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This report aims to make an empirical study about five companies’ equity securities, which include Exxon Mobil Company (XOM), Google Company (GOOG), Boeing Company (BA), Nash Finch food Distribution Company (NAFC) and Lithia Motors Company (LAD), using the Fama-French three factor model with monthly return, starting from August 2005 to June 2012, 83 observations in total. And it also makes a simple explanation about the regression results. Next, it enters into a two sub-periods’ regression with the same model, with period one from August 2005 to July 2008 and period two from August 2008 to June 2012. And it will illustrate the difference between the two sub-periods. Lastly, this report will make a suggestion about which company’s equity security is worth investing.

Given that the capital asset pricing model holds water under some restrictive assumptions which leads to the empirical study results from capital asset pricing model does not satisfy the researchers, Fama and French developed a three factor asset pricing model to improve its poor performance. In addition to the market risk factor, the three factor model takes size factor and book to market value factor into consideration, the added two factors turns out to be significantly correlated to the stock returns (Clive, 2004).

The Fama French three factor pricing model was proposed in 1993, which is described as follows:

And indicates the excess market return; SMB means the differential return on small firms versus large firms, which is also called the size factor; HML means the differential returns on high book to market ratios versus those firms with low book to market ratio, which is also named value factor. The coefficients of,, are respectively the betas of the equity on each of the three factors, i.e. factor loadings. And the standard deviation of the regression residual denotes the idiosyncratic risk. In contrast to capital asset pricing model, this model includes three systematic risk factors as mentioned above (Bodie, Kane and Marcus, 2012).

Fama and French find out that there is a negative relation between size and stock return, while the book to market value is stronger positive to the average stock return (Fama, French and Kenneth, 1993).

This report will study five different company’s stocks form U.S.based on Fama-French three factor model in the following sections.

The whole period regression results are presented in table 1 as follows. Alpha, beta, size and value are respectively the coefficients of the intercept, market excess return, SMB and HML.IV is short for the idiosyncratic volatility, and this report uses the standard deviation of the residual value to act as the idiosyncratic volatility, which is according to the research results of Fama- French in 1993 (Chen and Petkova. 2012, Fama, French and Kenneth, 1993).

Table 1 the regression results of the five companies

company |
alpha |
p-value |
beta |
p-value |
R-square |

XOM |
0.0053 |
0.2688 |
0.6877 |
0.0000 |
0.3176 |

GOOG |
0.0075 |
0.3986 |
1.3259 |
0.0000 |
0.3442 |

BA |
0.0032 |
0.6103 |
1.1829 |
0.0000 |
0.5295 |

NAFC |
-0.0046 |
0.6521 |
0.4891 |
0.0405 |
0.0739 |

LAD |
0.0062 |
0.7459 |
1.4116 |
0.0019 |
0.2366 |

It obviously can be seen from the table, the intercepts of the five stocks are all very close to zero, at the same time, the p value of each coefficient are all greater than 5 percent at the confidence level of 95 percent. The results indicate that the intercept of each regression equation is indifferent to zero. Then no significant evidence shows that any equity secuity outperform the three factor model.

The betas showed that only XOM and NAFC are defensive stocks, the other three are aggressive stocks; that is to say, the systematic risks of GOOG、BA and LAD companies are higher than the market risk. At the same time, the p values of the five beta coefficients are all less than 5 percent, which means the regression results are significant different from zero.

The factor loadings are consistent with the company fundamentals to some degree, which can be supported by the results showed in table 2. The previous literature revealed that the small capitalization stocks would have relatively higher investment return and higher book-to-market value company tended to earn a high rate of return (Nguyen & Tran, 2012). Table 2 shows that the size of XOM, GOOG, BA are much larger than NAFC and LAD, meanwhile, the coefficient of the first three companies are negative and the latter two are positive, which is in accordance with the previous results. Apart from company BA, the other four companies, NAFC, LAD, XOM and GOOG, the higher book-to-market value, the higher coefficient. As a whole, the factor loadings are at largely fit in with the company fundamentals.

Table 2 the fact loadings regression results

The table 3 presents the idiosyncratic volatility, the standard deviation of the residual (Chok, Jay and Sun, 2007), and LAD Company has the largest standard deviation, which suggests that LAD stock has the highest firm specific risk.

Table 3 the standard deviation of the residual value

Grounded on the regression results, the Fama-French three factor model is an appropriate model to price the five companies’ stocks to a certain degree. First of all, the p-values of alpha are not significant, which means that the hypothesis of the intercept being zero can be accepted. And most of the R-squares exceed 30 percent. And a large part of the size coefficients are significant, that is to say the size factor can explain the stock return, though the value coefficient is not that statistically significant.(文中部分图被省略.等其他代写请联系我们)