Liability Sensitivity in Cash Balance Plans

Under a traditional defined-benefit plan, the expected future benefit payments usually do not vary with changes in interest rates. In contrast, the majority of cash balance plans employ an interest-crediting rate linked to Treasury bond yields, so their expected benefit payments are subject to change as interest rates shift. Some plan sponsors calculate the expected cash flows of future benefits using an interest-crediting rate that is fixed at a specific level below the liability discount rate. Others set a single interest-crediting rate based on a blend of a qualitative actuarial overlay and quantitative analysis of the current Treasury yield curve and forward rates.

Either of these methods may lead to suboptimal investments of plan assets. We recommend a different methodology for projecting future cash flows: a mark-to-market approach that calculates the plan's expected future interest-crediting rates using implied forward rates from the Treasury yield curve.

Because both the benefit amounts and the liability discount rate are sensitive to changes in interest rates, overall interest rate durations—the sensitivity of liability values to changes in interest rates—tend to be much lower in cash balance plans than in traditional pension plans. However, cash balance plans' future cash flows may be quite sensitive to interest rate changes in bonds of longer tenor, depending on the interest-crediting rate the plan sponsor chooses.

To demonstrate this point, we've run an analysis of the unique interest rate durations at key points along the yield curve for three cash balance plans. We'll assume that all three plans have a typical participant demographic, with retirement dates varying from one year to 30 years in the future. We'll also assume that all three plans have the same initial cash balance level for each member at each age. The differences between our three sample plans lie in their interest-crediting rates. One is tied to 1-year Treasury yields, the second to 10-year Treasury yields, and the third to 30-year Treasury yields. Based on these assumptions, we've shocked the spot rate curve to calculate the sensitivities of the liabilities. Figure 1, below, presents the results—the overall interest rate duration and credit spread duration of each of the sample plans, along with the key rate duration (KRD) of each plan in relation to instruments of various tenors.

As you can see, the overall interest rate duration of each of our sample plans is 0. This is because if the entire yield curve shifts up or down, the change in the discount rate will be offset by the change in value of the projected benefit payment to plan participants. If yields fall across the board, then the discount rate will fall, but so will the value of the projected final benefit payment, which the interest-crediting rate ties directly to Treasury yields. The cumulative effect is that interest rate shifts do not change the overall cash flow forecast for the liabilities; thus, the overall duration is zero.

But although these plans are not sensitive to wholesale changes in the yield curve—i.e., parallel shifts—they are sensitive to changes in the shape of the yield curve. The plans with interest-crediting rates tied to 10- and 30-year Treasuries experience significant interest rate sensitivities at different points along the yield curve. For example, for the plan with an interest-crediting rate tied to 30-year Treasury yields, a 100 basis point decline in 5-year bond yields would, in isolation from any other interest rate changes, result in a 1.9 percent increase in the plan's liabilities. Continuing down the yield curve, a 100 basis point decrease in 10-year bond yields would, in isolation, increase the plan's liabilities by 6.2 percent. Interestingly, this relationship flips further along the curve; a 100 basis point decrease in 30-year bond yields would actually decrease liabilities by 4.4 percent.

These non-traditional sensitivities indicate that if a substantial flattening of the yield curve occurs—with long-dated yields either falling by more than short-dated yields, or rising by less than short-dated yields—then the value of liabilities in the cash balance plan will fall. In contrast, if the yield curve steepens—with long-dated yields rising by more than short-dated yields, or falling by less than short-dated yields—then the value of the plan's liabilities will rise. And as Figure 1 demonstrates, plans that use longer-dated crediting rates expose their liabilities to greater curve risk.

Despite the unusual sensitivities of some cash balance plans to shifts in interest rates, our analysis indicates that the credit spread exposures of cash balance plans are similar to those of traditional pension plans. This reflects the fact that benefits in a cash balance plan have nothing to do with changes in credit spreads—a plan is going to have the same sensitivity to changes in credit spreads, regardless of which interest-crediting rate it uses.

Why the Benchmarks Fall Short

Most defined-benefit pension plans use one of an assortment of standard market benchmarks to guide the management of their fixed-income asset portfolio as a hedge against their liabilities' exposure to interest rate risks. Taking the same approach with a cash balance plan would likely increase risk, rather than reducing it.

As Figure 2, below, illustrates, standard benchmarks do not track closely to the key rate duration profile of our sample plan with the 30-year crediting rate (from Figure 1). Using a common market benchmark to hedge the interest rate risks inherent in a cash balance plan's liabilities would almost certainly introduce some interest rate sensitivity. If yields fell, a fixed-income portfolio based on any of these benchmarks would outperform the plan's liabilities. Correspondingly, if yields rose, the fixed-income portfolio would underperform the liabilities.

Another point worth noting is that the differences in key interest rate duration are exacerbated at the long end of the curve. If 30-year rates rose, fixed income asset values based on one of these benchmarks would fall, yet the plan's liability values would actually increase. If 10-year yields remained flat, a $100 million plan would lose between $17 million and $20 million for every 100 basis point increase in yields on 30-year and longer bonds.

Our final observation is that even though the Treasury market is liquid only out to 30 years, the cash balance plan has short interest rate sensitivity to Treasury bond yields beyond that time frame, due to the forward-looking nature of interest-crediting rates. In other words, in 10 years' time, the 30-year crediting rate has some sensitivity to today's 40-year point on the curve.

Because of the mismatch they might create between plan assets and liabilities, the fixed-income benchmarks most commonly used for traditional defined-benefit plans are inappropriate for cash balance plans in most circumstances. The complex sensitivities of cash balance plans to shifts in yield curve slope would have led to substantial underperformance in plan assets vs. liabilities in the recent financial crisis, due to the extreme steepening of Treasury yield curves.

