Actuarial camouflage part I: Asset Smoothing*

by Eileen Norcross on June 7, 2012

in Pensions, Public Finance

I have posted frequently on one aspect of U.S. pension finance practice: liability valuation and discount rate selection. In terms of power to distort reality, the muddling of assets and liabilities for the purpose of valuation is by far the largest affecting defined benefit plans, particularly in the public sector. But there are other techniques that can warp the true picture of a pension plan’s condition.

First let’s consider asset smoothing. That is the partial recognition of asset gains or losses over a defined time period.

Asset smoothing is just that – a way to dampen on-book asset volatility. Did the plan’s assets have a bad year in the market? Instead of recognizing the full loss in the year it occurred, plans spread the damage over a five, ten, or even 20 year horizon. The same is true for gains.

Meant to protect the sponsor from “contribution shocks” triggered by a sudden drop in the market, according to actuarial thinking, smoothing, “does not impact long term costs or funded positions…only…timing.”

Asset smoothing produces a number called the Actuarial Value of Assets (AVA). The AVA is an engineered value that modifies the true value of the plan’s assets, known as the Market Value of Assets (MVA). Some asset smoothing formulas use a “corridor” to limit how far the technique can depart from MVA (typically it limits variation to no less than 80 percent and no more than 120 percent of market value).

Artificially reducing asset volatility may reduce funding pressure in the short-run. A plan is recognizing a portion of losses in a given year. The flip-side: the plan is reporting an over-inflated asset value basing important calculations on it (e.g., the  annual required contribution (ARC) and the plan’s unfunded liability.)

What are the effects of smoothing? It depends on the formula. Roman Hardgrave and I find in our 2011 paper that New Jersey’s smoothing formula allowed the AVA to remain far above the MVA for a decade. During the time, the assets looked larger than they were. Smoothing allowed an unpaid liability to accrue, pushing costs forward.

Here’s a chart of the difference between the AVA and the MVA**

Shouldn’t it even out eventually? There are years when the market outperforms expectations. We tested that.

New Jersey’s PERS plan use a 5-year smoothing algorithm, recognizing 20 percent of losses or gains over a five year window, defined as follows:

A0=Actuarial value of Assets, previous year

A1=Actuarial value of Assets, current year

M1=Market value of Assets, current year

r = Expected rate of return = 8.25%

s = Smoothing factor = 20% of difference of market and expected actuarial value

The formula:
A1= A0 + expected gain + smoothing adjustment based on market value

Expanding the formula and substituting in the expected rate of return and 20 percent adjustment gives:

A1= A0 + A0*.0825 + .2*( M1-(A0 + A0*.0825))

To calculate this year’s AVA, denoted (A1), the actuaries begin with an artificial number, last year’s AVA, denoted (A0). The 8.25 percent return the assets are expected to earn is calculated. Onto this number is grafted the “smoothing factor,” or 20 percent of the difference between the market return and the expected return.

This next chart shows how this formula operates, piece by piece.

The red line is the difference between the AVA and the MVA (or the difference between expectations and reality). For example, In 2010 the market value of the assets (MVA) was $23 billion. The expected value of the assets (AVA) was $29 billion. The plan expected $6 billion more than was earned in the market. Over the decade, the plan overestimated asset returns by an average of $4 billion.

Now for the smoothing. Actuaries slice off 20 percent of the red line. That piece, the fraction of market losses the plan is recognizing, is represented by the pink lineThe pink line is added to the plan’s expected gains on assets of 8.25 percent (the navy line) to produce, the adjusted gains, or the green line.

We found this formula is biased. It persistently overstates plan assets. Look at 2009. The market value of Assets (MVA) was $21 billion. The plan expected assets of $30 billion (the AVA). Their expectations were off by $9 billion. The red line shows how far they are from reality. And yet!  The actuarial value of the assets increased. Look at the green line in 2009. It’s positive. This formula does not easily self-correct. There isn’t a symmetrical undervaluation of plan assets when returns are higher than what’s expected.  (We have a working theory as to why).

Is there something else that happened during the decade that might explain this bias? If this was done at random would the results be the same? To test that we ran a Monte Carlo simulation. The results held. The smoothing formula consistently favors asset overvaluation. It holds even when we change expected returns from 8.25% to 2.8%, or what the plan actually returned, on average, over the period.

Further, we find that asset overvaluation doesn’t correct (downward adjust) until the AVA is 50 percent larger than the MVA. In other words, the assets can look inflated for a long time. It takes a big difference between expectations and reality, before reality kicks in.

This matters. The plan is basing contributions on artificial asset values. In 2009 NJ reported PERS was funded at 56 percent based on the actuarial value of the assets. But, according to the market value of assets, PERS was only funded at 45.1 percent. (And that’s saying nothing about how the liabilities are grossly undervalued)

GASB is reining in the use of smoothing for reporting (but not contribution) purposes. Until now, asset smoothing was embraced as a risk-management tool. But Waring (2012)  finds that asset smoothing doesn’t eliminate risk in the long run. In fact as the time period grows, a bigger and bigger portion of the risk from those first years is incorporated into the smoothed numbers. Risk accumulates for long periods. Asset smoothing is deferral. It may make today a little less painful, but it must be paid for eventually.

Asset smoothing may deliver some fleeting serenity to the plan sponsor. But there is no economic basis for pretending the assets are higher than they actually are. The accounting will follow the economics sooner or later (Waring).


*The title for this blog post is inspired by Bader and Gold (2002),

“Contrary to the teachings of financial economics, the actuarial pension model anticipates expected outcomes without reflecting on the price of risk. It then camouflages the risky distributions of outcomes by various smoothings and amortizations.”


  • MiltonsGhost

    This is amazing. So they’re overvaluing their pension assets by billions and undervaluing the pension obligations by billions.  

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