Many plan sponsors have responded to the increased risks and affordability challenges of traditional defined-benefit pension plans by transitioning to cash balance plans. However, because cash balance plans base future benefits on a predefined crediting rate—which is often tied to long-term interest rates, such as a 30-year par yield—both their benefit amounts and their liability discount rate are sensitive to changes in interest rates.
Hedging to mitigate a cash balance plan’s interest rate risk is complicated. For one thing, many cash balance plans include interest rate floors (e.g., 5%), so liabilities are fixed at low interest rates but variable as rates rise, resulting in shorter durations at higher yields. Second, cash balance plans tend to use long-term interest rates, rather than short-term (cash or T-bill) rates, for indexation.
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One approach to dealing with these floors is to consider the benefits as fixed whenever the par rate is below the floor and as floating when the par rate is above the floor. This is typical in actuarial practice, and is often called a “binary” approach. However, it does not adequately capture a cash balance plan’s interest rate exposure because the sensitivity to interest rates of the plan’s benefits should never be 0 percent or 100 percent—it should be somewhere in between. Delta hedging offers a more precise method of mitigating interest rate risk by adjusting the mix of fixed and floating assets using a stochastic model.
Why the Binary Approach May Not Be the Best Way to Hedge
To simplify the hedging process, actuaries may not allow for optionality when performing their valuations. As a result, if par rates are currently below the plan’s floor, the actuaries may assume that rates will increase in the future at the floor, whereas if rates are currently above the floor, they may assume increases in line with the par rate. This binary hedging approach, which ignores the volatility of interest rates, may seem appropriate from a short-term–valuation perspective.
There are three main issues with this approach. First, liabilities will be understated. Even at higher interest rates, the floor has some value to a cash balance plan member, since it protects their crediting rate from dropping to low levels should interest rates fall in the future. Failing to account for this could lead to a lack of prudence in funding among plan sponsors. See Figure 1.
Second, the binary approach leads to a suboptimal strategy. This becomes clear if you model the ultimate asset and liability cash flows. The first graph in Figure 2 illustrates how a liability cash flow payable in 20 years would be credited in line with 30-year par rates subject to a floor of 5 percent. The mismatch risk between asset and liability cash flows is almost double that of a delta-hedging approach when interest rates are close to the floor.
As the second graph in Figure 2 illustrates, when interest rates are high, the binary approach tends to overestimate the proportion that is floating and recommend underhedging the liabilities’ PV01, which is the present value impact on the liabilities of a 1 basis point (bps) move in interest rates. And when interest rates are low, the binary approach tends to suggest overhedging the PV01.
The third issue with the binary approach is that it can suggest abrupt changes in the hedge due to only slight changes in interest rates. For example, if the expected 30-year par rate moves from just below the floor to just above it, the model could require a significant change in the plan sponsor’s hedging. (See Figure 3.)
How to Delta-Hedge the Interest Rate Exposure
So, what is the optimal approach? While there’s no single answer, we believe a liability-driven investment (LDI) hedging solution ought to reflect the true economics of cash balance liabilities. In particular, the LDI approach should recognize that a floor represents an additional cost to the plan, even when interest rates are above that floor, since members effectively own a put option that protects them against a fall in interest rates. Quantifying and hedging this exposure require a model for the uncertainty of interest rates. In addition, we need to ensure that the hedging approach properly addresses cash balance plans’ complex sensitivity to movements in the yield curve.
One approach is to calibrate a model to the prices of interest rate options, such as swaptions. However, this can be challenging because of the limited availability of quotable markets on this type of derivative. A viable alternative is what we call a “real-world” approach, calibrated to historical interest rate moves. Taking a real-world approach involves five steps:
1. Split cash flows into floating and fixed tranches. As a first step, the plan sponsor needs to understand the different benefit tranches within the plan. For example, there could be a tranche that is purely fixed, a tranche that that is floating with a floor of 2 percent, and another tranche with a floor of 5 percent.
2. Project a central case evolution of 30-year par rates. This is done by taking the forward interest rate curve—which represents the market’s expectations for the evolution of short-term interest rates, rolling down the yield curve—and then computing the 30-year par rate of the new curve.
3. Estimate the size of the increase in each year and those years’ deltas. The plan sponsor can use a stochastic model, such as a Black model that takes interest rate volatility as an input, with the volatility term structure fitted to historical movements.
4. Allow for curve risk. As a cash balance plan’s interest rate increases are typically based on 30-year par rates, the sensitivity to bumps in the spot-rate curve is complicated. Figure 4 illustrates the PV01 ladders for an expected $100,000 cash flow payable in 20 years (remember, PV01 is the present value impact of a 1 bps shift in rates). The amount is indexed or increased in line with the 30-year par rate each year, with no floor to make it simpler. The overall PV01—combining crediting and discounting PV01s—is close to zero, as you would expect for a benefit with floating increases. However, there is considerable curve risk. For example, if the 20-year spot Treasury rate doesn’t increase but the 40-year rate does, the present value of the liabilities will increase.
5. Perform stochastic simulation of risk ladders. Having established the current PV01 ladders of the assets and liabilities, the plan sponsor can then simulate liability analytics. Figure 5 shows the distribution of duration under stochastic scenarios with instantaneous shocks to yield curves.
Tackling a Complex—but Solvable—Challenge
For plan sponsors adopting cash balance plans as an alternative to traditional defined-benefit plans, hedging the interest rate sensitivities is a complex but solvable challenge. The most-used market benchmarks employed by pension plans are almost wholly inappropriate for cash balance plans and can potentially increase risk, rather than reducing it. Thus, introducing a customized liability benchmark strategy is more feasible. Before rolling out a cash balance plan, the plan sponsor should understand the unique market risks these plans present.
At LGIMA, we continue to believe that setting explicit interest rate and credit spread hedge ratios for cash balance plans is appropriate, and in line with our previously released research. An optimal strategy would involve a combination of credit assets to achieve the appropriate credit spread hedge (determined within a total portfolio context), plus Treasury securities and both long and short interest rate derivatives to match the specific key rate duration sensitivities of the cash balance plan. Other considerations may also impact the ultimate solution. For more technical details, review our dedicated whitepaper.
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Additional resources:
- December 12: Join Treasury & Risk for a live webcast exploring strategies treasury and finance professionals can use to better manage the high cost of employee benefits. Register today!
- Risk Management Solutions for Cash Balance Plans
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John Southall
John Southall is head of solutions research at LGIM. He leads the quantitative research and strategy team of the solutions group in London, working on a combination of financial modeling, investment strategy development, and thought leadership. He is also involved in bespoke strategy work for some of LGIM’s largest clients.
Andrew Carter
Andrew Carter is co-head of fixed income solutions at LGIM America. In this role, he is responsible for the oversight of the construction and day-to-day risk management of LGIMA’s customized fixed income solutions. He further serves as LGIMA’s client-facing technical expert for all things related to asset management.
Sabrina Ren
Sabrina Ren is a portfolio manager at LGIMA. In this role, she is responsible for the day-to-day risk management of customized investment solutions for LDI funds. Prior to joining LGIMA in 2021, Ren was an actuarial senior consultant in risk management at Nationwide Insurance, where she specialized in asset liability management and equity derivatives hedging for annuities and life insurance liabilities.
