# Linear smoothing

Linear smoothing is a method to value the asset. It is similar to moving average method. The moving average method takes the arithmetic average 5 days of market value. The result 'moves' depending on the valuation date. Linear smoothing instead recognizes the gains and loss due to investment return over time. Over 4 years, it would recognize 25% from last year, 50% from two years prior, 75% from three years prior and 100% from 4 years prior. The purpose of the method is two folds. It reduces overreliance on current market value and it reduces the volatility of the resulting valuation.

## Calculation

The linear smoothing as approved by ERISA (automatic Approval 15 [1]) adjusts for a single year of expected returns. The example below use 7% expected returns and contributions at mid-year using compounded interest. The gains and loss at 12/31 for Year 1 is (-8,480) = 196,500 – 204,980. Of this, 75% is recognized and 25 % is unrecognized (-2,120) = (-8,480) * 25%. The linear smoothed value is the Market value at Year 4 less the sum of past unrecognized gains and loss 287,704 = 228,000 – (-2,120 + -5,781 + -51,803).

Linear smoothing
Year 1 Year 2 Year 3 Year 4
Market value as of 1/1 150,000 196,500 238,000 228,000
Cash flow mid-year 43,000 38,000 41,000
Expected value as of 12/31 204,980 249,563 297,071
Gains and (Loss) of 12/31 (8,480) (11,563) (69,071)
Unrecognized Gains and (Loss) of 12/31 (2,120) (5,781) (51,803)

## Desirable characteristics

There are many types of method to value asset each with their own merits and faults. For example, current market value, book value or moving average. The desirable characteristics of an asset valuation method should be[2]

• Achieves objectives
• Tracks to market value
• Does not unduly deviate from market value
• Has a reasonable and logical relationship to market value
• Is generally free of any bias
• Has no undue influence on investment transaction decisions or vice versa
• Is consistent with the length of typical economic cycles

## Phase-in

Making change in a valuation method is not to be taken lightly. It should only happen infrequently and with care. Instead of retroactively applying the method to year before the valuation method is change, we can apply a phase-in period. Say in the previous example year 2 was when the linear smoothing valuation method was selected. Year 2 market value as of 1/1 would be fully recognized. The linear smoothing with phase-in as of Year 2 would rather be 285,584 = 228,000 – (-8,480 * 0% + -11,563 * 50% + -69,071 * 25%).

## Corridor

In order to keep a closer relationship to market value, corridor can be implemented. Any linear smoothed value above 120% of the current Market Value(MV) and under 80% would be capped at 80% * MV or 120% * MV. This corridor strategy will help achieve better tracking to market value and recognize faster major change in market valuation.

## Controversy

The smoothing of asset is the subject of many articles against it[3][4]. The main concerns are : transparency issue, time lagging issue, manipulation issue. The method is less transparent than market value. It can confuse the unaware observer. Any gains and loss are recognize through time. This means that the 2008 crash is recognized between 2009 to 2014. During 2010-2014, it surprises the unaware observer that the value of asset diminish while investment were up during the last year. Finally, actively changing the valuation method to best fit our objective as time past, brings an unwanted bias in our asset valuation.

## References

1. Paulette Tino and Edward Sypher (September 2002). "Asset Valuation Methods under ERISA" (PDF). Society of Actuaries, Pension forum, volume 14, number 1.
2. "Guidance on Asset Valuation Methods" (PDF). Canadian Institute of Actuaries. September 2014.
3. Hope, Ole-Kristian (August 2003). "Provocative Pension Accounting" (PDF). Strategic Finance Magazine. Institute of Management Accountants.
4. Wiedman, Christine; et al. (April 2005). "Pension accounting the end of smoothing". Ivey Business Jouranl. Ivey Business School.