Liability Return and Excess Return

Liability returns are defined as

where

is the value of the liability at time n, and

is the liability’s normal cost minus experience benefit payments discounted to the beginning of the year. Liabilities, normal costs, and benefit payments are generated by the underlying core projections. It is useful to observe that the algorithm is parallel to the way one would calculate an asset return for a pool of assets.

Excess return is defined as the excess of the nominal asset return over the liability return, i.e. . Note the parallelism between the excess return and real return calculations.

ProVal’s Efficient Frontier command lets you find asset mixes that optimize “excess returns” rather than optimize solely asset returns. Generally, excess return efficient frontiers produce better asset allocation options if:

the plan sponsor’s idea of risk is related to surplus, contributions, or expense and
the associated liability moves with interest rates.

The excess return is calculated for each asset class for each year and trial. Then the empirical means, standard deviations and correlations are used to generate an efficient frontier. Years with Stochastic Assumptions overrides that impact liabilities will be ignored. When the shift simulated values and prepend overrides treatment is selected for the stochastic assumption overrides, asset class and liability returns are synchronized so that they are associated with the appropriate year.

Excess return reflects the actual particularities of the plan over the referenced time period, not a generic assumption about liability duration.