“The Value Premium and the CAPM” paper, written by Eugene Fama and Kenneth French was published in the Journal of Finance in October 2006. Eugene Fama is an American economist, known for his work on portfolio theory and asset pricing and is working as a Professor of Finance at the Chicago University; while Kenneth French is a research associate at the United States’ National Bureau of Economic Research and Professor of Finance at Tuck School of Business.
The paper has three main goals which it attempts to explore; First, to provide a simple picture of how value premiums vary with firm size. Second, to explain if and when CAPM market β’s explain observed value premiums and third, to examine whether in general, variations in β across stocks is related to average returns in the way predicted by the CAPM.
Other authors’ previous studies related to value premium and the CAPM have revealed that: a) Tim Loughran (“Book-to-market across firm size, exchange and seasonality”, Journal of Finance and Quantitative Analysis, 1997): Contends that value premium is limited to small stocks. b) Andrew Ang & Joseph Chen (“The CAPM over the long run: 1926-2001”, Working Paper, Columbia University, 2005): Contend that CAPM can explain U.S. value premiums. c) Eugene Fama & Kenneth French (“The cross section of expected stock returns”, Journal of Finance, 1992): Contend that there is a value premium in U.S. stock returns for the post 1963 period. d) Eugene Fama & Kenneth French (“Common risk factors in the returns on stocks and bonds”, Journal of Financial Economics, 1993): Contend that the post-1963 value premium is left unexplained by the Capital Asset Pricing Model.
The findings of Fama and French in this paper suggest that: a) There is a value premium in U.S. and international stock returns for the post 1963 period and this value premium is similar for big stocks as well as for small stocks. b) CAPM can explain the value premiums in the average returns of 1926 to 1963, but it is not able to explain the observed post 1963 value premiums. c) It is the stock size, the Book-to-Market value or other risks related to them and not β that are rewarded in average returns. Process & Methodology:
The term “value premium” refers to the greater risk-adjusted return of value stocks over the growth stocks. The authors consider as value stocks those having a high Book-to-Market ratio or high Earnings-to-Price ratio while as growth stocks those having a low Book-to-Market ratio or low Earnings-to-Price ratio. Both Time-Series and Cross Sectional Data were used in the analysis
The Book Value of Equity is derived by subtracting liabilities and adding deferred taxes from total assets while market value of equity is derived by multiplying the price of a share of stock by the number of shares outstanding.
Initially, the article attempts to provide a simple picture on how the value premium varies with firm size. To prove the non-existence of a relationship between the value premium and the firm size, Fama and French created 6 portfolios of U.S. stocks by categorizing them based on their size and Book-to-Market ratio. The six portfolios of stocks created were: SV (Small and Value Stocks), SG (Small and Growth Stocks), SN (Small and Normal Stocks), BV (Big and Value Stocks), BG (Big and Growth Stocks) and BN (Big and Normal Stocks).
Firms having a market capitalization below the NYSE median were considered as small stocks while those having a market capitalization above NYSE median were considered as big stocks. On the other side, firms having a B/M ratio belonging to the bottom 30% of NYSE, AMEX and NASDAQ B/M ratios were considered as growth stocks, those belonging to the middle 40% were considered as Neutral and those belonging to the top 30% were considered as Value Stocks.
After defining the six portfolios of stocks, Fama and French identified the size factor by measuring the average monthly return of the three small stocks (SV+SN+SG)/3 and subtracted it from the average monthly return of the three large stocks (BV+BN+BG)/3. The results suggested that there is a negative relationship between value premium and a firm’s size meaning that small firm’s had a higher value premium than large firms. However, when Fama and French applied the same method but classified Value & Growth Stocks based on E/P ratio and not on B/M ratio they found a strong value premium on the largest stocks and little relation between the value premium and the firm size.
The same approach was used to identify value premiums in the International Stocks as well. Fama & French analyzed the stocks of 14 major markets outside U.S. and concluded that international returns show strong value premiums and this value premium is as large among the biggest stocks as among smaller stocks. After analyzing the relationship between value premium and firm’s size for the U.S. stocks as well as for International stocks Fama and French suggest that the weak relation between B/M and average returns for the big U.S. stocks may be random and due to the small number of stocks under the BV (Big & Value stocks) category.
Secondly, Fama and French attempted to identify if and when CAPM market βs explain the observed value premiums. After identifying the βs for the period 1926-2004 they concluded that for the pre 1926 period where value stocks had higher βs than growth stocks, CAPM captured value premium near perfectly while for the post 1963 period where value stocks had lower βs than growth stock CAPM failed to predict the observed results. Third, According to the Capital Asset Pricing Model theory, all variations in βs across stocks are compensated in the same way in expected returns. However, when Fama and French formed their portfolios based on size, B/M and βs they found that variations in βs that came as a result of variations in size or B/M were compensated in expected returns while variations in βs unrelated to either size or B/M were left unrewarded.
Finally, based on the findings of Fama and French, we can conclude that CAPM has fatal errors for the period 1926-2004. Size, B/M and other risks related to them are important in expected returns whether or not they relate to βs in the way predicted by CAPM and also it is important to emphasize that βs have little or no independent role.
Fama, F. E., French, R. K. (2006). The Value Premium and the CAPM. The Journal of Finance, 61, 2163-2185.