Fama and French Model and Capm Finance Essay

Estimating the expected return of the asset is the fundamental of finance subject and it is vital to the existence of the business. There are two models of asset pricing widely used to calculate the cost of equity: Capital asset pricing model (CAPM) and Fama and French three factor model. This report will critically analyze the strength as well as weakness between two models; also, it will explain the reason why CAPM are widely used by the manager even though it has quite a lot of shortcomings. CAPM (Capital asset pricing model) is used to calculate the expected return on one stock, indicating the close relationship between the expected return of the risky asset and the Beta (specific systematic risk, derived from the time-series regression analysis). CAPM predicts that stocks with high expected return should have high risk because the expected return has positive linear relation with the non-diversifiable risk i.e. Beta. (IRJ) CAPM equation: E(r) = rf + Beta[E(rm) - rf] CAPM is widely used to estimate the discount rate of the firm's future cash flows. Another application of CAPM is the Sharpe ratio e.g. reward to variability ratio, it measures the performance of the asset by dividing the expected return by the standard deviation. (investment) SML (Security market line) graphs the relationship between Beta and the expected return, it measures the rate of return needed to compensate for the risk born by the investors, and for the time value of money as well. As long as CAPM holds, all assets should lie on the SML. Securities lie above the SML will have greater expected return with the same risk, which means they are underpriced, the difference between the actual and expected return is called alpha or abnormal return. In reality, the investor would like to buy the underpriced and sell the overpriced securities. CML (Capital market line) shows the relationship between the expected return and the standard deviation by mixing risky portfolio with the risk free asset.(Bodie) The Sharpe-Lintner model indicates that the Jensen's alpha or intercept is zero. Actually, according to recent tests of Douglas (1968), Black, Jensen and Scholes (1972), Blume and Friend (1973) as well as Fama and French (1992), the intercept is greater than the risk free rate. (JEP) According to Banz(1981), CAPM model fails to explain the relation between the firm size and the expected return, which is called size effect. Similarly, the book-to-market ratio is another important factor that can affect the return of the stock. Several tests have proved that Beta alone is not enough to explain all the risks in reality. (IRJ) CAPM works by estimating beta from the market, combining it with the risk free rate and market return to calculate the cost of equity capital. However, several empirical tests have proved that the actual relation between Beta and the expected return is much lower than the prediction of CAPM. According to Friend and Blume, CAPM indicates that high beta stocks have high returns and low betas stocks have low returns, which is imprecise. (JEP) To overcome this weakness, researchers such as Jensen and Scholes (1972), Friend and Blume (1970) have tested and they conclude that using Beta of a portfolio would be more precise than using Beta of individual stock. Beta can explain individual stock return therefore it is able to explain the portfolio return; using portfolio beta can help reduce errors in variable problems. Although this method still has a small problem, it decreases the statistical power; it can be fixed by sorting portfolios by the beta, from the lowest to the highest. (JEP) To examine the efficiency of Beta, an empirical test on the Athens Stock Exchange (ASE) has been run: 100 stocks have been selected from FTSE/ ASE 20, FTSE/ ASE Mid 40 and FTSE/ ASE Small Cap and they were formed into 10 portfolios. The table below is the summary of the result from the regression analysis.

Portfolio

beta (p)

a10 0.0001 0.5474 b10 0 0.7509 c10 -0.0007 0.9137 d10 -0.0004 0.9506 e10 -0.0008 0.93 f10 -0.0009 0.9142 g10 -0.0006 1.0602 h10 -0.0013 1.1066 i10 -0.0004 1.1293 j10 -0.0004 1.2024 Average Rf 0.0014

Average rm=(Rm-Rf) 0.0001 Source: Metastock (Greek) Data Base and calculations (S-PLUS) (IRJ) One of the main points of CAPM is that high Beta should result in high expected return. Nevertheless, the test on 100 stocks of ASE has provided an opposite conclusion. Portfolio a10 has the lowest Beta (0.5474) but it has the highest return (0.0001) while j10 has the highest Beta with the lowest return.

