If one or more benchmark bond yields have been projected in the Capital Market Simulation referenced in this set of Stochastic Assumptions, the topics grouped under the Valuation Assumptions heading become accessible, giving you the opportunity to specify stochastic interest rate valuation assumptions.

This article discusses the following future valuation assumption interest rates:

• Funding Interest Rate (OPEB, U.S. public, universal, Canadian registered and U.K. modes),

• Actuarial Liability Interest Rate (U.S. qualified mode),

• Tax / Funding Interest Rate (German mode),

• Accounting Discount Rate and

• Accounting Expected Return on Assets (U.S. qualified, OPEB, U.S. public, universal and Canadian registered modes).

(See also Legislated Interest Rates – U.S. qualified mode and Solvency Liability Interest Rates – Canadian registered mode.)

ProVal permits significant flexibility in the specification of stochastic interest rates, allowing you to specify, in all modes, whether to vary these assumed valuation interest rates over the forecast period and, if so, the relevant benchmark yield basis for variation.

Check the Vary based on benchmark yield box to indicate an election to vary stochastic interest rates based on a benchmark yield. Under the Accounting Expected Return on Assets topic, check the Vary based on box to indicate an election to vary stochastic interest rates based on either a benchmark yield or an asset mix (specified under the Asset Mixes topic).

For example, under the Funding Interest Rate topic, if the Vary based on benchmark yield box is checked, the assumed funding valuation interest rate will vary over the forecast period, whereas if you do not check this box, the funding interest rate(s) will be the same, for all forecast years and all sensitivity dimensions, as the corresponding interest rate(s) entered under the Interest Rates topic of the Valuation Assumptions command. Similarly, under the Accounting Expected Return on Assets topic, if the Vary based on box is not checked, the value entered for the expected return on assets under the Accounting Methodology topic of the Asset & Funding Policy will be used for all forecast years and all sensitivity dimensions.

The following parameters apply when the Vary based on benchmark yield box, or the Vary based on box, is checked.

Except for the option to vary the accounting expected return on assets by asset mix, the Benchmark yield parameter is accessible. The available choices depend upon whether only government bond returns, or corporate bond returns as well, have been generated by the referenced Capital Market Simulation (CMS).  

For the funding interest rate in all modes except Canadian registered pension, and for the accounting discount rate, when stochastic interest rates vary based on a benchmark yield, ProVal permits up to three methods for forecasting the stochastic interest rates: (1) Apply a parallel shift based on change in benchmark yield, (2) Forecast to the full yield curve or (3) Derive an interest rate directly from the benchmark yield, using the following parameters:

• A Target rate spread over Benchmark,

• Detailed controls over determining the interest rate, based on changes in the benchmark yield, involving the difference between the stochastic interest rate and the target rate,

• A Rounding rule and

• A Maximum rate and/or a Minimum rate.

These parameters are discussed below. Many of them are optional and are noted as such, on the dialog box, by an asterisk.

For the funding interest rate in Canadian registered mode, the actuarial liability interest rate in U.S. qualified mode and the accounting expected return on assets, if stochastic interest rates vary based on a benchmark yield, ProVal permits one method (the third listed above) for forecasting stochastic interest rates, to derive an interest rate directly from the benchmark yield.

If a parallel shift is applied, ProVal takes the valuation assumption yield curve and moves it up or down in a parallel fashion based on the difference between the year 0 benchmark yield specified under the Benchmark Yields topic and the corresponding benchmark yield produced by the capital market simulator for each trial and forecast year. This method can be used to move a duration-based variable interest assumption in a parallel fashion.

Forecasting to a full yield curve (i.e., determine forecast interest rates by using the full yield curve generated by the CMS) may be selected only when an explicit corporate yield curve CMS is specified. (Otherwise, the Forecast to the full yield curve option is inaccessible.) If you forecast to a full yield curve and the valuation assumption interest rates have a segment structure (rates flat for up to three portions of the yield curve), ProVal will convert the full corporate bond yield curve generated by the CMS to segments by averaging the rates for each segment (excluding durations over 60). Note that whenever you forecast to a full yield curve, all interest sensitivity fractions (except the fractions for lump sum factors and optional payment form conversion factors) entered under the Valuation Assumption Sensitivities topic of the Projection Assumptions must be zero.

If an interest rate is derived directly from the benchmark yield, ProVal determines the forecasted interest rate as a constant rate, based upon the benchmark yield as adjusted according to the specified parameters of the bulleted list discussed below. This option requires that the valuation interest rate entered in the Valuation Assumptions have a constant, rather than varying, structure. If constant interest rates that vary among pre-decrement, in-deferment and post-commencement periods are entered in the Valuation Assumptions, the Stochastic Forecast interpolates results by moving the entire set of interest rates (pre-decrement, in-deferment and post-commencement) up or down in a parallel fashion according to how the stochastically determined forecasted rate from the capital market simulator compares to the benchmark yield. If a single interest rate is required in a Valuation Set or forecast, for example, the accounting discount rate in a FASB expense calculation or the funding interest rate in a Canadian minimum contribution calculation (such as to amortize bases), the pre-decrement rate is used. Viewing the effective rate in the Valuation Set or Stochastic Forecast output likewise will display the pre-decrement rate (so that it is clear what was used).

