N-Year Average
This asset valuation method starts with the market value of assets and subtracts a proportion of the specified prior year gain (loss), with the proportion determined by the length of the averaging period. For example, for a 3-year averaging period, the smoothed value of assets will be equal to the market value minus one third of the gain (loss) from 2 years ago and minus two thirds of the prior year gain/loss. Note that this is mathematically equivalent to taking an average of the current and prior two year asset values, where the prior two year asset values have been adjusted for cash flow and expected return during the period.
Once you specify the Years in Averaging Period, a spreadsheet becomes accessible in which you enter the amount of historical Asset Gain (Loss) (for funding or solvency assets, or Prior (Year) Asset Gain for accounting assets) for each relevant prior year (one year less than the number of years in the averaging period). Year -1 is the current year, or year ending on the Valuation Date or, for accounting asset valuation methods, the year ending on the Measurement Date; Year -2 (relevant for N greater than 2) is the year immediately preceding the year ending on the Valuation Date or Measurement Date, and so forth. ProVal will average the historical values entered with the gain/loss amount it computes for the current year (i.e., year beginning on the Valuation Date or Measurement Date). In a forecast, ProVal will average the historical values entered (as appropriate for the future valuation date) with values it determines for future years in the averaging period.
If you wish to smooth over non-annual periods, you can handle this smoothing in a Valuation Set by setting the Years in Averaging Period parameter value as the number of periods to smooth. However, because ProVal performs calculations only on an "annual" basis, this is not supported in a forecast. In a Deterministic Forecast or a Stochastic Forecast, an approximate annual smoothing method must be used.
The funding Asset Gain/(Loss) to be Spread, or accounting Asset Gain Definition, used during a forecast to determine the amounts of asset gains and losses in future years, is defined by your selection from the following options:
The “Excess return over expected return” option amortizes the difference between the actual and expected total returns of the assets, where the total return is the sum of the income return (interest and dividends) and capital gains/losses (whether realized or unrealized). This option is discussed in detail in a separate section of this article (below).
The "Realized and unrealized capital gains" option averages the historical total asset gain or loss of each prior Year and, in a forecast, future calculated total gains / (losses), whether realized or unrealized. Historical Asset Gain / (Loss) amounts, or (for accounting assets) Prior Asset Gain amount(s), entered are presumed to be the total gain or loss, whether realized or unrealized.
The "Unrealized capital gains only" option (available only for funding and solvency, not for accounting) averages the historical unrealized) asset gain or loss of each prior Year and, in a forecast, future calculated unrealized gains / (losses). Historical Asset Gain / (Loss) amounts entered are presumed to be the unrealized gain or loss only. The portion of any future year’s total gain or loss that is unrealized is determined by the assumed turnover fraction specified for a Deterministic Forecast under the Asset Smoothing Parameters topic of Deterministic Assumptions or for a Stochastic Forecast under the Asset Classes topic of the referenced Capital Market Simulation.
The "Total return" option averages the historical total return for each prior Year and, in a forecast, future calculated total returns on the plan fund, where the total return is the sum of the income return (interest and dividends) and capital gains/losses (whether realized or unrealized). Historical Asset Gain / (Loss) amounts, or (for accounting assets) Prior Asset Gain amount(s), entered are presumed to be the sum of the income return and realized and unrealized capital gains and losses. The total return in a future year is determined as: end-of-year Assets – (beginning-of-year Assets + Contributions – Benefit Payments – Expenses). This method was designed for the U.S. qualified mode “PPA” or "Pre-PPA and PPA" applicable law selections. It is mathematically equivalent to averaging the fair market value as of the valuation date with the adjusted fair market values as of earlier determination dates.
For forecast purposes (only), indicate whether to Value fixed income assets at market. When this box is checked, the value of assets will be defined as the market value for the proportion of the portfolio specified as being invested in fixed income assets, plus an n-year weighted average of gains/losses for the complementary proportion of the portfolio invested in equities. The asset allocation that determines the proportion invested in fixed income versus equities is specified for a Deterministic Forecast under the Asset Smoothing Parameters topic of Deterministic Assumptions or for a Stochastic Forecast under the Asset Classes topic of the referenced Capital Market Simulation.
Check the Exclude administrative expenses from asset gain box to exclude administrative expenses, and in the U.S. qualified mode the PBGC premium (if any), from cash flow in the development of actuarial assets (for a funding asset valuation method) or market-related value of assets (for an accounting asset valuation method) at future valuation dates in a forecast. In the Canadian registered mode, this check box is available only for funding and accounting asset valuation methods (not for a solvency asset valuation method).
