Higher Rewards Equal Higher Risks?

Review of "The Value Premium and the CAPM" by Fama and French

It is common wisdom that higher risks equal higher rewards. Indeed in the world of finance and investment, "higher risks equal higher rewards" is stated as a self-evident truth. Anyone who believes and says otherwise would suffer ridicules. Of this I have personal experience.

"Higher risks equal higher rewards" not only has common sense appeal, it also has academic foundation. In 1964, William Sharpe invented the Capital Asset Pricing Model (CAPM). It asserts that the return of an asset or an asset class is a function of its systematic risk plus a random component. In 1966, Eugene Fama in his PhD dissertation put the term "Efficient Market Hypothesis" (EMH) into public awareness. The premise of the EMH is that the market is so efficient, that at any give time it has already incorporated all available information. Therefore, it is futile trying to beat the market with any subset of the information. The only sensible way to invest in the stock market is to invest in the "market portfolio" making up of all stocks in the market proportional to their market capitalizations. One ready corollary of the EMH is that if one wants to earn a higher than equilibrium market return, one must take on a higher risk than equilibrium market risk.

The CAPM and the EMH thus form the theoretical foundation of the efficient market school of thought in financial economics. This school of financial economists proscribes a style of investing that shuns stock picking. For them, all stocks are priced properly according to their risks. Investors should hold two funds, a fund of market portfolio and a fund of riskless treasury bills. Using the sliding scale between these two funds, investors will find their own balance between risks and returns.

The altar of efficient market began to crack when a pair of researchers, one of whom none other than Professor Eugene Fama himself, published a joint research paper "The Cross-Section of Expected Stock Returns" in 1992. In the paper, they documented evidence from stock market data from 1963 to 1990 that small cap stocks consistently outperform large cap stocks; and value stocks (or high B/M stocks) consistently outperform growth stocks (or low B/M stocks) ¹. (See my summary of their research at http://www.mzcap.com/insight.htm.) This was a significant discovery that shook the foundation of the efficient market school of thoughts. That fact that it was done by Eugene Fama, the godfather figure in the efficient market school of thoughts, makes it all the more significant. This discovery has tremendous implication on investment tactics. Now, investors can segment the whole market by stock valuation and capitalization. (And as you will find out by the end of this article, some market segments have higher returns and lower risks!) In the academic world, this discovery also opened the gate of mad dashes to find the better ways to beat the market.

The efficient market purists could however still argue that small cap stocks are more risky than large cap stocks and value stocks are more risky than growth stocks and thus "higher risks equal higher returns" still stands. (See my summary of prior research on this topic at .) The recent joint paper "The Value Premium and the CAPM" by Professor Fama and Professor French drove a stack into the heart of that argument. In the remainder of this article, I will review their research methodology and explain their findings from the research.

Construction of portfolios based on size and B/M ratio

To find the risk/return characteristics of stocks, Fama and French segmented the whole stock market into 6 portfolios using the following methodology: At the end of June of each year from 1926 to 2004, they (Fama and French) formed six value-weighted portfolios, SG (small growth), SN (small neutral), SV (small value), BG (big growth), BN (big neutral) and BV (big value) by the following procedure: first they sorted all NYSE, AMEX and Nasdaq stocks into two size groups, S (small cap firms with June market cap below market cap medium) and B (large cap firms with June market cap above market cap medium); then they sorted all stocks into three book-to-market equity (B/M) groups, G (growth firms in the bottom 30% of B/M), N (neutral firms in the middle 40% of B/M) and V (value firms in the upper 30% of B/M); finally, they intersected these two independent sorts to form the six portfolios mentioned above. They then performed statistics analyses (means and standard deviations) on the monthly returns of all six portfolios for the whole period 7/26 - 12/04 and two sub-periods 7/26 - 6/63 and 7/63 - 12/04. For easy viewing, I annualized the monthly statistics and present the results in Table 1:

Table 1: Annualized Statistics of the Six Value-Weighted Portfolios

Several salient features emerge from the statistics:

1. Value portfolios outperform growth portfolios regardless of market capitalization;
   
   
2. Small capitalization portfolios outperform large capitalization portfolios regardless of valuation.

The key take-away from these statistics is that--historically, small cap and value stocks have consistently outperformed large cap and growth stocks. Some investment talking heads like to propagate the notion that since the small cap and the value stocks have outperformed for so long, it's time for the large cap and the growth stocks to outperform. They are apparently not aware of history.

How significant are the return differences? Very! Let's take a look at the small value portfolio (SV) of stocks which has the best return and the large growth portfolio (BG) of stocks which has the worst return. The small value portfolio has an average annualized return of 15.66% from 1926 to 2004, the large growth portfolio merely 7.7%. If you had invested $1 in the large growth portfolio in 1926, in 2004, you would have $325. In contrast, if you had invested $1 in the small value portfolio in 1926, in 2004, you would have $84779!

Returns are not correlated to volatilities

Now let's look at the volatilities of these six portfolios as shown on Table 1. The volatilities of the portfolios are measured by their respective standard deviations. Several additional salient features emerge:

3. For all the different portfolios, volatilities in the latter period are smaller than that of the earlier period.
   
   
4. Regardless of valuation, small cap portfolios are more volatile than large cap portfolios.
   
5. For the earlier period, value portfolios are more volatile than growth portfolios regardless of valuation; but for the latter period, growth portfolios are more volatile than value portfolio regardless of valuation.

For all portfolios, the volatilities as represented by the standard deviations are lower in the more recent period. This reflects the maturation of the US equity market. While comparing emerging markets and mature markets like that of the U.S, we observe that emerging markets are more volatile. In the 20s and 30s, the US market was an emerging market, it is therefore not surprising to find that the volatilities in the period much higher than latter period.

