Benchmark Yields
For a capital market simulation of the classic mean/variance type, this topic is entitled “Benchmark Yields”. ProVal uses these parameters to develop yields on thirty-year government bonds and, optionally, on corporate bonds.
For a capital market simulation of the multi-factor term structure type, this topic is entitled “Corporate Bond Benchmark Yield”. ProVal uses these parameters to develop yields on corporate bonds (if the user opts to simulate corporate bond returns). Ordinarily, the multi-factor term structure simulator is used, or perhaps the explicit corporate bond yield curve simulator, when bond yields are needed to compute lump sum values or to value plan liabilities, because (unlike the mean-variance simulator) the 30-year bond yield is determined directly from a simulation of the yield curve.
To simulate benchmark yields for a mean-variance simulator:
Check at least the 30-Year Government Bonds box, to simulate 30-year government yields; if you check that box, you may also check the Corporate Bonds box, to simulate corporate bond yields as well. For each selected benchmark yield, two additional parameters become accessible:
RY: Expected real yield is the (constant) excess of total long-term bond yields over inflation assumed for the entire time period of the simulation. This (annual) rate may be the expected excess of total long-term bond returns over inflation, or you may choose to adjust it to get appropriate real, rather than total, yields. Enter the rate as a decimal number between 0 and 1, inclusive, not as a percentage.
sd(e): Standard deviation of real yield is the standard deviation of the error term, e, for the expected long-term real yield, or excess yield over inflation. This error term is normally distributed and lognormally transformed. Enter the standard deviation as a decimal number between 0 and 1, inclusive. This value generally should be very low (e.g., 0.0001) because yields without a strong trend have a low standard deviation and the simulated bond yields based on this equation will have a standard deviation at least as high as inflation.
The mathematical equation used to compute the 30 year government bond yield or corporate bond yield at time t, Yld(t), from these parameters and the inflation rate, Inf(t), is the following:
Yld(t) = [(1 + RY) * (1 + Inf(t)) * (1 + e)] – 1.
Note that if you wish to forecast funding or accounting valuation interest rates (including the accounting expected return on assets) that vary with changes to interest rates (such as for Canadian solvency liability) or if you wish to base lump sum values on a lump sum benchmark yield, then you must check one of the boxes, to simulate either the 30-year government yield benchmark or the corporate bond yield benchmark. (You may, of course, simulate both.)
To simulate benchmark yields for a multi-factor simulator:
Check the box to Simulate Corporate Bond Benchmark Yield. Four additional parameters become accessible:
GBond: Government Bond maturity (years) is the maturity that will be used to determine the government bond yield from the generated yield curve. Corporate bond yields are presumed to be equal to government bond yields of the same maturity (for example, 20 years) plus a risk premium representing credit risk. Thus, ProVal will determine the yield on corporate bonds by starting with the yield on government bonds and adding a risk premium. Enter the maturity in years of the government bonds upon which you wish to base this calculation.
RP: Expected risk premium is the expected annual excess yield, or spread, of corporate bond yields over government bond yields at the specified maturity, which is assumed for the entire time period of the simulation. This credit spread arises primarily due to greater default risk, but it may also be impacted by the lower liquidity, higher taxability (in the U.S., corporate bonds are generally subject to state as well as federal taxes), and the “callability” feature of some corporate bonds. This spread may be the expected excess of total long-term bond returns over inflation, or you may choose to adjust it to get appropriate real, rather than total, yields. Enter the value as a decimal number between 0 and 1, inclusive, not as a percentage.
sd(e): Standard deviation of risk premium is the standard deviation of the error term, e, for the expected long-term spread of corporate bond yields over government bond yields. The credit spread of corporate bond yields over government bond yields varies over time, generally becoming narrower in times of robust economic growth and wider during times of economic contraction or uncertainty. Enter the standard deviation for the distribution of the expected risk premium that best describes these expected fluctuations, as a decimal number between 0 and 1, inclusive.
c(e, ui): Correlation of risk premium and unexpected inflation, i.e., of the unexpected risk premium and unexpected inflation. To the extent that you wish ProVal to model an additional risk premium variance that increases or decreases with unexpected inflation, please enter the correlation coefficient, as a decimal number between -1 and 1 inclusive, to indicate how closely you expect the risk premium to follow changes in unexpected inflation. For example, a correlation of 1 would indicate that risk premium and unexpected inflation move in lockstep. A correlation of 0 would indicate that the corporate bond risk premium is unrelated to unexpected inflation.
The mathematical equation used to compute the corporate bond yield at time t, BYld(t), from these parameters is the following:
BYld(t) = GBondYld(t) + RP + e, where GBondYld(t) is the government bond yield at time t.
Note that if you wish to forecast funding or accounting valuation interest rates (including the accounting expected return on assets) that vary with changes to interest rates (such as for Canadian solvency liability) or base lump sum values on a lump sum benchmark yield, then you must check the box and simulate the corporate bond benchmark yields.