This discussion pertains to the Asset Class dialog box of each asset class defined for a ProVal Capital Market Simulation. For each asset class included in the simulation (for all simulation types), information relating specifically to that type of investment is furnished in its Asset Class dialog box.

The format in which these parameters are displayed differs somewhat for the custom simulator from the presentation below; see also Custom Simulation Type.

Class Name (Name in a custom simulator) is the identifier ProVal is to associate with this asset class. The asset class will be displayed under this name in the correlation matrix and in output.

Description of the class can be a phrase of any length and may contain any character or symbol.

For all simulation types except custom, there are parameters, in the middle of the dialog box, that are used to develop the nominal rate of return of the asset class for any year t in the simulation. The methodology and available parameters for this computation differ among the capital market simulator types, but each is at least touched on below.

The RR: Expected real return and sd(e): Standard deviation parameters are available (only) for the Classic Mean/Variance simulator type. See Classic Mean/Variance Simulation Type for the details of these parameters.

The Return on N year zero coupon bond portfolio check box (Multi-Factor Term Structure Simulation Type) or Return on N year zero coupon bonds check box (Explicit Corporate Yield Curve Simulation Type) allows you to define an asset class that is a zero coupon bond of a specified single duration (maturity). If this option is chosen, enter a full or half year duration (N) from 1 through 30 years in the text field that becomes accessible when you check the box. This parameter is available for the multi factor term structure and the explicit corporate yield curve simulators. Government zero coupon bonds are modeled for the multi factor term structure simulator. For the explicit corporate yield curve simulator, choose whether to model Government or Corporate zero coupon bonds by clicking the desired radio button. The return for the zero coupon bond asset class is calculated as the change in price occurring between purchase of an N-year zero coupon bond and its sale one year later (now with duration N-1). Note: if you choose to model a zero coupon bond for an asset class, all the remaining parameters in the dialog box are inapplicable and thus inaccessible.

Return coefficients are available, for asset classes other than zero coupon bonds, under the Multi-Factor Term Structure and Explicit Corporate Yield Curve capital market simulator types. These parameters determine asset class returns based on a regression equation relating their returns to changes in the yield curve(s). The simulators arithmetically combine, for each asset class, up to six components at each point in time, t, to get the total, or nominal, rate of investment return NR(t) for that asset class. Each of the possible components is defined below, after the equations.

The Multi-Factor Term Structure simulator type uses this equation (reflecting government bond returns) to determine the nominal return in year t, NR(t), for each defined asset class:

NR(t) = a + [b * NRgov1] + [c * NRgov30] + e

The Explicit Corporate Yield Curve simulator type uses this equation (reflecting both corporate and government bond returns) to determine the nominal return in year t, NR(t), for each defined asset class:

NR(t) = a + [b * NRgov1] + [c * NRgov30] + [d * NRcorp1)] + [f * NRcorp30] + e

The regression equation parameters are defined, and input into ProVal, as follows:

• a is the coefficient for the Interest rate-independent return, i.e., the annual rate of return that is assumed to be earned on this asset class, independently from the return on bonds. Enter a rate as a decimal number between -0.05 and 0.5, inclusive. This term is the residual of the regression formula for the overall return.

• b is the coefficient for the 1-year Government bond return, i.e., the portion of the nominal rate of return on 1 year government bonds that you consider a component of the nominal rate for this asset class. Enter a rate as a decimal number between -6 and +20, inclusive.

• NRgov1 represents the actual nominal 1 year government bond (1-year Treasury Bill in the U.S.) return, which is determined internally by ProVal for each year and trial as the return on a 1 year zero coupon government bond. These returns appear in the output, under the View button, in the column headed “NRgov1”.

• c is the coefficient for the 30-year Government bond return, i.e., the portion of the nominal rate of return on default and credit-risk-free bonds, that you consider a component of the nominal rate for this asset class. Enter a rate as a decimal number between -3.5 and +3.5, inclusive.

• NRgov30 represents the actual nominal 30 year government bond return, which is determined internally by ProVal for each year and trial by pricing the 30 year government bond based on changes in yield from your simulation. These returns appear in the output, under the View button, in the column headed “NRgov30”.

• d is the coefficient for the 1-year Corporate bond return, i.e., the portion of the nominal rate of return on 1 year corporate bonds that you consider a component of the nominal rate for this asset class. Enter a rate as a decimal number between -6 and +20, inclusive.

• NRcorp1 represents the actual nominal 1 year corporate bond return, which is determined internally by ProVal for each year and trial as the 1 year corporate bond spread plus the return on a 1 year zero coupon government bond. These returns appear in the output, under the View button, in the column headed “NRcorp1”.

• f is the coefficient for the 30-year Corporate bond return, i.e., , the portion of the nominal rate of return on corporate bonds that you consider a component of the nominal rate for this asset class. Enter a rate as a decimal number between -3.5 and +3.5, inclusive.

• NRcorp30 represents the actual nominal 30 year corporate bond return, which is determined internally by ProVal for each year and trial by pricing the 30 year corporate bond based on changes in yield from your simulation. These returns appear in the output, under the View button, in the column headed “NRcorp30”.

• The error term e represents deviation of actual experience from expected regression values. The residual is based on a normal distribution; thus the input parameter, or coefficient, sd(e) represents your expected long-term Standard deviation of interest rate-independent return, the standard deviation of the residual of the regression equation for a, the interest rate-independent return. Enter the rate as a decimal number between 0.000001 and 0.9, inclusive.

Three parameters at the bottom of the dialog box, under the heading Asset valuation method data, or Asset Valuation Method Information for a classic mean/variance simulator, affect asset values generated by the Stochastic Forecast, according to the asset valuation method selected (under the Asset & Funding Policy command), but are not used directly in a Capital Market Simulation:

• Class Type indicates whether the asset class is Equity (such as stocks) or Fixed Income (such as government bonds). This parameter is used when the asset valuation method specifies that equity returns should be smoothed, while fixed income returns should be valued at market.
• Income Return (called Income in a custom simulator) is the non-capital gains portion of the total annual investment return (e.g., coupon interest rate for bonds, dividend rate for stocks). During a forecast, this parameter is used to split total return into capital gains and yield. For a fixed income investment, this yield would constitute the total expected return rate for the asset class. For an equity investment, the rate of return from capital gains would be computed as the total return rate less the dividend rate specified here. (For example, if a class of stock is assumed to pay 3% annual dividends, then enter 0.03 here. If the forecast produces a 9% total return for a particular year, then ProVal will subtract 0.03 from 0.09 to get a 6% capital gains return for that stock type for that year.) Enter the yield as a number between 0 and 0.3, inclusive.
• Turnover is the portion of total return assumed to be realized (because of the sale or maturity of the investment) each year. During a forecast, this parameter is used to split capital gains into realized and unrealized capital gains. The realized capital gains return rate would be the product of the capital gains return rate and the turnover fraction specified here. The unrealized capital gains return rate would then be the remainder: the total capital gains return rate less the realized capital gains return rate. (For example, if a class of stock is assumed to have 25% turnover, then enter 0.25 here. If the forecast produces a 6% capital gains return for a particular year, then ProVal will multiply 0.06 by 0.25 to get a 1.5% realized capital gains return and a 4.5% unrealized capital gains return for that stock type for that year.) Enter the rate of turnover as a decimal number between 0 and 1, inclusive.