The Forecast Yield Curves command allows you to input and store, for future valuation dates in a forecast, duration-based valuation interest rate assumptions that are referred to as “yield curves”. These yield curve library entries may be used later to forecast interest rates in a Deterministic Forecast, by selecting the Forecast Yield Curve Library entry under the Future Valuation Interest Rates topic of the Deterministic Assumptions command.

You may specify assumed interest rates separately for each forecast valuation date, with the first forecast valuation date (one year after the baseline Valuation Date) denoted as Fcst Yr 1. The assumptions for the second forecast valuation date (two years after the baseline Valuation Date) would be entered in the row (if you define the yield curve using rates at bend points) or the column (if you input explicit rates at all durations) for Fcst Yr 2, and so forth.

• If you have many years of rates, with identical rates for several years, then, under the option that uses bend points, you may save time inputting rows of rates for Fcst Year 1, Fcst Year 2, …, Fcst Year n by clicking (Ctrl+D) to duplicate a row downward. For example, if you have two sets of segment rates, one set for the first 10 years and another set for all years thereafter, you may type the three values in the first row and click (Ctrl+D) and then type the other segment rate values in the eleventh row and click (Ctrl+D); the values in the eleventh row will be used for Fcst Year 11 and all years thereafter.

• If you have identical rates that you are inputting explicitly for several years, then you may copy and paste a column of rates to several other columns in the spreadsheet. You need not complete all columns (Fcst Yr 1, Fcst Yr 2, …, Fcst Yr 100) in a blank spreadsheet; if the last column of rates entered is for Fcst Yr n, these rates will be used for Fcst Yr n, Fcst Yr (n+1), and so forth through Fcst Yr 100. (There are 100 columns because 100 is the maximum number of forecast years, after the baseline year, permitted in a Core Projection.)

Under either option, for each forecast valuation date, the duration of each rate is measured from that forecast valuation date (not from the baseline valuation date).

Note that if a Deterministic Forecast references a yield curve library entry that has rates defined for fewer years than are needed to run the forecast (that is, the number of rows or columns for Fcst Yr 1, Fcst Yr 2, …, Fcst Yr n, are fewer than the number of Forecast Years entered for the Deterministic Forecast library entry), the last year (row or column) specified in the yield curve library entry will be used for all subsequent years. Thus, ProVal will automatically extend the table as needed, so that the yield curve for the valuation date of the last forecast year specified will be used for any subsequent valuations at later forecast valuation dates in the Deterministic Forecast.

Name is a text field for entering a description of the Forecast Yield Curve being defined.

To avoid having to enter an interest rate at every duration for every forecast valuation date, select Define curves using rates at bendpoints and specify, for each Fcst Year (forecast valuation date), interest Rates at up to three Bendpoints, using the three bend point parameters for the rates to be used starting at durations 0, m and n, where m is the value entered for the second Bendpoint and n is the value entered for the third Bendpoint. Note that the first Bendpoint is always at duration zero and may not be changed.  Note that ProVal presumes the three rates entered are 24 month averages of segment rates.  

The Type parameter tells ProVal how to interpret the rates entered:

• If you select segment rates, ProVal will create the yield curve by keeping the specified interest rate constant from the duration corresponding to the bend point for which it is entered until the duration corresponding to the next specified bend point (if any); that is, the interest rate is constant between the bend points. The segment rate at the duration specified for the last bend point entered will be used for all longer durations. Thus each specified interest rate represents a portion of the yield curve that is flat until the next specified rate (if any), or level between bendpoints. The three columns of the Rates grid are labeled Segment rate from duration 0 up to m, Segment rate from duration m up to n and Segment rate from duration n, where m is the value entered for the second Bendpoint and n is the value entered for the third Bendpoint.

• If you select full yield curve, ProVal will interpolate between the interest rate points provided and extrapolate beyond the last point entered (if necessary) to create the full yield curve, by fitting a reasonable curve to the points provided. Thus the specified interest rates, once interpolated, form a graduated full yield curve that is changing between bendpoints (rather than flat). For extrapolation purposes, the yield curve is assumed to flatten out at durations greater than the last bend point entered but not before duration 30 (that is, if the last specified bend point is at a duration shorter than 30, the yield curve will not flatten out until duration 30). The three columns of the Rates grid are labeled Rate at duration 0, Rate at duration m and Rate at duration n, where m is the value entered for the second Bendpoint and n is the value entered for the third Bendpoint.

