Convexity – The Forgotten Risk for Pension Plans

by | Oct 2, 2019 | bytesize, Defined Benefit, Investment

Pension risk is asymmetric in more ways than one

Most sponsors of corporate pension plans are familiar with their risk being asymmetric: they only benefit to a point if a plan’s funding level improves, but are on the hook for all underfunding if it does not. This recognition of asymmetry has led to a large increase in plans adopting Liability Driven Investing (LDI) frameworks.

Many plan sponsors though are less familiar with the risk asymmetry that is inherent in how liability cash flows are valued, specifically regarding a term called convexity. Convexity is the second-order effect on liability values as interest rates move, with the first order effect being duration. Duration is the value that denotes how much the present value of a set of cash flows will move as the interest rate used to discount those cash flows moves. For example, pension liabilities with a duration of 12 years will move up or down by roughly 12% if interest rates move by 1% (from 4% to 5% or 3%, for example).

Most of the time, just worrying about the difference in duration between pension assets and liabilities is sufficient. However, as interest rates fall, the sensitivity of liabilities to further changes in interest rates starts to increase: this is convexity. The table below shows this impact on liability value for a typical pension plan with a duration of 12 years:

Discount RateLiability Value
($ billions)
Change in liability value
for a 1% change in rates

As the table shows, as interest rates decline, the liability value changes at an increasing rate. While market observers used to scoff at the possibility of long-term interest rates falling to levels like 2% or 1%, we can see examples from Europe and Japan the potential for long term interest rates to not only fall to those levels, but to even fall below zero.

Convexity exacerbates the asymmetry problem for plan sponsors. Not only does the sponsor lose if funding levels decline, but she loses even more if the underlying reason is because of a decrease in long term interest rates. As well, if rates rise, the benefits of the rise weaken (at the margin) as rates increase.

With discount rates decreasing significantly in 2019 (see chart below), pension plans are feeling the effect of this uneven relationship.

So what can a plan do?

To help protect funding levels from unexpected impacts from this asymmetric relationship, plans should work with an advisor that has experience hedging liabilities. Tools such as Treasury STRIPS, interest rate swaps, and swaptions can all be used to help manage both duration and convexity risk. Convexity risk is one reason that plan sponsors should consider hedging more interest rate risk than they have historically, despite the fact that rates are low. A long-term view that long-term interest rates will rise is fine, but acknowledging the significant, and asymmetric, risk of getting this wrong cannot be ignored.


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