For the Accounting Expected Return on Assets topic, if you select the “Asset mix” option for the Vary based on parameter, which instructs ProVal to vary the rate based on the expected return calculated separately for each asset mix, then the expected return will be computed for each asset mix based on returns for all years from the CMS. An arithmetic average will be used if annual rebalancing was selected under the Asset Mixes topic (of these Stochastic Assumptions). Otherwise, the geometric average will be used. Thus each asset mix will have the same expected rate of return (EROA) for each year beginning on a future forecast valuation date (or future forecast measurement date, if the measurement date is not the same as the valuation date); for the year beginning on the baseline valuation date (or baseline measurement date, if the measurement date is not the same as the valuation date), the value entered for the Expected Return on Assets parameter of the Accounting Methodology topic of the Asset & Funding Policy will be used. Thus there will be separate returns for each asset mix but returns for any given asset mix will not vary by forecast year. Note that if your CMS creates separate accounting returns, they will be ignored and the funding returns will be used.

For a forecast in the U.S. qualified mode under the “Pre-PPA and PPA” law selection, the parameters of the Actuarial Liability Interest Rate topic will affect results only for the period after PPA takes effect and only if the selected contribution policy (under the Contribution Policy topic) is “normal cost plus supplemental cost” (NC+SC). If the contribution policy is not NC+SC, no Actuarial Liability is computed for years after transition to PPA.

In the U.S. qualified and universal pension modes, the stochastic accounting discount rate specifications will apply to the interest rate used to determine ASC 960 liability, unless an alternative ASC 960 valuation interest rate is specified, in which case the ASC 960 liability will not vary over the forecast period.  To reflect variation in an alternative ASC 960 interest rate, you may run a separate forecast (for purposes of obtaining only the ASC 960 liability), whose underlying Core Projection(s) are based on an accounting discount rate set equal to the desired (constant) ASC 960 interest rate.   

Parameters for deriving an interest rate directly from benchmark yield or (for EROA) from asset mix

The following parameters are accessible under the option to vary the stochastic interest rates based on a benchmark yield:

• For the Target rate spread over benchmark, enter the value of the increment to the benchmark yield that you wish the CMS to apply to develop this return rate, for example, 0.01 (= 1%) if you wish the return rate to exceed the benchmark yield by 0.01 (1%). Enter -0.01 if the desired return rate is 1% less than the benchmark yield. A spread of up to 20% (+0.20 or -0.20) may be entered.

• The Required absolute difference from Target before reflecting a change when Rates are decreasing applies when the current target rate (benchmark yield + spread) is less than the prior year rate and indicates the minimum excess, of last year's rate over the current target rate, required for this year's rate to be changed from last year's. For example, if last year's rate was 8.5% and this year's target is 8% (an absolute difference of 0.005), a value of 0.005 or less would be the necessary input for this parameter if rates are to change. Similarly, the Required absolute difference from Target before reflecting a change when Rates are increasing applies when the current target rate (benchmark yield + spread) is greater than the prior year rate and indicates the minimum excess, of the current target rate over last year's rate, required for this year's rate to be changed from last year's. For example, if last year's rate was 8% and this year's target is 8.3% (an absolute difference of 0.003), a value of 0.003 or less would be the necessary input if rates are to change.

• The Fraction of difference from Target to reflect when Rates are decreasing applies when the current target rate (benchmark yield + spread) is less than the prior year rate and indicates how much of the difference between the prior year rate and the target rate should be reflected in the current year stochastic rate, provided that rates have decreased sufficiently to meet the absolute difference requirement. For example, a value of 0.8 indicates that 80% of the difference between last year's rate and the target rate should be subtracted from last year's rate to develop this year's rate. Similarly, the Fraction of difference from Target to reflect when Rates are increasing applies when the current target rate (benchmark yield + spread) is greater than the prior year rate and indicates how much of the difference between the prior year rate and the target rate should be reflected in the current year stochastic rate, provided that rates have increased sufficiently to meet the absolute difference requirement. For example, a value of 1 indicates that 100% of the difference between last year's rate and the target rate should be added to last year's rate to develop this year's rate. You have the option to enter the Maximum absolute change in one year, to limit the annual change in the stochastic rate. A value of 0.02, for example, indicates that rates cannot change more than 2%, or 200 basis points, annually.

The following parameters are accessible under either option for varying stochastic interest rates, whether based on a benchmark yield or, for deriving the return rate for the accounting expected return on assets (EROA), based on the asset mix:

• The Rounding rule indicates what degree of rounding to apply to the derived stochastic interest rates. A value of 0.0025, for example, entered for the Amount indicates that rates should be rounded to (one quarter of 1% or) 25 basis points. To indicate no rounding, 0 cannot be entered and thus you should enter the smallest value permitted, 0.0000001. (The largest degree of rounding that can be entered is 0.01, 100 basis points.) Select the Direction, “Nearest”, “Up” or “Down”, to indicate whether rates should be rounded up, down or to the nearest multiple of the Amount.

• You may optionally limit the final derived rate to an overall maximum rate, entered as the Maximum rate value.

• Likewise, you may optionally limit the final derived rate to an overall minimum rate, entered as the Minimum rate value. Note that a minimum rate below 0% is not permitted and the specified minimum rate cannot exceed 20%.