# The Empirical Explanatory Power of CAPM and the Fama and French Three-Five Factor Models in the Moroccan Stock Exchange

^{*}

## Abstract

**:**

## 1. Introduction

- To test the ability of the CAPM, FF3F and FF5F models to capture the variations in Moroccan stock returns;
- To compare the performance of the three models in order to determine which model outperforms the others in explaining Moroccan returns;
- To examine redundant factors, with the purpose of finding out which factors explain the greater part of Moroccan stock returns.

## 2. Literature Review

## 3. Data and Variables Description

#### 3.1. Data Selection

#### 3.2. Factors Formation

_{B/M}), two others size factors related respectively to size–OP and size–Inv (hereafter SMB

_{OP}and SMB

_{INV}) are produced.

#### 3.3. Left-Hand-Side Portfolios Formation

## 4. Results and Discussion

#### 4.1. Descriptive Statistics for RHS Factors’ Return

#### 4.2. Average Excess Returns for LHS Portfolios

#### 4.3. Factor Spanning Tests

#### 4.4. Summary Asset Pricing Tests (GRS)

_{i}|, the intercepts’ mean absolute value; (2) $A{a}_{i}^{2}/A{\overline{r}}_{i}^{2}$, the mean squared intercept divided by the mean squared ${\overline{r}}_{i}$—this value corresponds to the difference between portfolio i’s mean return and the market portfolio’s mean value-weighted return; (3) $A{s}^{2}\left({a}_{i}\right)/A{a}_{i}^{2}$, the mean of the squared sample standard errors of the intercept values divided by $A{a}_{i}^{2}$, and (4) AR², the mean adjusted R².

#### 4.5. Asset Pricing Details

#### 4.5.1. Size–B/M Sorts

#### 4.5.2. Size–OP Sorts

#### 4.5.3. Size–Investment Sorts

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | M. M. Carhart (1997) proposed the Carhart Four Factor Model by introducing into the FF3F model a momentum-mimicking risk factor. |

2 | In North Africa, Morocco takes the lead in terms of the equity of market capitalization in the Maghreb (USD 65.6, 57.1% of GDP), followed by Egypt (USD 41.4 billion, 11.3% of GDP) and Tunisia (USD 8.5 billion, 20.6% of GDP). In sub-Saharan Africa, South Africa has the highest market capitalization (USD 1 trillion, 313.5% of GDP), followed by Nigeria (USD 56 billion, 12% of GDP), Kenya (USD 21.4 billion, 13.1% of GDP) and Ghana (USD 9.2 billion, 13.5% of GDP). EIB, La finance en Afrique, naviguer en eaux troubles, 2022. |

3 | Available on the Moroccan stock exchange website: www.casablanca-bourse.com. (Accessed on 4 April 2022) |

4 | Fama and French (2015) employed three separate methods—2 × 3, 2 × 2 and 2 × 2 × 2 × 2—to contrast the five factors. The authors argue that the choice of any sort is arbitrary, as the results are similar. |

5 | Due to the small sample of our study, it was difficult to form effectively diversified portfolios. The 20th and 40th percentiles are the best combinations. For their part, Cox and Britten (2019) used the 33rd and 66th percentiles for the Johannesburg stock exchange. |

6 | Fama and French (2017) revealed that, for Japan, the average Mkt Return is near zero (0.01% per month). Negative average value is also found by several authors in different markets’ stock exchanges, such as the Nairobi stock market (Achola and Muriu 2016), Amman’s stock market (Alrabadi and Alrabadi 2018) and the Polish stock market (Zaremba et al. 2019). |

7 | According to Fama and French (2017), a low value of Aai²/Ari² bodes well for an asset pricing model. In contrast, a low value of As²(ai)/ Aai² is less favorable. |

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Factors | Mean (%) | t-Statistic | Standard Deviation (%) |
---|---|---|---|

