**Smoothed average — A better way to estimate pension**

Smoothed average is a moving average with a twist. Moving average is the average of the past few balance. Smoothed average also add adjust for the expected rate of return for the fund. Smoothed average have also the benefits of converging to the real fund if expected interest rate is the same as the experience.

Here’s a Smoothed average versus a Moving average example:

Graphic of rate of return from year to year using either Real fund, Moving average 3 years, or Smoothed average 5 years.

As you can the yellow line (MA) and the gray line (SA) somewhat mimic the real fund (RF), but it have a smoother ride, without the several spikes. This have incredible advantage if you want to get an estimate of your fund value for pension projection purpose, contribution purpose or withdrawal purpose.

A simple smoothed average for 3 years (SA3) would be the fund balance 3 years ago + 2/3 of experience interest 2 years ago + 1/3 of expected interest 2 years ago + 1/3 of interest experience last years + 2/3 of expected interest last years. Common adjustment include putting a corridor, in other way say that SA3 is not above x% of real fund or underneath it. Ideally this corridor is unbiased and reflects the current fund. Other SA method exist which leads to slightly different average, but in essence this simple SA captures most what we want.

From a pension point of view, SA removes the need to worry if we are in a up or down. We would always be somewhere in the middle. SA thus have a lot of advantage to make adequate projection. Indeed, using the SA instead of the real fund from one balance date to the next remove as much as 10% of Standard deviation (SD) over equity fund.

Note that this advantage disappear in strength over a long estimate. So the projection over 10 years period using RF you get a 5,1% SD vs 4,6% sd USING SA5. The 0.5% is still not negligible at the higher end of the confidence intervals (+/- 1.65 * standard deviation to get the 90% interval).

On the Pros;

- It fluctuates a lot less than the fund value
- It delays the immediate impact of a sustain change
- It remove unsubstantial change
- It reduces the fund in period of high value and increase it in period of low value.
- It reflects he expected rate of return up to the current period, so it’s better than Moving Average.

On the Cons:

- It doesn’t reflect the value of the fund directly. If you would sale the fund, no one is going to give you the Smoothed Value.
- It lags behind the real curve, if the interest rate is below real average rate of return or is in front of it if using too optimistic rate.
- It delays sustained change.
- Huge stress would be recognize over a long period. Thus the impact of the 2008 is felt even in when market were up a few years later.
- Last year negative return can be offset by prior high increase year. 2000 SA5 was higher than 1999 even though 2000 experience a negative interest year.

,I believe that Smoothed Average should be use as a better estimate of the fund in order to more appropriately set the withdraw or contribution that you want.