To specify rates for all durations for every forecast valuation date, select the Input rates at every duration radio button and then click the Rates button, to access a spreadsheet in which you specify a yield curve for each forecast valuation date. As noted at the beginning of this article, the Fcst Yr 1 column provides the valuation assumption rates (yield curve) for the first forecast valuation date, the Fcst Yr 2 column provides the yield curve rates for the second forecast valuation date, and so forth. For each column, enter in the rows of the spreadsheet the desired interest rates for the various durations. All durations must be completed, but if you are using a yield curve with the same rates at consecutive durations, you may “condense” the rows by changing the From column, which indicates the starting duration at which the interest rate in that row applies; for example, if 0.046 is the desired interest rate for durations up to 10, you may change the entry in the second row of the From column (from the pre-set value of 1) to 10. The Up to column indicates the ending duration (that is, the first duration at which the interest rate no longer applies); its values depend on your entries in the From column and cannot be changed. The interest rate for the last duration (row) specified will be used for all subsequent durations

Under either option, enter rates in the spreadsheet as decimal equivalents, not percentages (e.g., for 6%, enter 0.06).

Regardless of whether you are defining curves by using rates at bend points or inputting rates at every duration, the nature of the valuation assumption interest rate determines how the forecasted yield curve is interpreted in the forecast; if the Valuation Assumptions specify spot rates, the yield curve will be interpreted as spot rates and if the Valuation Assumptions specify forward rates, the forecasted yield curve will be interpreted as forward rates. If the Valuation Assumptions specify segment rates, this is a special case of “spot rates”, and thus the rates are interpreted as spot rates, not forward rates, for this purpose. If the Valuation Assumptions specify rates that vary by calendar year, they are interpreted as forward rates. An ambiguity occurs only if the valuation assumption is a constant interest rate (including bifurcated interest rates pre-decrement and post-decrement). The If the valuation assumption is a constant interest rate, the rates above are parameter resolves this ambiguity by letting the user specify whether the rates should be interpreted as spot rates or forward rates. If the valuation assumption is not a constant interest rate, this parameter will have no effect.

• If the rates at the bend points, or the rates you enter at all the durations, are specified as spot rates, then the rate specified at a particular duration is used to discount the payment at that duration for the entire period from the payment date to the forecast valuation date. For example, if the Type is segment rates, 5 is entered for the second Bendpoint, 20 for the third Bendpoint, 0.06 is entered for the Segment rate from duration 5 up to 20 and 0.04 for the Segment rate from duration 20, then all payments considered to be at durations 5 through 19 are discounted back to the valuation date at 6%. Likewise, all payments at durations 20 and later are discounted back to the valuation date at 4%. Note that these durations are measured from the forecast valuation date, not from the baseline valuation date.

• If the rates at the bend points, or the rates you enter at all the durations, are specified as forward rates, then the rate specified at a particular duration from the forecast valuation date is used to discount, during the time interval from that duration to the next specified duration, all payments made during or after that period. For example, if the Type is segment rates, 5 is entered for the second Bendpoint, 20 for the third Bendpoint, 0.06 is entered for the Segment rate from duration 5 up to 20 and 0.04 for the Segment rate from duration 20, then for the time interval starting at 20 years after the valuation date, payments are discounted back at 4% to the date 20 years after the valuation date. These payments’ discounted values, as of 20 years after the valuation date, are then discounted at 6% to the date 5 years after the valuation date, along with payments made at least 5 but fewer than 20 years after the valuation date. Note that these durations are measured from the forecast valuation date, not the baseline valuation date. If, instead, the Type is full yield curve, 5 is entered for the second Bendpoint, 20 for the third Bendpoint, 0.06 is entered for the Rate at duration 5 and 0.04 for the Rate at duration 20, then a payment made at duration 22 is discounted back for 2 years (to duration 20) and then its discounted value as of duration 20 is discounted back for 15 years (to duration 5). Because of extrapolation and interpolation, the interest rates used to discount will vary over these durations, but the rate used to discount from duration 21 to duration 20 will be 4% and the rate used to discount from duration 6 to duration 5 will be 6%.