Mkt | −1.77245 | −5.2688 * | 4.94413 |

SMB | 0.92233 | 2.2008 ** | 6.15922 |

HML | 0.79783 | 1.9919 *** | 5.88671 |

RMW | 0.40951 | 0.9639 | 6.24408 |

CMA | 0.23419 | 0.595 | 5.78424 |

Mkt | SMB | HML | RMW | CMA | |
---|---|---|---|---|---|

Mkt | 1 | ||||

SMB | −0.312 | 1 | |||

HML | −0.050 | 0.115 | 1 | ||

RMW | 0.047 | 0.382 | −0.186 | 1 | |

CMA | −0.114 | −0.159 | −0.182 | −0.444 | 1 |

Sort A: Size–B/M | |||
---|---|---|---|

Low | Medium | High | |

Small | −0.017 | −0.004 | −0.011 |

(−3.2625) | (−0.6292) | (−2.5646) | |

Standard deviation | 7.705% | 10.141% | 6.458% |

Big | −0.019 | −0.019 | −0.006 |

(−5.4056) | (−5.0198) | (−0.9878) | |

Standard deviation | 5.216% | 5.615% | 9.00% |

Sort B: Size–OP | |||

Weak | Medium | Robust | |

Small | −0.011 | −0.009 | −0.003 |

(−2.5193) | (−1.4973) | (−0.4503) | |

Standard deviation | 6.724% | 9.014% | 10.971% |

Big | −0.016 | −0.019 | −0.017 |

(−2.6514) | (−4.8500) | (−4.8422) | |

Standard deviation | 9.107% | 6.013% | 5.267% |

Sort C: Size–INV | |||

Conservative | Medium | Aggressive | |

Small | −0.003 | −0.018 | −0.005 |

(−0.5916) | (−3.6919) | (−0.6534) | |

Standard deviation | 7.686% | 7.283% | 10.861% |

Big | −0.017 | −0.021 | −0.011 |

(−5.0468) | (−3.9738) | (−1.9411) | |

Standard deviation | 5.051% | 7.661% | 8.329% |

Coefficient | t-Statistic | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Int | Mkt | SMB | HML | RMW | CMA | Int | Mkt | SMB | HML | RMW | CMA | Adjusted R² | |

Mkt | −0.015 | −0.309 | 0.001 | 0.115 | −0.095 | −4.680 * | −5.429 | 0.012 | 1.774 | −1.478 | 0.123 | ||

SMB | −0.001 | −0.397 | 0.199 | 0.444 | 0.041 | −0.341 | −5.429 | 3.056 | 6.603 | 0.564 | 0.273 | ||

HML | 0.008 | 0.001 | 0.213 | −0.395 | −0.338 | 2.141 ** | 0.012 | 3.056 | −5.540 | −4.706 | 0.148 | ||

RMW | 0.006 | 0.128 | 0.386 | −0.321 | −0.461 | 1.810 *** | 1.774 | 6.603 | −5.540 | −7.647 | 0.385 | ||

CMA | 0.004 | −0.108 | 0.037 | −0.281 | −0.471 | 1.176 | −1.478 | 0.564 | −4.706 | −7.647 | 0.268 |

Model Factors | GRS | p(GRS) | $\mathit{A}\left|{\mathit{a}}_{\mathit{i}}\right|$ | $\mathit{A}{\mathit{a}}_{\mathit{i}}^{2}/\mathit{A}{\overline{\mathit{r}}}_{\mathit{i}}^{2}$ | $\mathit{A}{\mathit{s}}^{2}\left({\mathit{a}}_{\mathit{i}}\right)/\mathit{A}{\mathit{a}}_{\mathit{i}}^{2}$ | AR² |
---|---|---|---|---|---|---|

