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), and

• Accounting Discount Rate

(See also Legislated Interest Rates – U.S. qualified mode, Solvency Liability Interest Rates – Canadian registered mode, and Accounting Expected Return on Assets)

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 box to vary your stochastic interest rates based on a bond yield or in Public Pension and Canadian modes, asset mix return. If you do not check this box, the interest rate(s) will be the same, for all forecast years and all sensitivity dimensions, as your valuation assumption.

You can vary rates using the methods described below. Your available options on how to vary rates (Government yields, Corporate yields, or Custom yields #1 or #2) depends on the type of Capital Market Simulation you have referenced. For example, the Custom yield options are only available for a Custom type CMS. In Public Pension and Canadian registered modes, interest rates may also vary by asset mix. 

Full yield curve plus determines forecast interest rates by using the full yield curve generated by the CMS and is available when an explicit corporate yield curve or custom CMS is specified. A constant may be added to the full yield curve rates. The constant allows you to adjust the curve produced by the CMS up or down by a fixed amount (e.g., 0.01=1%).  Note that whenever you forecast using 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. 

Parallel shift based on change in benchmark yield determines forecast interest rates by taking the valuation assumption yield curve and moving 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. 

Target rate = benchmark yield plus determines forecast interest rates by deriving a constant rate directly from the benchmark yield. It can be adjusted according to parameters found either on the screen for the funding interest rate in Canadian registered mode and the actuarial liability interest rate in U.S. qualified mode or under the Params… button. Note that many of these parameters are optional and are noted as such, on the dialog box, by an asterisk. 

• The No change if prior rate is within -/+ of target rate indicates the minimum excess of the prior year’s rate over the current target rate (benchmark yield + spread) 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. 
• The Multiply (target rate - prior rate) by 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 Multiply (target rate - prior rate) by 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 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.
• 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%
• 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.

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 Stochastic Forecast output likewise will display the pre-decrement rate (so that it is clear what was used).  

When varying by Asset mix,  ProVal will use the entered returns if override expected return was selected on the Asset Mix topic, otherwise ProVal will determine the interest rate separately for each asset mix based on returns from the Capital market simulator for the number of years in the Horizon. The rate is then multiplied by the specified scaling factor if Times is selected, or added to the adjustment if Plus is selected. 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. For the year beginning on the baseline valuation date, the value entered in the Interest Rates topic in the funding Valuation Assumptions will be used. In future years, for a particular asset mix, the asset mix expected return will be used. With Dynamic asset allocation the funding interest rate will vary with the asset mix expected return with a 1-year lag.

The Horizon indicates the number of years of CMS data you want to be used in the interest rate calculation. Select Last simulation year to use all years run in the CMS. Select Last forecast year to use the number of years in your stochastic forecast. Select Fixed number of years to base the interest rate on a custom horizon (less than or equal to number of years run in the CMS). These parameters are only applicable if expected returns are not overriden on the Asset Mix topic.

 

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 the 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.  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.