Methodology for Calculating Asset and Liability Mismatches
Calculating Liability Returns
The liability return for a given period is obtained by dividing the today’s present value by last period’s present value of liabilities. Pension assets need to grow at a rate equal to the liability returns to prevent a deterioration of funding levels. Even though the liability structures of active plans are likely to change and are generally refreshed on a yearly basis, for purposes of calculating the liability returns, they are held constant over the course of the year. This assumes that benefit accruals equal benefit payments, i.e., that the roll-down effect is offset by new benefit accrual. For hard-frozen plans, the liability structure is assumed to decay.
The present value of a given liability structure changes over time due to two separate effects: First, the Accrual or Roll-Down Effect captures the maturing of future liability payments. After the passage of one period, a future liability cash flow moves one period forward and thus gets discounted for one period less. Therefore, the present value of a given liability stream increases at the implied market-weighted discount as it matures. For instance, if the discount rate is 4% at the beginning of a period and does not change, the present value of liabilities increases by 4% over that period due to the accrual effect.
Second, the Interest Rate Effect captures the change in present value of liabilities due to changes in the discount rate. As interest rates move over time, each liability payment gets discounted with a different discount rate. This could cause an increase or decrease in the present value of liabilities. For instance, the present value of a liability structure with duration of 15 years would increase by approximately 15% if the yield curve experienced a parallel decrease in rates by 100 bps. The total liability return is the combined return from the accrual and the interest rate effect, i.e., 4% + 15% = 19%. If the pension assets of a fully funded plan do not match or exceed this total liability return of 19%, the funded status of the pension plan will decline.
To discount the pension liabilities of our three plans, we construct a single three tier market weighted discount rate from the Citigroup Pension Discount Curve. This discount curve is based on high grade corporate bonds, is published monthly and available on the website of the Society of Actuaries. The three curve segments are 0- 5 years, 5.5 – 20 years, and 20 – 30 years. A market weighted discount rate is the single discount rate at which the present value of liabilities equals the present value of liabilities as if each liability payment would be discounted with its respective segment discount rate.
For asset returns, we calculated the monthly and year-to-date returns of a 70% S&P 500 (Total Return Index) and 30% Barclays Agg. strategy.
The Asset-Liability Mismatches are calculated by subtracting the liability returns from the asset returns. While a positive asset-liability mismatch indicates an improvement of funding status for a fully or over funded plan, underfunded plans may fall further behind in funding status since monthly benefit payments may exceed the excess return. Liability Driven Investment (LDI) strategies are designed to minimize the asset-liability mismatch by investing in fixed income assets that closely track the liability behavior.
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