Sort A: 2 × 3 size-B/M | ||||||

Mkt | 2.86 | 0.01 | 0.0064 | 0.86 | 0.45 | 0.29 |

Mkt SMB HML | 4.26 | 0.00 | 0.0048 | 0.56 | 0.44 | 0.55 |

Mkt SMB HML RMW CMA | 3.73 | 0.00 | 0.0043 | 0.49 | 0.43 | 0.60 |

Mkt HML RMW | 2.97 | 0.01 | 0.0049 | 0.56 | 0.52 | 0.46 |

Sort B: 2 × 3 size-OP | ||||||

Mkt | 1.58 | 0.15 | 0.0046 | 0.68 | 0.73 | 0.30 |

Mkt SMB HML | 1.67 | 0.13 | 0.0046 | 0.65 | 0.59 | 0.50 |

Mkt SMB HML RMW CMA | 1.47 | 0.19 | 0.0038 | 0.51 | 0.47 | 0.63 |

Mkt HML RMW | 1.33 | 0.24 | 0.0035 | 0.47 | 0.79 | 0.45 |

Sort C: 2 × 3 size-Inv | ||||||

Mkt | 2.38 | 0.03 | 0.0069 | 0.74 | 0.47 | 0.31 |

Mkt SMB HML | 2.04 | 0.06 | 0.0056 | 0.57 | 0.39 | 0.49 |

Mkt SMB HML RMW CMA | 2.41 | 0.03 | 0.0054 | 0.51 | 0.32 | 0.62 |

Mkt HML RMW | 1.92 | 0.08 | 0.0057 | 0.53 | 0.53 | 0.40 |

**Table 6.**Regression results of the CAPM, FF3F model and FF5F model for the 6 value-weighted size–B/M portfolios (July 2002–June 2020).

Dependent Variables | CAPM | FF3F Model | FF5F Model | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Alpha | Rm-Rf | R² | Alpha | Rm-Rf | SMB | HML | R² | Alpha | Rm-Rf | SMB | HML | RMW | CMA | R² | ||

SL | Coeff. | −0.01 | 0.416 | 0.067 | −0.008 | 0.649 | 0.678 | −0.505 | 0.435 | −0.008 | 0.613 | 0.640 | −0.522 | 0.025 | −0.139 | 0.442 |

t-stat | −1.808 | 4.054 * | −1.857 | 7.718 * | 9.987 * | −7.477 * | −1.836 | 7.167 * | 8.482 * | −7.157 * | 0.307 | −1.739 | ||||

SMHL | Coeff. | 0.007 | 0.621 | 0.087 | 0.001 | 1.074 | 1.094 | 0.475 | 0.597 | 0.000 | 0.967 | 0.959 | 0.459 | 0.156 | −0.330 | 0.648 |

t-stat | 0.951 | 4.644 * | 0.172 | 11.485 * | 14.500 * | 6.325 * | 0.097 | 10.812 * | 12.159 * | 6.016 * | 1.844 | −3.936 * | ||||

SH | Coeff. | −0.003 | 0.458 | 0.119 | −0.007 | 0.666 | 0.48 | 0.371 | 0.449 | −0.005 | 0.822 | 0.739 | 0.301 | −0.452 | 0.247 | 0.718 |

t-stat | −0.719 | 5.476 * | −1.962 | 9.576 * | 8.545 * | 6.633 * | −1.844 | 16.128 * | 16.425 * | 6.930 * | −9.367 * | 5.184 * | ||||

BL | Coeff. | −0.001 | 1.036 | 0.965 | 0.000 | 1.027 | −0.008 | −0.099 | 0.977 | 0.000 | 1.025 | −0.011 | −0.099 | 0.003 | −0.007 | 0.977 |

t-stat | −1.153 | 76.825 * | −0.201 | 90.117 * | −0.878 | −10.765 * | −0.21 | 87.569 * | −1.049 | −9.924 * | 0.275 | −0.648 | ||||

BMHL | Coeff. | −0.008 | 0.616 | 0.291 | −0.009 | 0.599 | −0.057 | 0.080 | 0.294 | −0.009 | 0.618 | −0.039 | 0.091 | −0.009 | 0.078 | 0.294 |

t-stat | −2.415 * | 9.454 * | −2.526 * | 8.747 * | −1.037 | 1.452 | 5.551 ** | 8.810 * | −0.623 | 1.515 | −0.137 | 1.189 | ||||

BH | Coeff. | 0.010 | 0.891 | 0.236 | 0.004 | 0.844 | −0.252 | 0.844 | 0.545 | 0.004 | 0.869 | −0.228 | 0.859 | −0.01 | 0.107 | 0.545 |

t-stat | 1.713 | 8.210 * | 1.018 | 9.571 * | −3.540 * | 11.913 * | 0.985 | 9.631 * | −2.859 ** | 11.171 * | −0.113 | 1.267 | ||||

Average Adjusted R² | 0.294 | 0.550 | 0.604 |

**Table 7.**Regression results of the CAPM, FF3F model and FF5F model for the 6 value-weighted size–OP portfolios (July 2002–June 2020).

