Is Smallcap Volatility Pain Worth the Gain?

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.

Comments

[richjoy:]

Though I appreciate the statistics on smallcap gains over various time periods, I have no use for the suedo-science of emotional metrics.

2008 May 30 01:07 PM

[Just Say Whoa!:]

Someone who can't spell "pseudo" should probably not use the word "science" in the same sentence.

Emotions are simply secretions of neuropeptides by the brain (or the immune system) that spread throughout the body.

These "emotional" neuropeptides contain something called "ligands" which act as a "key" to unlock the receptors in cells. When unlocked or activated, cells produce a cascade of chemical reactions, which can have long-lasting and persistent effects on the physical body.

In other words, emotions are real, physical bio-chemical reactions that cause changes in your body on a cellular level. Emotions are not just "all in your head". They are real and they influence how you think and feel on a moment-to-moment and day-to-day basis.

Excellent thought, Mr. Zhuang.

Yes, the emotional impact of investing is about the "risk to reward ratio".

According to Daniel Kahneman, you should probably not invest in small caps unless the potential reward is at least twice what a lower Beta volatility investment would yield.

Thank you for bringing up-to-date science into the "dismal" so-called "science" of economics.

2008 May 30 02:12 PM

[jdspain:]

i assume we are talking index vs stock picking.

2008 May 31 08:35 AM

[hypratt:]

Bear Stearns was a large cap. No pain there. Or Enron, Worldcom need I go further. As for neuropeptides give me a break. You forgot to analyze what color the logo of the company has to do with whether or not the stock does better in even or odd years. Don't count on me to subscribe to your newsletter M. Zhuang.

2008 Jun 02 11:53 AM