# Is Smallcap Volatility Pain Worth the Gain?

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by: Michael Zhuang

Over the last 60 years, the simple average annual return of the Fama/French benchmark small-cap portfolio* was 16.3%. For the same period, the large-cap portfolio* was only 12.76%. Do you think small cap beat large cap by a wide margin? I put my mathematicianâ€™s hat on to find out.

Volatility shrinks the return difference

The small-cap portfolio return volatility for this period was 26%, and 16.4% for the large cap. Taking into account the drag to return by volatility , I calculated the geometric mean return for both portfolios. My results showed 12.9% for small cap, and 11.4% for large cap. Mathematically, the return advantage of the small-cap portfolio is significantly reduced by its volatility.

The odd favors smallcap â€¦ somewhat

For most investors, long-term investing means holding a stock for three to five years. What is the odds of the small-cap portfolio beating the large-cap portfolio? Not by much.

In any given three-year period during the last 60 years, the odd of the small-cap portfolio beating the large-cap portfolio were only 51%. It increases to 58% when the investment horizon is 5 years and 72% when the investment horizon is 10 years. For most investors, the odds barely favor small-cap investing.

 Investment horizon 1 year 3 years 5 years 10 years 20 years 30 years Odds of small cap beating large cap 53% 51% 58% 72% 75% 90%

Data source: Kenneth French data library

Emotional accounting

Daniel Kahneman, the 2002 Economic Nobel laureate and the father of behavioral finance observed that the pain from a loss is twice the pleasure from a gain of the same size.

Applying his principle: I assigned one unit of positive emotion to each 1% gain and deducted two units of positive emotion to each 1% loss. So a resulted positive number represents pleasure and a negative number represents pain. The sum of monthly results over the last 60 years showed: -788 for the small-cap portfolio and -482 for the large-cap portfolio. It is clearly painful to invest in stocks, small cap stocks especially. (This also explains why people prefer to put their money in CDs.) Is the pain of small cap investing worth the gain? You decide.

*Fama/French benchmark small cap portfolio contains stocks in the bottom 30% of market capitalization. Fama/French benchmark large cap portfolio contains stocks in the top 30% of market capitalization.