Dependent Variables | CAPM | FF3F Model | FF5F Model | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Alpha | Rm-Rf | R² | Alpha | Rm-Rf | SMB | HML | R² | Alpha | Rm-Rf | SMB | HML | RMW | CMA | R² | ||

SW | Coeff. | −0.003 | 0.509 | 0.136 | −0.006 | 0.76 | 0.603 | 0.283 | 0.497 | −0.002 | 0.936 | 0.938 | 0.139 | −0.666 | 0.114 | 0.852 |

t-stat | −0.555 | 5.902 * | −1.695 | 10.978 * | −1.695 | 5.094 * | −1.181 | 24.364 * | 27.696 * | 4.243 | −18.342 * | 3.174 * | ||||

SMRW | Coeff. | −0.001 | 0.479 | 0.065 | −0.001 | 0.725 | 0.657 | −0.142 | 0.241 | −0.001 | 0.803 | 0.747 | −0.116 | −0.080 | 0.277 | 0.274 |

t-stat | −0.111 | 3.980 * | −0.220 | 6.360 * | 7.143 * | −1.553 | −0.218 | 7.032 * | 7.412 * | −1.192 | −0.744 | 2.595 ** | ||||

SR | Coeff. | 0.009 | 0.708 | 0.098 | 0.005 | 1.255 | 1.391 | 0.108 | 0.660 | 0.002 | 1.047 | 0.002 | 0.211 | 0.626 | −0.305 | 0.828 |

t-stat | 1.221 | 4.929 * | 1.115 | 13.522 * | 18.575 * | 1.446 | 0.621 | 15.458 * | 17.407 * | 3.649 | 9.770 * | −4.811 * | ||||

BW | Coeff. | 0.004 | 1.149 | 0.386 | 0.002 | 1.033 | −0.349 | 0.33 | 0.467 | 0.007 | 1.115 | −0.073 | 0.081 | −0.743 | −0.406 | 0.624 |

t-stat | 0.762 | 11.672 * | 0.510 | 10.705 * | −4.474 * | 4.254 * | 1.796 | 13.428 * | −1.003 | 1.140 | −9.465 * | −5.222 * | ||||

BMRW | Coeff. | −0.011 | 0.524 | 0.182 | −0.012 | 0.556 | 0.058 | 0.161 | 0.204 | −0.010 | 0.613 | 0.189 | 0.081 | −0.295 | −0.047 | 0.261 |

t-stat | −2.685 ** | 6.979 * | −3.025 * | 7.139 * | 0.930 | 2.568 ** | −2.650 ** | 7.977 * | 2.784 ** | 1.231 | −4.057 * | −0.655 | ||||

BR | Coeff. | 0.001 | 1.015 | 0.907 | 0.001 | 1.002 | −0.022 | −0.064 | 0.912 | 0.000 | 0.979 | −0.092 | −0.005 | 0.181 | 0.086 | 0.940 |

t-stat | 0.546 | 45.802 * | 0.994 | 44.262 * | −1.211 | −3.518 * | −0.047 | 51.069 * | −5.423 * | −0.334 | 9.996 * | 4.765 * | ||||

Average Adjusted R² | 0.295 | 0.497 | 0.630 |

**Table 8.**Regression results of the CAPM, FF3F model and FF5F model for the 6 value-weighted size–Inv portfolios (July 2002–June 2020).

