SMB (small minus large) is the return on the portfolio of small stocks minus the return on a portfolio of large stocks, while HML (high minus low) is the return on the portfolio of value stocks minus the return on a portfolio of growth stocks. WML is the return on the portfolio of winner stocks minus the return on a portfolio of loser stocks (winners minus losers in terms of returns). SMB is the average return on the three small portfolios (S/L, S/M, S/H) minus the average return on the three large portfolios, the return on the three large portfolios (B/L, B/M, B /H). ).
Rm-Rf, is the return of the value weight of all NYSE, AMEX, and NASDAQ stocks (from CRSP) minus the one-month Treasury note rate (from Ibbotson Associates). 4) Momentum Factor. 1 Rm-Rf The excess return on the market portfolio Rm is the weighted monthly percentage return for all stocks in the 25 size EU/ME portfolios plus the negative BE stocks excluded from the 25 portfolios. 2 SMB Small Minus Big (return to . by mimicking the portfolio for the usual size factor in stock returns).
4 MOM the average return on the two prior high return portfolios minus the average return on the two prior low return portfolios. After performing the time series regression with the previous two models, it is then necessary to test how well the average premium for the three factors as well as the four factors representing risk is in explaining the cross-section of the average stock return. This analysis aims to observe whether the stock market factors that capture the average return of size and EU/ME portfolios have performed size and momentum.
Findings and Discussions
Descriptive Statistics
For this purpose, the value-weighted monthly excess return as a percentage of portfolios that formed size and momentum is required. This portfolio is constructed monthly from the intersections between 5 portfolios formed on size (market share, ME) and 5 portfolios formed on past (2-12 months) returns. Next is analysis of whether Rm-Rf, SMB, HML and MOM can explain the returns on portfolios formed by size and momentum, time series regression, as previously performed on portfolios based on size and book-to-market equity.
The portfolio of stocks in both the largest size and the lowest BE/ME (B-L) alone represents more than 32% of the total value of the 25 portfolios. In the largest size quintile, the market value shows a strong downward trend with increasing BE/ME. Therefore, the inverse relationship between size and BE/ME is likely caused by the largest size quintile.
The clear pattern of each size and book-to-market equity quintile portfolios with respect to firm size and market value of equity can be seen in figure 2a and 2b below. Average of annual percentage of market value for 25 stock portfolios run on Size and BE/ME. In addition, stocks with low book-to-market ratios outperformed stocks with high BE/ME.
These patterns confirm the result of FF (1993) while also specifying Fama and French's (1992) evidence that size and average return show negative relationship. On the contrary, a strong positive relationship between average yield and BE/ME is also evidenced. In the overall BE/ME portfolio, except for the lowest, the average return tends to decrease from small to large portfolio.
This evidence also confirms the previous description of firm size and market value in Figures 2a and 2b. In the portfolios of BE/ME quintiles, the standard deviations of the average return range from 4.429% to 8.117%, which is quite high.
Time Series Regressions
The fourth factor, momentum, indicates average returns of around 0.716% per month (t=3.968), while the correlation to all other factors is negative. Dependent variable: Excess return on 25 portfolios formed on size and book-to-market equity Book-to-market equity (BE/ME) quintiles. First, SMB was able to capture shared variation that cannot be explained by market factors and by HML.
Second, HML can also capture common variation that cannot be explained by Rm-Rf and SMB. The R2 value also confirms the result that adding SMB and HML factor together with market factor can increase the ability to explain excess stock returns. These findings suggest that SMB and HML are able to describe variation in stock returns that is missed by the market factor.
In other words, the market factor is not the only component that can describe excess return variability, as the standard CAPM claims. Furthermore, a three-factor model in the spirit of the multifactor model as proposed by Merton (1973) might provide a better explanation of risk. 2) Model 2: Market, SMB, HML and MOM. The results show that under the four-factor asset pricing model, all four factors, MP, SMB, HML, and MOM, help explain the variation in average returns in the US stock market.
All are significant and are systematically related to size from the smallest to the largest quintile. Overall, the SMB coefficient pattern is similar to Model 1 as well as the original FF (1993). Most of them are positive instead of the smallest size quintile and all are significantly different from zero.
The R2 value of regression of the four-factor model indicates only slight increase from the three-factor model. This evidence seems to suggest that the return variation is somewhat better explained by the four factors associated with larger firms.
Cross-Section Average Returns
This result indicates that the MOM factor can somewhat explain the variation of time series returns. By focusing on the cross-sections derived from the three regression models used in this paper, the ability of the risk factors of the mean premium to explain the cross-sectional stock returns can be examined. For model 1, where all three factors are analyzed, the values of the intercepts are closer to zero.
The observed t-statistic also indicated that only six out of 25 portfolios differ significantly from zero, while others are insignificant. This implies that extending the data to the longest period still approximately maintains the main results of the three-factor model. Intercept not different from zero indicates that Rm-Rf, SMB and HML can satisfactorily explain the cross section of average stock returns.
On the other hand, the four-factor model with an extension to the four-factor, where MOM (momentum) is linked to the model, still causes some indifference to the three-factor model. Only six of the 25 portfolios seem to deviate significantly from zero, with the interception coefficient ranging from -0.420 to 0.151, which is slightly higher. The evidence confirms the importance of the four-factor model in explaining the time-series variation of average returns in the US.
Robustness Test
Overall, it suggests that the three-factor model could explain the cross-section of average stock returns. Meanwhile, the four-factor model that used the portfolio of excess returns formed on size and previous month's returns can be seen in Table 9 below. It can be seen that the overall four-factor model is slightly better compared to the result of the three-factor model in Table 8.
The intercept coefficient is slightly better compared to the three-factor model, with 9 out of 25 not significantly different from zero. Since Model 2 is somewhat better at capturing stock return variation, another robustness check related to seasonality is considered relevant for the residuals of the four-factor model. Therefore, the January seasonality test is also performed in the residuals from the four-factor model.
The full result of the January seasonal test from the four-factor model is shown in Table 10 below. The January seasonality in the stock returns can be explained by the corresponding seasonal fluctuations in the risk factors in the four factor models. The main objective of this paper is to examine the validity of four-factor asset pricing in comparison with the Fama French three-factor model using current data on US monthly stock returns.
In contrast, the four-factor asset valuation reinforces the three-factor model by adding the fourth factor, called momentum (MOM), which represents winners minus losers in terms of returns. In particular, there are some implications that this paper offers in the spirit of the four-factor model. This is consistent with Carhart (1997) who argued for the power of the four-factor model as a performance attribution model, where the premium coefficients for each factor: the market, SMB, HML and MOM measure relative strength in explaining volatility. of the equity returns attributable to this.
The four-factor model has been shown to have, to some extent, a significant ability to explain the variation in average excess returns. The significant coefficient on the four factors in overall as well as insignificant intercepts contributes to support the ability of the four-factor model to explain the US stock returns. Since the four-factor model seems to be able to explain the variation in stock returns, it would be useful to analyze the time variation associated with each factor (SMB, HML and MOM) as well as the time variation in market premiums to best explain the variations in portfolio stock returns.
Finally, the results should contribute to a better understanding of how investors value assets, as well as checking the validity of the four-factor model in different market contexts.