The most notable finding however is that over an extended period of time from 1963 to 2004, value portfolios were both less volatile and had higher returns comparing to their growth counterparts. Take the small cap portfolios for example: the small cap value portfolio has an average annualized return of 13.76% which is much higher than 5.91%, the average annualized return of the small cap growth portfolio. Despite that, the annual volatility of the small cap value portfolio is 19%, less than 24% which is the annual volatility of the small cap growth portfolio. So much for the notion that higher risks equal higher rewards, unless of course one defines risks differently. Indeed, leaving no stone unturned, Fama and French did investigate the scenario under the CAPM risk definition.

Construction of factor portfolios

The construction of factors uses as building blocks the 6 size and B/M portfolios constructed previously. The size premium factor, denoted by SMB (small minus big), is the simply average of the returns on the three small cap stock portfolios minus the simple average of the returns on the threes large cap stock portfolios. The value premium factor, denoted by VMG (value minus growth), is the simple average of the returns on the two value portfolios minus the simple average of the returns on the two growth portfolios. The small cap value premium factor, denoted by VMGS is obtained by the return of the small value portfolio SV minus the return of the small growth portfolio SG. The large cap value premium factor, denoted by VMGB is obtained by the return of portfolio BV minus the return of portfolio BG. The market risk premium factor, denoted by Rm-Rf, is the difference between the value weighted market return and the one month treasury bill rate. The market risk premium factor is what investors can expected to be rewarded investing in risky stocks instead of riskless treasury bills. Note that SMB, VMG and Rm-Rf are the three factors in Fama/French three factor model in their 1994 paper "Size and Book-to-Market Factors in Earnings and Returns". Table 2 summarizes the annualized return statistics of the above 5 factors:

Table 2: Annualized Statistics of the Five Factors

The value premium is persistent, even expanding among small cap stocks

The size premium factor can be considered as a hedged portfolio of buying the small cap portfolio S and selling short the large cap portfolio B. Likewise, the value premium factor can be considered as a hedged portfolio of buying the value portfolio V and selling short the growth portfolio G. From the fact that both the size and the value premiums are consistently positive, we can draw the conclusion that small cap stocks outperform large cap stocks and value stocks outperform growth stocks. While comparing the size and the value premiums between the two periods, we also observe that both the size premium and the value premium have not diminished. To the contrary, they have expanded! (The size premium expanded from 2.4% to 2.88% and the value premium expanded from 4.2% to 5.28% between the two periods). Surely, investors have not learned to take advantage of either premium.

With further scrutiny, we found that among large cap stocks, the value premium diminished slightly from 4.32% to 3.12% between the two periods but the value premium among small cap stocks actually expanded significantly from 4.1% to 7.4%! That is a huge premium. If one invests in small cap stocks, it is foolish not to concentrate the investment in the small cap value sector.

CAPM regression to explain monthly returns

The Capital Asset Pricing Model ("CAPM") was the invention of William Sharpe in 1964 who subsequently won the Economics Nobel Prize in 1990 for his invention. Under the CAPM, the risk of an asset (class) is made up of a systematic risk component and a diversifiable risk component. Though both components contribute to the volatility of the asset (class), only taking the systematic risk component is reward-able in the equilibrium marketplace.

It is important to look at the risk-reward issue from the lenses of the CAPM. Though the Fama and French paper thus far has established that the superior returns of the value portfolios are unrelated to their volatilities, but perhaps they can be explained by their systematic risks. To further investigate how returns are related to systematic risks, Fama and French ran the CAPM regression for all 6 size - B/M portfolios.

The CAPM regression function is:

Ret_t = alpha + beta*[Rm_t-Rf_t] + e_t,

where Ret_t is the return on any of the six size - B/M portfolios in excess of the one month treasury bill rate, Rf_t is the bill rate, and Rm_t is the value-weighted market return. If the returns of assets (or asset classes) are entirely explained by their systematic risks, then the alphas should be zero for all assets (or asset classes). The annualized regression results, as displayed in Table 3, indicate otherwise.

Returns are not correlated to systematic risks

Two observations emerge from the regression results:

1. For the earlier period, the CAPM model largely holds. Note that the t-statistics for the alphas of all six portfolios are less than 2, therefore the alphas are not significantly different from zero.
   
   
2. For the latter period, the CAPM model no longer holds. The alphas for the small neutral (SN), small value (SV) and large value (BV) portfolios are all significantly larger than zero. Specifically for the small value portfolio, the alpha is 7.32%. This is the excess return of the portfolio that can not be explained by the systematic risk of the portfolio. It is huge!

The paper did not explain why the CAPM model works for one period but fails for another. However, we must not ignore that the CAPM fails for an extended period of time from 1963 to 2004, and therefore we must conclude that returns are not correlated to systematic risks.

Table 3: The CAPM Regressions of the 6 Size - B/M Portfolios

Conclusion

The major findings from this research paper include: 1) small cap stocks and value stocks consistently outperform large cap stocks and growth stocks throughout history; and 2) There are no consistent evidences that taking on more risks (weather defined as volatilities or systematic risks) are rewarded. Collectively speaking, investment rewards are not necessarily related to risks. If an investor wants better return (who doesn't?), instead of increasing the investment risks of his portfolio, he would be wise to move more of his assets to small cap value stocks.

References
Fama, Eugene and Kenneth French, 1992, "The Cross-Section of Expected Stock Returns", Journal of Finance 47, 427-465
Fama, Eugene and Kenneth French, 2005, "The Value Premium and the CAPM", Journal of Finance 61, 2163-2185
Sharpe, William F., 1964, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk", Journal of Finance 19, 425-442