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 mathematician’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 … 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.*