The Classic Mean/Variance capital market simulator geometrically combines, for each asset class, three components at each point in time, t, to get the total, or nominal, rate of investment return NR(t) as follows:

 NR(t) = [(1 + RR) * (1 + Inf(t)) * (1 + e)] – 1,

where:

• RR represents the real rate of return and is assumed to be constant over all years in your capital market simulation.

• Inf(t) represents inflation and accounts for both expected and unexpected inflation. It is discussed in detail under the Inflation topic.

• The error term (e) represents deviation of actual experience from expected values for real return rates only, is normally distributed and is lognormally transformed. The error terms for real returns for all asset classes are related to each other and to unexpected inflation by means of the correlation matrix.

The parameters, entered via the Asset Classes topic, are:

• RR: Expected real return, the (constant) annual real rate of return that you wish to assume on this asset class for the entire time period of the simulation. This is the expected long-term rate of investment return in excess of the inflation rate. Enter the rate as a number between 0 and 0.3, inclusive (not as a percentage).

• sd(e): Standard deviation, the standard deviation of the real rate of return of this asset class. Enter the rate as a decimal number between 0 and 1, inclusive.

Although the multi-factor term structure and explicit corporate yield curve simulators do a far superior job of generating bond yields that are consistent with bond returns, the Classic Mean/Variance simulator can also generate government and corporate bond yields. The parameters to do so can be found under the Benchmark Yields topic and are also briefly described below.

• For 30-Year government yields, the parameters are the expected real yield (RY), i.e., the expected premium of 30 year government bond yields over inflation, and its contribution to the error term.

• For corporate bond yields, the parameters are the expected real yield (RY), i.e., the expected premium of corporate bond yields over inflation, and its contribution to the error term.

In the Classic Mean/Variance simulator type, ProVal input values and output values are essentially the same, that is, typically the mean variance simulator (unlike the multi-factor and explicit corporate yield curve simulators) does not require the user to calibrate, or iteratively adjust, each of the required inputs until all of the simulation results match the desired outputs. Said differently, to achieve, for example, an 8% expected return for a given asset class within the classic mean variance simulator (e.g., where long term inflation is 3%), you would simply calculate a real expected return of 0.048544 (1.08/1.03 – 1) and enter it, and you are “done” with real return input at that point.