“Excess return over expected return” option
Under this option, the difference between the actual and expected total returns of the asset fund is amortized over the number of years entered for the Years in Averaging Period parameter. Differences for each prior Year and, in a forecast, future years are amortized. Historical Asset Gain / (Loss) amounts, or (for accounting assets) Prior Asset Gain amount(s), entered are presumed to be the excess of the actual total return over the expected total return, where the total return is the sum of the income return (interest and dividends) and capital gains/losses (whether realized or unrealized).
The actual return is determined as: Interest and Dividends + Realized Gains / (Losses) + Unrealized Gains / (Losses). The expected return varies depending on the type of calculation (funding, solvency or accounting) as well as on the user’s parameter choices.
The Expected Return Based on Prior Year Assets parameter indicates the asset base to be used, in a forecast, to determine the expected return on assets. For funding assets, this base can be either "Market Value" or "Actuarial Value". For solvency assets in the Canadian registered mode, this value can be either "Market Value" or “Solvency Value”. For accounting assets, this value can be either "Market-Related Value" or “Market Value”.
The Expected Return Based on Prior Year Return rate parameter pertains to funding and (Canadian mode) solvency assets in a forecast and determines the appropriate expected rate of return. It can be set as either the "Valuation Rate" or a "Market-based Rate". In addition, in the U.S. qualified mode, under a “PPA” or “Pre-PPA and PPA” applicable law selection, you may select either the “3rd Segment Rate” or "Min. 3rd Segment & Expected Rate" options. This parameter does not exist for accounting because the rate of return entered for the Expected Return on Assets parameter of the Accounting Methodology topic is always used. If you select the "Valuation Rate" option, whether for funding or solvency, ProVal will use the prior year funding interest rate (generally entered under the Interest Rates topic of the Valuation Assumptions) as the prior year return rate.
If you select the "Market-based Rate" option (for funding or solvency assets) for the Expected Return Based on Prior Year Return rate parameter, the asset value will change commensurately with how the value of a portfolio of 30-year bonds invested at par at the Current year rate would change if the portfolio was sold the next year and then reinvested at the then current year rate. Thus ProVal will use, as the prior year return rate, the Current year rate you enter plus the Premium over rate you enter plus the change in the price of a 30-year bond caused by the change in the value of the Current year rate. The Current year rate determines the coupon and next year's comparable rate is used for discounting. The Premium over rate is the additional return reflecting the incremental yield (that the plan investments are expected to produce) over long term fixed income securities. The change in price is determined using the formula:
Let
F = Face Value ($1 discounted for 30 years at the end of year “Current year rate”)
C = Coupon rate (uses “Current year rate” as of the beginning of the year)
PV = Present Value Factor (30-year annuity immediate at the end of year “Current year rate”)
Then the change in the price of a 30-year bond equals F + C * PV - 1
If you select either the “3rd Segment Rate” or "Min. 3rd Segment & Expected Rate" option for the Expected Return Based on Prior Year Return rate parameter, ProVal will determine the expected return on assets by reflecting the Funding 3rd segment rate entered under the Interest Rates topic (or Target Liabilities topic for a “Pre-PPA and PPA” law selection) of the Valuation Assumptions for the underlying Valuation(s). If segment rates have not been entered as the valuation interest rates (i.e., if a full yield curve is used and thus spot rates have been entered), ProVal will look to the Current year rate parameter for the baseline valuation date 3rd segment rate. If segment rates have been entered as the valuation interest rate assumption, then any entry made for the Current year rate will be ignored. To see what third segment rate was published for the month and year relevant to the underlying Valuation(s), look up the rate under the Interest Rates topic of the Valuation Assumptions.
If you select the "Min. 3rd Segment & Expected Rate", you will need to enter the Expected Rate. The Expected Rate is the long-term expected rate of return on plan assets. When calculating the expected return on assets for each future year, ProVal will use the minimum of the 3rd segment rate and the expected rate entered here.
For each future valuation date after the baseline valuation date, ProVal will calculate and use the Funding 3rd segment rate. If the interest rates used in a forecast do not match the PPA segment rate structure, ProVal will not “know” what the 3rd segment rate should be and will have to use a proxy. In this case, ProVal will assume that the 3rd segment rate at a future valuation date is equal to the baseline valuation date 3rd segment rate (per the Valuation Assumptions if they reference segment rates; otherwise, per the Current year rate parameter) plus the change, between the baseline valuation date and the future valuation date, in the duration 30 yield curve rate.
In the U.S. qualified mode, under a "PPA" or "Pre-PPA and PPA" applicable law selection, to code the asset valuation method described in WRERA, generally, you would select the "Excess return over expected return" option and then select the "Min. 3rd Segment & Expected Rate" option. Note that under a "PPA" law selection, when the Expected Return Based on Prior Year Return parameter is set to “Valuation Rate”, ProVal calculates the prior year valuation rate as the alternative interest rate entered under the Actuarial Liability topic of the Valuation Assumptions or, if there is no alternative interest rate specified, the effective interest rate.