Liability duration (i.e., duration of projected liabilities) = 12

The funding gap and funding ratio for this hypothetical plan are $100 million and 0.857 (or 85.7% in percentage form),respectively.

Let's look at the dollar duration of the projected liabilities and fund assets assuming a100-basis-point-change parallel shift in interest rates:

Fund assets will change by about 7% for a 100-bp change in rates.
Projected liabilities will change by about 12% for a 100-bp change in rates.

The dollar duration (per 100 bp) change in rates is then:

Portfolio dollar duration = 7% × $500 million = $35 million
Liability dollar duration = 12% × $600 million = $72 million

This means that the change in the funding gap for a 100-bp change in interest rates isroughly Change in Liability dollar duration minus Change in Portfolio (Asset) dollar duration =$72 – $35 = $37 million. More specifically, the risk is that interest rates will decline. In thatcase, the value of the liabilities will increase by $72 million and the value of the fund assetswill increase by $35 million, increasing the funding gap by $37 million.