Dependent Variables | CAPM | FF3F Model | FF5F Model | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Alpha | Rm-Rf | R² | Alpha | Rm-Rf | SMB | HML | R² | Alpha | Rm-Rf | SMB | HML | RMW | CMA | R² | ||

SC | Coeff. | 0.007 | 0.579 | 0.135 | 0.005 | 0.848 | 0.673 | 0.131 | 0.414 | 0.005 | 1.05 | 0.894 | 0.214 | −0.173 | 0.753 | 0.790 |

t-stat | 1.388 | 5.875 * | 1.095 | 9.931 * | 9.757 * | 1.914 | 1.744 | 20.034 * | 19.340 * | 4.781 * | −3.492 * | 15.362 * | ||||

SMCA | Coeff. | −0.009 | 0.503 | 0.112 | −0.011 | 0.672 | 0.415 | 0.137 | 0.237 | −0.009 | 0.781 | 0.629 | 0.039 | −0.435 | 0.049 | 0.352 |

t-stat | −1.892 | 5.309 * | −2.443 ** | 7.275 * | 5.570 * | 1.847 | −2.068 ** | 8.966 * | 8.187 * | 0.521 | −5.276 * | 0.599 | ||||

SA | Coeff. | 0.008 | 0.716 | 0.102 | 0.002 | 1.259 | 1.33 | 0.459 | 0.715 | 0.002 | 1.056 | 1.107 | 0.376 | 0.174 | −0.760 | 0.906 |

t-stat | 1.056 | 5.042 * | 0.371 | 14.958 * | 19.570 * | 6.790 * | 0.717 | 21.379 * | 25.401 * | 8.936 * | 3.730 * | −16.434 * | ||||

BC | Coeff. | −0.003 | 0.830 | 0.659 | −0.003 | 0.835 | 0.008 | 0.031 | 0.657 | −0.004 | 0.858 | −0.006 | 0.101 | 0.125 | 0.238 | 0.709 |

t-stat | −1.232 | 20.406 * | −1.328 | 19.455 * | 0.237 | 0.887 | −1.974 | 21.183 * | −0.182 | 2.914 * | 3.261 * | 6.290 * | ||||

BMCA | Coeff. | −0.004 | 0.924 | 0.353 | −0.005 | 0.923 | −0.017 | 0.099 | 0.352 | −0.004 | 0.942 | 0.034 | 0.059 | −0.129 | −0.050 | 0.353 |

t-stat | −0.973 | 10.868 * | −1.11 | 10.316 * | −0.238 | 1.379 | −0.921 | 10.283 * | 0.427 | 0.758 | −1.493 | −0.582 | ||||

BA | Coeff. | 0.010 | 1.170 | 0.480 | 0.008 | 1.088 | −0.266 | 0.350 | 0.562 | 0.009 | 1.033 | −0.280 | 0.258 | −0.119 | −0.382 | 0.612 |

t-stat | 2.242 ** | 14.121 * | 1.98 | 13.600 * | −4.113 * | 5.446 * | 2.419 ** | 13.381 * | −4.118 * | 3.919 * | −1.626 | −5.285 * | ||||

Average Adjusted R² | 0.307 | 0.490 | 0.620 |

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## Share and Cite

**MDPI and ACS Style**

Alaoui Taib, A.; Benfeddoul, S.
The Empirical Explanatory Power of CAPM and the Fama and French Three-Five Factor Models in the Moroccan Stock Exchange. *Int. J. Financial Stud.* **2023**, *11*, 47.
https://doi.org/10.3390/ijfs11010047

**AMA Style**

Alaoui Taib A, Benfeddoul S.
The Empirical Explanatory Power of CAPM and the Fama and French Three-Five Factor Models in the Moroccan Stock Exchange. *International Journal of Financial Studies*. 2023; 11(1):47.
https://doi.org/10.3390/ijfs11010047

**Chicago/Turabian Style**

Alaoui Taib, Asmâa, and Safae Benfeddoul.
2023. "The Empirical Explanatory Power of CAPM and the Fama and French Three-Five Factor Models in the Moroccan Stock Exchange" *International Journal of Financial Studies* 11, no. 1: 47.
https://doi.org/10.3390/ijfs11010047