Cash Balance Hedging Strategies

Instead of simply basing asset purchases on the benchmarks commonly used by defined-benefit pension plans, cash balance plan sponsors need to work with their actuaries and trusted advisers on the investment side to analyze the specific risks that their plan is exposed to. Then they should consider setting explicit interest rate and credit spread hedge ratios to help mitigate those risks.

Calculating KRDs entails a very similar approach to that taken in calculating duration. At its most basic, the calculation of duration involves changing the entire yield curve (yearly spot rates) by 0.01 percent and analyzing the resulting change in value of the assets and liabilities. Find the percentage change in value, then multiply this number by 10,000, and you have the duration. KRDs are a little more granular. Instead of shifting the entire yield curve by 0.01 percent, you shock individual rates at different points on the curve to understand how the value of the assets or liabilities might change if specific points on the curve were to move relative to other points on the curve.

To assess the sensitivity of a cash balance plan's cash flow to changes in interest-crediting rates, the plan actuary should look at how his or her calculation of cash flows changes as the assumed interest-crediting rate changes. From these calculations, we can build a model to assess the KRD exposures of the liabilities and replace actuarial assumptions on future interest-crediting rates with actual rates implied by the yield curve.

The optimal strategy for managing a cash balance plan's assets involves purchasing credit assets to achieve the appropriate credit-spread hedge (determined within the context of the overall portfolio), and then investing the rest of the portfolio in Treasury securities and long and short interest rate derivatives that match the plan's specific key interest rate duration sensitivities. Customizing a plan's hedging program becomes increasingly important as the cash balance plan grows relative to the size of the company's traditional defined-benefit liabilities.

Many cash balance plans add further complexity to their hedging needs by combining a Treasury bond-linked interest-crediting rate with a floor, or minimum, on the level of balance increases in any year. For example, a plan might set the annual interest-crediting rate to be equal to the greater of either the 30-year Treasury bond yield or 3 percent. This can result in significant economic consequences; the plan is effectively giving participants an option for free. Not surprisingly, floors can also present challenges from an interest rate hedging perspective. If Treasury bond yields move from being below the floor to being above the floor (or vice versa), then the interest rate sensitivity of the liability cash flows can change rapidly. If not managed correctly, such a situation can be extremely detrimental to the performance of a liability-driven investment (LDI) portfolio.

We have identified a number of approaches to hedging these complex exposures, including:

• Projecting the liability cash flows using the approach described above, but applying the plan's floor to each projected crediting rate and hedging the changes in duration as each rate moves above or below the floor. This involves careful monitoring of the forward rates as each nears the level of the floor. This may be the most pragmatic and simple solution, particularly when the floor is low or the cash balance component represents only a small proportion of the overall liabilities being hedged.

   

• Using a Monte Carlo simulation to value the plan optionality and hedging the delta of this optionality with standard market instruments. Put simply, if the model assesses a 50 percent chance that rates will take the interest crediting rate above (or below) the floor, a pragmatic approach is to split the difference. Such a method should be considered for large cash balance plans, particularly when the level of the floor is close to the projected forward rates. However, the market calibration of such a model can be complex, particularly given the lack of liquidity in Treasury-based option models (although a proxy may be achieved by taking volatility assumptions from the swaptions markets). The plan retains the short gamma position under this approach, but the effect will be smoother than under the previous approach.

   

• Purchasing a series of payer swaptions struck at the levels of the floor when the floor is much higher than the projected interest-crediting rate, while hedging liabilities similar to a traditional defined-benefit plan (positive duration). The purchased payer swaptions will reduce the duration of the asset portfolio to match that of the liabilities should interest rates rise substantially. Similarly, when the floor is much lower than the projected crediting rate, the plan sponsor can purchase a series of receivers struck at the level of the floor, while hedging liabilities like a cash balance plan (no duration). The purchase of receiver swaptions will increase the duration of the asset portfolio to match that of the liabilities should interest rates fall substantially. While such a strategy may provide the optimal hedge, as it removes the short gamma position, it can be extremely costly, particularly when the strike of the floor is close to the current implied interest-crediting rate.

For plan sponsors that have introduced cash balance plans as an alternative to more traditional defined-benefit plans, the challenges of hedging the interest rate sensitivities that these plans introduce are complex but not insurmountable. We recommend that every plan sponsor transitioning to a cash balance plan should have a strong understanding of the unique market risks these plans present.

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Andrew Carter, head of LDI Portfolio Management for Legal & General Investment Management America (LGIMA), is responsible for overseeing the LDI portfolio management team and the construction and management of customized investment solutions, including LDI for U.S. pension clients. Prior to joining LGIMA, Andrew was a derivatives structurer at LGIM, where he was responsible for delivering risk management solutions to clients. He joined LGIM from KPMG, where he worked as an investment consultant.

Jodan Ledford, head of U.S. Solutions for LGIMA, is responsible for developing risk management solutions for clients. Prior to joining LGIMA, Jodan was executive director and business head of asset liability investment solutions at UBS Global Asset Management. His responsibilities included product development and implementation of investment and risk management solutions for large institutional clients, including defined-benefit pension plans.

DISCLAIMER: Views and opinions expressed herein are as of January 2015 and may change based on market and other conditions.The material contained here is for informational purposes only and is not intended as a solicitation to buy or sell any securities or other financial instrument or to provide any investment advice or service. LGIMA does not guarantee the timeliness, sequence, accuracy, or completeness of information included. Past performance should not be taken as an indication of guarantee of future performance, and no representation, express or implied, is made regarding future performance.