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Valuation Assumption Sensitivities

In order to perform a forecast with various inflation rates, the sensitivity of liabilities to inflation changes in various interest rate environments must be measured. The Valuation Assumption Sensitivities topic specifies the range of interest rate sensitivities you wish to evaluate over the time period of the Core Projection that your forecast will reference, as well as how assumed valuation

under the various inflation environments are related to the various interest rate environments assumed for valuation purposes at the forecast valuation dates. Interest rate sensitivity runs are strongly recommended (required to populate a ProVal PS data file) because they may provide valuable information if the plan is subject to ASC 715 rules, (U.S.) ERISA funding requirements or in other situations where annual interest rate changes are generally required. By use of interest rate sensitivities, you can reflect, in your deterministic and stochastic forecast results, annual variations in the various valuation interest rate assumptions.

The Sensitivity change to interest rates parameter contains text fields for entering the interest rate adjustment amounts that determine the “Low: -- ” and “High: + “ interpolation anchor points for the low and high valuation interest rate assumptions, respectively. That is, the amount that should be subtracted from or added to any baseline interest rate assumed for valuation purposes (e.g., funding valuation interest rate, accounting valuation discount rate, current liability interest rate, solvency liability interest rate, target liability interest rates) to derive the assumed value of that valuation interest rate in the low or high interest rate environment, respectively, is entered here. In general, the spread of interest rate adjustments should be set symmetrically and almost as wide as the range of interest rates that are feasible, over time, for valuations of your plan.

Sensitivity of other valuation assumptions to interest rate changes contains a list of valuation assumptions that may be expected to vary with changes in inflation rates or interest rates (or both). There are two groups of topics under this parameter, divided according to the corresponding topic for that valuation assumption in the Valuation Assumptions command. How the parameters of the topic affect values assumed for valuation purposes in a Core Projection is explained in the discussion of the respective topic. To define the relationship between interest rate sensitivity and other valuation assumptions, click the name of a topic and edit its parameters.

Increase/Crediting rates – heading is for descriptive purposes only; click indented subtopic name

Lump Sum Interest Rates – heading is for descriptive purposes only; click indented subtopic name

Selecting a topic from the listed valuation assumptions leads to a dialog box containing a spreadsheet that lists the relevant items, except that selecting the Cost-of-Living Adjustments (COLAs) topic or the Modified Cash Refund Annuities topic leads to a dialog box containing a single item which, for modified cash refund annuities is “Interest during deferral period”, that is, the interest crediting rate that applies during the deferral period.

If you wish, for Benefit Formula Components, Accrual Basis Components, Employee Contributions, Lifetime and Annual Limits and Lump Sum & Optional Payment Forms, you may select a Plan Filter (in German mode, a Promise Filter) from the dropdown list, to reduce the list of possible choices to those items associated with a particular Plan Definition (or in German mode a particular Benefit Promise). Please see Filters for details.

All lump sum factor components unhidden in the current Project will be listed, as will all unhidden regulatory items. Benefit Formula Components and Accrual Basis Components that were defined with a check in the Apply increase rates to this component box will be listed. An unhidden Payment Form Definition will be listed if it is referenced as an Optional form by some Benefit Definition. An unhidden Lifetime Maximum or Annual Limit will be listed if it is defined with Apply increase rates to limit selected or, for a Lifetime Maximum, with Apply increase rates to outstanding balance (med. Spending account) selected.

For each Item, such as the increase assumption for the Social Security National Average Wage, you indicate What fraction of the assumed interest rate sensitivity change should be applied to the following valuation increase rates, where your specifications may vary between funding and accounting valuation assumption sets.

(For Benefit Formula Components, this parameter is worded What fraction of the assumed interest rate sensitivity change should be applied to the following valuation increase / crediting rates. For modified cash refund annuities, this parameter is worded What fraction of the assumed interest rate sensitivity change should be applied to the following valuation crediting rates. For lump sum factors, it is worded What fraction of the assumed interest rate sensitivity change should be applied to the following assumed Lump sum factor interest rates and for optional forms it is worded What fraction of the assumed interest rate sensitivity change should be applied to the following assumed Optional payment forms conversion interest rates.)

