The Fama And French Three-Factor Model is both a historical milestone and modern mystery in the study of finance. In 1964, economists Eugene Fama and Kenneth French analyzed decades of stock prices and found consistent and significant return premiums related to both small-cap and value stocks. Decades later we still find that these premiums are often present.

It is important to note here that there is still no widely accepted explanation for these premiums. Economic theory suggests that the outperformance of these two types of stocks should either never happen, or should be arbitraged away immediately upon identification. The existence and persistence of these premiums remains a puzzle.

Fama and French continued to investigate this question, and in early 2007 published "Migration", a research paper that came much closer to identifying the source of these premiums. Their findings are useful for indexers, portfolio managers, and for any investor who invests in either small cap or value stocks. (For background reading, see Working Through The Efficient Market Hypothesis and The Capital Asset Pricing Model: An Overview.)

Index Migration
Fama and French's first insight was to treat indexes as dynamic portfolios. Indexes that appear static and stagnant can hide considerable complexity and movement, which in turn can affect their long-term performance.

For example, the S&P 500 is almost certainly different than it was six months ago. During that time, mergers and acquisitions, delistings, spinoffs, and other events have required additions and deletions to the index, resulting in a list of 500 stocks that is gradually modified over time. The movement of stocks into and out of an index or portfolio is known as "migration", and it can have a very significant impact on returns.

The research portfolios that Fama and French constructed to evaluate the small-cap and value premium are also dynamic. Six market-cap weighted portfolios were created: Small value, small neutral, small growth, big value, big neutral and big growth.

Every year, individual stocks are assigned to a portfolio based on their relative size and book-value-to-market-value ratios and may move between portfolios in successive years. As in past research, the small-cap and value portfolios had a return in excess of market (Figure 1). (For more, see Digging Into Book Value and Small Cap Research Can Have Big Impact.)

Annual Return In Excess Of Market
Large Caps - Small-Caps
Big Growth -0.8 - Small Growth 0.0
Big Neutral +0.6 - Small Neutral +5.8
Big Value +2.8 - Small Value +8.0
Source: "Migration" study by Fama and French (data set: June 1934 to June 2006)
Figure 1

When stocks migrate between portfolios, they are in effect sold by one portfolio and purchased by another, resulting in gains and losses. The research found that these portfolio migrations are the source of most, if not all, of the value and size premiums.

Small-cap Migrations
Most of the small-cap premium comes from small companies that grow up to become large companies. Few small companies actually achieve this growth, but the few that do contribute the highest level of returns in the portfolio.

Small-cap growth companies have the best opportunity to migrate to a large-cap portfolio, based upon percentages, but neutral and value are not far behind (Figure 2).

Annual Percentage Of Small-Cap Portfolio
That Migrated To Large Cap
Small Growth 9.9%
Small Neutral 9.0%
Small Value 7.2%
Source: "Migration" study by Fama and French (data set: June 1934 to June 2006)
Figure 2

In the study, a significant market premium was only found in small neutral and small value stocks. Although these stocks have a somewhat lower likelihood of becoming a large-cap stock than small growth in a given year, they can also benefit greatly by moving into a neutral or growth portfolio or by becoming the target of an acquisition.

Value Migration
By creating three portfolios for valuation, Fama and French assured that most stocks that move from value to growth or vice versa would usually pass through neutral, the category in the middle. This provides an opportunity to study upward and downward migration, and to compare the performance of stocks that do not migrate.

Value-driven migrations are very frequent, and each year about 10% to 20% of stocks will move from one value category to a neighboring category. These migrations contribute positive or negative returns, depending upon whether the migration was upward or downward.

Migrations Between Growth, Neutral and Value Portfolios
Large Caps - Small Caps
From To % - From To %
Big Neutral Big Growth 12.5% - Small Neutral Small Growth 10.9%
Big Value 9.2% - Small Value 20.1%
Big Growth Big Neutral or Big Value 13.3% - Small Growth Small Neutral or Small Value 27.0%
Big Value Big Neutral or Big Growth 20.3% - Small Value Small Neutral or Small Growth 16.5%
Source: "Migration" study by Fama and French (data set: June 1926 to June 2006). Transition vectors are based upon individual firm counts, and returns on market-cap weighted portfolios.
Figure 3

Value and growth migration is slightly different for small caps, as can be seen in Figure 3. Small growth has the greatest tendency to migrate back to neutral or value, and the 27% of small growth stocks that migrate downward each year helps explain why these stocks have no market premium despite their slightly higher tendency to migrate to large cap.

When stocks stay in the same portfolio for two successive years, i.e. they don't migrate, they produce returns that are close to the market average, regardless of the category. This helps show that migrations account largely for the return premium.

Survivorship
However, migration or stagnation is not the only alternative. Companies can fail or can be acquired. The likelihood of these events also contributes to the small cap and value premiums.

Using more than 80 years of securities data, Fama and French investigated each removal (delisting) from the data set and determined whether it was as a result of either a "Good Delist" or a "Bad Delist". Good delists are acquisitions, mergers, or other events in which a premium was usually paid. Bad delists are bankruptcies, negative book value situations, and other negative events. (To learn more, see The Dirt On Delisting.)

Removals From The Data Set
- Good Delist Bad Delist
Large Caps - -
Big Growth 1.4% 0.2%
Big Neutral 2.0% 0.2%
Big Value 2.5% 0.1%
Small Caps - -
Small Growth 2.0% 2.2%
Small Neutral 2.6% 1.2%
Small Value 2.4% 2.5%
Source: "Migration" study by Fama and French
(data set: June 1926 to June 2006)
Figure 4

Thankfully for most investors, bad delists are rare (Figure 4). Less than 0.2% of the stocks in the large portfolios are delisted for cause every year, and even in the small portfolios, failures are still very infrequent.

The majority of the stocks that exited the study did so as a result of a good delist. These events are more common for smaller stocks and for value stocks, and the market premiums tend to be higher, which also contributes to their average outperformance (Figure 5).

Premiums For Good Delists
(Average In Excess Of Market)
Large Caps -
Big Growth +15.6
Big Neutral +18.7
Big Value +17.2
Small Caps -
Small Growth +18.9
Small Neutral +21.9
Small Value +35.1
Source: "Migration" study by Fama and French
(data set: June 1926 to June 2006)
Figure 5


Portfolio Application
Fama and French's analytical methods can be applied to any investment portfolio. By analyzing the investment purchases and sales over time and comparing their returns, insights can be gained into both the performance characteristics of different types of stocks and the application of specific investing rules and strategies.

According to the study, the value premium appears to be the result of capturing the natural tendency of stocks to oscillate between higher and lower book values. Purchasing these stocks when the price-to-book ratio is low provides a portfolio with the opportunity to profit when values change favorably and to then reinvest the proceeds in other value stocks. Favorable changes include: market re-evaluation, improved performance or acquisition. (For added insight on the use of the price to book ratio, see Value By The Book.)

Conclusion
If the value premium is a result of favorable pricing and timing, the small-cap premium can be viewed as a fistful of lottery tickets. Every small company has an opportunity to become a large company, or to be acquired by one for a premium. Although these individual probabilities are rare, the payoffs are so high that a relatively small number of successes can boost a small-cap portfolio's returns.

But even with this new research, it is still difficult to explain exactly why the small-cap and value premiums exist. Is there additional risk in these securities that demands a greater premium from investors? Or are the premiums the result of biased, irrational, and systematic mispricing, as many financial behaviorialists suggest? Fama and French end the paper by admitting that their results do not allow them to make that distinction, but only to frame the issues.

For added insight, see our Behavioral Finance: Anomalies tutorial.

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