Results from the Fama-French 3-Factor Regression

6x6 strategy provides the lowest return of 1.32 percent per month. If the momentum profits we saw in panel A were driven by a market risk factor the alpha value should have disappeared now.

Instead, the alpha values from our zero-cost portfolios are actually slightly higher than the returns we observed from our base study. Only the 3x9 portfolio has an alpha value that is lower than the return from the base study. We therefore find that systematic risk is not able to explain the momentum profit we identified. This is in line with previous findings of Jeegadesh & Titman (1993) and Jegadeesh & Titman (2001). Looking at the winner portfolios we see that only 3x6, 3x9 and 3x12 have positive alpha values. All the negative alpha values are statistically significant except for 9x3, 9x6 and 12x3 which can be seen in Table 7-3. The alpha values for the loser portfolios range from -0.021 to -0.028. As in our base study it is the loser portfolios that are driving the momentum profits.

The alpha values for the zero-cost portfolio range from 0.0187-0.0246 and they are all statistically significant at the one percent level. We can conclude that the CAPM is not able to explain the momentum profits.

Table 7-8Results 3-Factor Model – Zero-Cost Portfolio

Table 7-9 Results 3-Factor Model – F-Test

We will now turn our attention towards the regression results from the 3-factor model. We perform an F-test to see whether the 3-factor model is useful or not at explaining the dependent variable.

H0: meaning that all the regression parameters are zero (except the intercept).

HA: At least one of the parameters is nonzero.

We obtain a P-value of 0.03 for the zero-cost portfolios meaning that we can reject the null hypothesis at a 5 percent significance level. The P-values for the winner and loser portfolio are very small and the null hypothesis can be rejected at any reasonable level of significance. The 3-factor model is therefore not useless at explaining the winner, loser or the zero-cost portfolio.

The adjusted R-square values of the winner and loser portfolios are 0.833 and 0.749 respectively.

The adjusted R-square from the OLS regression is 0.062 meaning that the three factors are only able to explain 6.2 percent of the returns of the zero-cost portfolio. The 6x6 portfolio in the CAPM had an R-square value of 0.781 for the winner portfolio, 0.678 for the loser portfolio and 0.003 for the zero-cost portfolio. This means that the 3-factor model seems to do a better job at explaining momentum returns than the CAPM.

Intercept ^{0.0144 0.0032 4.49 <.0001 0.0036 3.98 0.0001}

OSEAX ^{0.0272 0.0846 0.32 0.7485 0.1303 0.21 0.8351}

SMB ^{0.0628 0.1838 0.34 0.7336 0.2003 0.31 0.7547}

HML ^{-0.4703 0.1550 -3.03 0.0031 0.1881 -2.5 0.0142}

OLS Parameter Estimates Parameter

Estimate

Newey-West corrected Std Err Standard

Error

P-value t Value P-value

t Value Standard

Error Variable

P-values from F-test Adjusted R-square

Winner portfolio ^{<.0001 0,8331}

Loser portfolio ^{<.0001 0,7491}

Zero-cost portfolio ^{0,0296 0,0622}

Table 7-10 Results 3-Factor Model - Correlation

Looking at the market risk factor we see that it is statistically significant at the 1 percent level for the winner and the loser portfolio. As our dependent variable and explanatory variables are in logarithmic form; the beta coefficient measures the percentage change in excess momentum returns for a percentage change in the market factor, keeping all other explanatory variables constant. We see that the OSEAX coefficient has increased from 1.0142 (in the CAPM model) to 1.1657 for the winner portfolio. A parameter coefficient will change if: 1) at least one of the new variables are correlated with the variable that already is in the model. 2) at least one of the new variables are correlated with the dependent variable (“StackExchange,” n.d.). The OSEAX coefficient has increased for the winner portfolio because it is negatively correlated with the size factor which is illustrated in the correlation matrix above. To decide whether the market factor is able to explain the momentum profit we need to look at the coefficient value for the zero-cost portfolio. We see that the beta value is insignificant and it is therefore not able to explain the momentum profits that were documented in section 6.2 (base study).

The size risk factor is positive and statistically significant at the one percent level for both the winner and loser portfolio. This means that both the winner portfolio and the loser portfolio load up with considerable amounts of small stocks, which confirm the size analysis from section 6.6.

However, looking at the zero-cost portfolio we see that the size factor is statistically insignificant making us conclude that it is not able to explain the momentum profits.

The value factor is insignificant for the winner portfolio while it is positive and significant for the loser portfolio. This means that the loser portfolio contains more value stocks then growth stocks.

The HML coefficient is negative for the zero-cost portfolio which suggests that value and momentum are negatively correlated. Asness et al. (2013) also find that value and momentum are negatively correlated. Our zero-cost portfolio therefore contains more growth stocks then value stocks. It is important to emphasize that value factor is the only variable we have found that is statistically significant for the zero-cost portfolio meaning that it is partly able to explain the

OSEAX SMB HML

OSEAX 1,00 -0,49 0,13

SMB -0,49 1,00 0,02

HML 0,13 0,02 1,00

Correlation

The alpha value estimated to be 0.0144 for the Zero-Cost portfolio. The alpha value is the part of the excess return on our momentum portfolio that cannot be attributed to the overall sensitivity of the momentum portfolio to the movement of the general stock market, the size-factor and the value-factor. The alpha value is statistically significant at the 1 percent level even when we use Newey-West standard errors. As the alpha value is still present, it means that the 3-factor model is not able to explain the momentum profits. This is consistent with previous empirical research and Fama &

French (1996) admit that this is “the main embarrassment of the three-factor model”.