For example, in an accounting Core Projection, your practice for a particular client may be to assume that, in general, ASC 715 discount rate changes reflect a change in the short-term underlying inflation expectation. Accordingly, if you wish to maintain all assumptions on the same economic basis, you indicate by specifying a “1” in all rows of the Accounting column that all economic valuation assumptions for ASC 715 purposes should move by the same amount. Thus, for example, if the interest rate adjustment entered (for the “Low: -- ” and “High: + “ interpolation anchor points) is -0.02 and +0.02 and the salary inflation rate in the Valuation Assumptions is 0.04, then a “1” in the row for Salary Inflation results in a valuation assumption that salaries will increase 2% per year because of inflation in the low interest rate scenario, 4% per year in the baseline interest rate scenario and 6% per year in the high interest rate scenario. Similarly, if you have specified that regulatory items, Benefit Formula Components, and/or Accrual Basis Components have increase rates associated with them, you are given the opportunity to specify alternative valuation assumption increase rates, in the low and high interest rate scenarios, that are dependent on the interest discount rate and the type of assumption set. Likewise, if any modified cash refund annuity payment forms have a deferral period for benefit commencement, you may specify alternative valuation assumption interest crediting rates and you may specify alternative valuation assumption increase rates, in OPEB mode, for lifetime and annual limits.

On the other hand, in a funding Core Projection, if underlying liability interest rates (such as current liability or target liability interest rates or solvency liability transfer value and annuity purchase rates) may change annually but no other economic assumption changes might be appropriate for valuation assumptions, then you would specify “0” for each row in the Funding column. For example, in the U.S. qualified mode, it has been common to enter a “0” for the regulatory items Maximum Benefit and Maximum Compensation but a “1” for Salary Inflation and other Items.

Finally, if your assumptions tend to fall somewhere between these two extremes, you may specify any value between 0 and 1.

In the following situations, you must specify “0” for all fractions (except those for lump sum factors and optional payment form conversion factors): (1) to run a Deterministic Forecast, if you select a Forecast Yield Curve as the basis of some type of future valuation interest rate (for example, a funding liability interest rate or a U.S. qualified mode target liability interest rate) or (2) to run a Stochastic Forecast, if you forecast to the full yield curve for some future valuation interest rate. This is because, in order to determine the effective duration of the liabilities, which ProVal needs for making an accurate non-parallel yield curve shift, it is necessary to determine the change in the liabilities that results solely from interest rate changes. When the valuation interest assumption at some future valuation date is a full yield curve (specified in the Deterministic Assumptions or Stochastic Assumptions), ProVal cannot isolate the change caused by the interest rate change, for a reason we’ll explain by example. Consider a forecast with (1) future valuation interest rates defined as a full yield curve, 4% grading down to 2.5% at duration 25, and (2) an underlying Core Projection whose Projection Assumptions specify (a) a sensitivity fraction of 0.5 for salary inflation and whose Valuation Assumptions specify (b) an interest rate assumption that is a full spot yield curve, 1% grading up to 5% at duration 30. Thus the baseline valuation interest rate basis is “1%, at the initial duration, grading up to 5% 30 durations later”, which must shift to “4%, at the initial duration, grading down to 2.5% just 25 durations later”, so there are several interest rates moving in different amounts and different directions (because, remember, the shift is not parallel, so there is no uniform amount of interest rate change at all durations). As a consequence, to derive the amount of change in the rate of salary inflation, it is not clear how to compute 50% of the change in the interest rate; that is, it is unclear which interest rate to select (from among several duration-based rates). Note that if a Forecast Yield Curve is the interest basis at some future valuation date(s) only for funding (not accounting), then only the fractions in the Funding column need be set to zero; similarly for accounting, if a Forecast Yield Curve is the interest basis at some future valuation date(s) only for accounting, then only the fractions in the Accounting column need be set to zero.

When setting the sensitivities for Lump Sum & Optional Payment Forms, it is important to note that the sensitivity fractions for a lump sum factor or conversion factor Item are ignored for setting the assumed valuation lump sum factor interest rates to be used to calculate liabilities when the Lump Sum & Optional Payment Forms topic of Valuation Assumptions is coded to use underlying liability interest rates (that is, to use the valuation interest rates). When a lump sum interest rate is defined as the underlying liability interest rate, the underlying interest rate will always be used in full, regardless of whether the sensitivity fraction for the lump sum factor is coded as “1” or “0” (or any fractional amount in between). Also, the sensitivity fractions for the optional form conversion factor Item are ignored when a conversion factor is defined by a table (in lieu of a mortality and interest basis).

When setting the sensitivities for Benefit Formula Components and Accrual Basis Components that have increase rates or crediting rates applied, or when setting sensitivities for the crediting rate on Employee Contributions or the guaranteed amount during a deferral period of a modified cash refund annuity, note that setting the Valuation Assumptions increase and crediting rates to the table option and selecting “<no rates>” does not produce the same results as setting the increase and crediting rates to a constant value of zero, because sensitivities are applied to the constant of zero but not applied to the table option if “<no rates>” is selected.  For COLAs, however, selecting “<no rates>” does produce the same results as setting the valuation assumption COLA rates to a constant value of zero, because sensitivities are not applied in either case.