Pension Confusion - The Problem with Averages

Source: Pension Confusion - The Problem with Averages

Pension Confusion:

The Problem with Averages

Most pension have assets managed to generic market index benchmarks and/or liabilities. In both cases, the focus of these assets is to match or beat some average (i.e., duration, total return, YTM). Unfortunately, few understand how these averages can be misleading if not erroneous.

Liabilities (Duration Matching)

Duration matching is a common LDI strategy for pensions where the plan sponsor looks to immunize their bond portfolio versus the interest rate sensitivity of the liabilities they are funding. To achieve this interest rate immunization, the strategy is to match the average duration of the liabilities. There are at least four problems here:

1. The actuary does not provide the average duration of projected benefits.

2. The actuarial report usually comes out annually… months after the fiscal year. Duration is a present value calculation that changes with interest rates and time, both of which change daily.

3. Assets do not fund gross projected benefits. They fund net benefits after contributions. This net liability is not calculated by the actuary which can be much different than the gross liability in dollars and duration especially for Corporate and Public pension plans that have a high contribution rate. Pension assets need to know what they are funding. The economic reality is… assets are funding net liabilities after contributions!
   

4. Duration is a present value calculation based on a discount rate yield curve. ASC 715 is the most prominent and acceptable for corporate and multiemployer pension plans. Moreover, Moody’s has adopted ASC 715 discount rates to assess municipal credits instead of the ROA discount rate commonly used under GASB accounting. FASB requires that this ASC 715 discount rate yield curve be converted to a single rate average discount rate. The duration of this single discount rate is certainly different than the average of a multiple discount rate yield curve. In the sample liability term structure shown on the next page priced with ASC 715 discount rates, we calculate:

	ASC 715 Yield Curve	Single Rate	Difference
Average Yield	2.29%	2.72%	0.43%
Duration	13.84 years	14.34 years	0.50 years

Note: For an accurate immunization, you need to match the duration of the ASC 715 yield curve (all liabilities) not the single rate average duration.

Solution: $ Duration Matching with Modified Duration

Maturity is an indicator of interest rate risk because longer maturity bonds move more in price than shorter maturity bonds given a change in yield. However, maturity is not a good measure of interest rate risk because maturity only considers the timing of the final principal cash flow at maturity and ignores the sizes and timing of all the other cash flows leading up to maturity.

The present value or price volatility of pension liabilities behaves just like bonds. A pension liability schedule is a term structure or yield curve of ASC 715 rates. Therefore, the interest rate risk in a pension liabilities schedule (actuarial projected benefits) can be matched with a portfolio of bonds.

A better measure for interest rate risk in the form of price sensitivity is called Modified Duration. Modified Duration considers all the bonds cash flows and is the weighted average time to receipt of all the cash flows, with the weights being the present values of the cash flows divided by a factor of (1+Y) where Y is the annual yield to maturity of the bond.

Modified Duration represents the percentage price change in market value in response to a change in the asset or liability yield. By weighting modified duration by the market value of the holding, that is, by multiplying the market value of the position by its modified duration, we get dollar-weighted duration. This dollar-weighted duration is known as Dollar Duration and represents the actual dollar change in market value for a bond given a change in its yield. Dollar duration is typically expressed in the dollar value change per one basis point change in yield (DV01).

The major advantages of using dollar duration are that it is additive and better suited for asset liability management. Dollar duration extends easily from individual securities to entire portfolios. The dollar duration of a portfolio is simply the sum of the dollar durations of all the individual holdings. The dollar duration of a bond portfolio can be matched to the dollar duration of pension liabilities. Bond durations cap out around 20-years so for liabilities with durations longer than 20-years it is not possible to match duration but… it is possible to match the Dollar duration of liabilities with durations longer than 20-years. Therefore, Dollar duration is very useful in asset liability management for liability driven investors such as defined benefit pension plans.

Ryan ALM uses dollar duration matching to help reduce pension volatility as defined as the dollar value difference in interest rate sensitivity between the present value of assets and liabilities. Ryan ALM starts by creating a Custom Liability Index (CLI) for each pension client. The Custom Liability Index is derived from the unique liabilities cash flow schedule provided by the plan actuary. The CLI measures and monitors the change in present value for the liabilities given a change in ASC 715 discount rates and is the proper benchmark for a plan sponsor and their liability driven investor(s).

Once we have determined the interest rate risk in the liabilities, the next step is to ensure that the bond portfolio has the same amount of interest rate risk as liabilities in order to reduce volatility between the present value of assets and liabilities. Ryan ALM builds a bond portfolio called the Liability Beta Portfolio (LBP) that matches the cash flows of the bonds to the liability cash flows (benefit payments). Since dollar duration is additive, we can set the dollar duration of the bond portfolio equal to the dollar duration of liabilities. Ryan ALM believes that cash flow matching liabilities with bond cash flows along with the use of dollar duration is a lower cost and lower volatility approach to pension asset liability management. It is certainly more accurate than traditional duration matching to immunize interest rate sensitivity.