FAMA

Beside CAPM, the three factor model (or Fama and French model) is another alternative to achieve asset pricing. According to the model, the sensitivity of the expected return depends on those three factors: + The difference between the return on the market portfolio and the risk free rate: rm - rf + The difference between the return on the portfolio of small stocks and the portfolio of large stocks: SMB (small minus big) + The difference between the return on the portfolio of high book- to- market- value stocks and portfolio of low book to market value stocks: HML (high minus low) The expected return of stock "i" is: Er(i) - rf = alpha(i) + Beta(i) (rm - rf) + Beta(SMB) r(SMB) + Beta(HML) r(HML) + e(i) Fama and French indicate that firms with high book to market value ratio and positive slope on HML are more likely to gain higher returns and in return, have higher possibility in facing financial distress because small firms are more sensitive to changes of the market. (Multifactor) One of the most serious defects of Fama and French model is the momentum effect of Jegadeesh and Titman (1993), which indicates that stocks which showed high returns in the past 3 or 12 months will continue to gain high returns in the next several months and similarly, stocks performed badly in the past would continue to have poor performance. This assumption is left unexplained. (JEP)(Multi) Also, bad-model is another problem that Fama as well as other asset pricing model fail to explain. Although the three factor model seems to give more accurate result, it is still based on the empirical model of expected returns; however that model cannot completely explain the average return. The bad-model effect is less serious in the short term returns (daily); however, it becomes important in long term returns, especially on small stocks. (10.1) Finally, because Fama and French explain more clearly the factors of risk, it requires detailed forecast of market index return, SMB as well as HML return, which make it difficult and expensive to apply this method.(Bodie)

Compare:

Beta from CAPM alone cannot fully explained the total risk of the stock, while Fama and French model indicates that the sensitivity of the return depends on the market, size and book-to-market ratio to explain the expected return, many studies have proved that the Fama and French model provides a more accurate estimation for the expected return. CAPM fails because Beta shows little relation to variables such as BE/ME, PE and CP ratio which are important in determining the expected return. Here is an example of applying Fama and French model and CAPM in Thailand Stock Exchange: 421 companies are divided into 6 groups: SH, SM, SL, BH, BM, BL. S and B are the size of the company, whereas H, M, L represents the book-to-market value. SH BH SM BM SL BL 114 14 122 56 52 63 (Thailand) The table below shows the adjusted R squared of CAPM and Fama and French model in Thailand Stock Exchange from 2002 to 2007: According to Bodie, adjusted R-squared is the square root of the correlation coefficient, it estimates the regression line. It is called the measure of goodness -of-fit; adjusted R-squared is also a tool to compare the usefulness among models because it can measure how much of the difference in individual stock return can be explained by the estimation. (Compare)

CAPM Fama and French SH 0.295 0.567 BH 0.077 0.91 SM 0.143 0.33 BM 0.231 0.885 SL 0.351 0.384 BL 0.671 0.669 According to the table above, the value of adjusted R-squared of Fama and French model dominates the CAPM. The average value of FF model is 0.63 where as CAPM's is 0.3. The range of CAPM is from 0.077 to 0.671 while FF model's range is from 0.33 to 0.91. Apparently, Fama and French model can express more efficiently than CAPM model. (Thailand) Here is another test ran by Zhi Da (2008) to compare the efficiency between two models: A set of 30 portfolio has been created and analyzed:

Cross sectional Analysis

CAPM FF 3 Factor Average Factor Return Intercept 0.0034 0.005

-1.76 -2.41 [1.75] [2.39] MKT 0.0058 0.0038 0.0067

-2.22 -1.41

[1.85] [1.18] SMB

0.0041 0.0021

-1.98

[1.72] HML 0.0017 0.0042

-1.11

[0.88] adj R2 32.51% 35.91% (item) According to the table, the intercept of Fama and French model is consistent with it's theory, it is greater than CAPM's (0.005 versus 0.0034), while FF's market factor is less than CAPM's. The significant strength of the three factor model is that it acounts for the risk of the size and book-to-market ratio of the company, and therefore the model has higher coefficient as opposed to CAPM, Fama and French model can explain nearly 36% of the expected return, whereas CAPM can explain only 32.5%.

Conclusion:

CAPM indicates that Beta alone can explain all the risks related to the expected return, the discount rate and Beta is strongly related. However, several tests have proved that CAPM failed. The first point is that the intercept is actually greater than the risk free rate. Secondly, Beta alone is not enough to explain the risk; the expected return can be affected by other factors such as the size and book-to-market ratio. And finally, in reality, Beta does not have the relationship with expected return as strong as predicted by CAPM. Fama and French model provide a more accurate estimation as opposed to CAPM. It indicates that the expected return are affected by three factors: market return, size effect (SMB) and book-to-market ratio (HML). However, it still has shortcomings. The first defect is that it failed to explain the momentum effect. Secondly, not only Fama and French but others asset pricing model are based on the empirical model of expected return, which cannot completely explain the average return. Finally, the three factor model is quite complex and expensive to apply. If the forecast of the market return, SMB or HML is not accurate, then the result might be worse than CAPM's. Thus, although CAPM model still has a lot of defects, it is still widely used by managers. (Bodie)

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