The Investment Scientist

Archive for May 2008

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 small cap … 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.

There are ways to reduce the pain and enhance the gain through diversification and valuations. They are the subjects of my future newsletter, which you can subscribe here.

*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.

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In my last article, I explained why volatility does not measure risk. It’s an assertion by none other than Warren Buffet himself. I hope the historical data I used convincingly illustrated the point.

If volatility doesn’t measure risk, then what can we learn from it?

Let’s look at this simple example. Let’s say you invest $100 in asset A, whose volatility is 10%. In year one, the asset returns 10%. In year two, it returns -10%. What is the terminal value in year two? If you’re like most of us mortals, you’d call it a wash. You’d guess $100. Not so, the terminal value is $100*(1+10%)*(1-10%)=$99.

Now let’s assume you invest $100 in asset B, whose volatility is 20%. In year one, the asset returns 20%. In year two, the asset returns -20%. What is the terminal value in year two? This time you should get it right, it is $100*(1+20%)*(1-20*)=$96. So, everything else being equal, we can say higher volatility means lower investment return.

Mathematically speaking, volatility is a drag on return.

Steve Shreve, the math professor in my quantitative finance class, would give you this formula:

Reduction in return = ½ volatility2

For instance, if the annual volatility is 20%, then the drag on annual return is ½*(20%)2=2%. This drag on return is not risk, since it is deterministic – there is nothing uncertain about it.

How to reduce volatility drag on return?

This simple answer is diversification. However, diversification requires special care. Blind diversification could do more harm than good. This is a topic best left for another article.

The author is president of MZ Capital, a RIA serving DC/MD/VA. Get his monthly newsletter in your mailbox.


Michael Zhuang is principal of MZ Capital, a fee-only independent advisory firm based in Washington, DC.


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