# Analysis of the Spanish IBEX-35 Companies’ Returns Using Extensions of the Fama and French Factor Models

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data and Methodology

#### 3.1. Data

_{M}) proxied by IBEX-35 returns, the nominal interest rate (i), the size factor (SMB), the growth factor (HML), MOM, LTREV and LIQV. On the other hand, we present the extended five-factor model of Fama and French [2], which adds to the above explanatory factors the following factors: the profitability factor, RMW (Robust Minus Weak) and the investment factor, CMA (Conservative Minus Aggressive).

#### 3.2. Methodology

#### 3.2.1. QR Methodology

_{i}is the dependent variable; ${\beta}_{\theta}$ indicates an unknown k x 1 vector of regression parameters; and ${Q}_{\theta}\left({y}_{i}|{x}_{i}\right)$, that is, the conditional quantile theta follows this assumption about the error term: ${u}_{\theta i}{Q}_{\theta}\left({u}_{\theta}{x}_{i}\right)=0$. The QR estimates show a marginal change in the dependent variable at quantile theta to marginal changes in a particular regressor.

#### 3.2.2. Extensions of the Fama and French Factor Models

_{jt}is the IBEX-35 company returns, R

_{Ft}is the risk-free return, R

_{Mt}is the stock market return, $\Delta {i}_{t}^{u}$ is the unexpected change in the long-term nominal interest rate, SMB

_{t}is the return on a diversified portfolio of small capitalization stocks minus the return on a diversified portfolio of large capitalization stocks (size factor), HML

_{t}is the difference between the returns on diversified portfolios of high and low B/M stocks (value or growth factor), MOM

_{t}is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios (MOM), LTREV

_{t}is the average return on the two low prior return portfolios minus the average return on the two high prior return portfolios (LTREV), and LIQV

_{t}is the weighted value on the weighted portfolio (10). Finally, e

_{jt}is the error term.

_{t}is the difference between the returns on diversified portfolios of stocks with robust and weak profitability (profitability factor), and CMA

_{t}is the difference between the returns on diversified portfolios of the stocks of low- and high-investment firms (investment factor).

## 4. Analysis of Results

#### 4.1. Whole Sample Period

^{2}coefficient is studied in Figure 2. Specifically, this figure shows the mean (Panel A) and maximum (Panel B) values of the adjusted R

^{2}coefficient for Models A and B, distinguishing between different theta values (0.1, 0.25, 0.5, 0.75 and 0.9).

^{2}coefficients of both Models A and B show a U-shape along the theta values, which means that these models will have a strong explanatory power in the extreme quantiles. In this case, the highest explanatory power corresponds to the lowest quantile 0.1. This result is in line with [3], where the best results of the adjusted R

^{2}are obtained at quantile 0.1.

^{2}values (Panel B) in Figure 2, we observe a U-shaped trend across the quantiles, showing a higher explanatory power of both models in the extremes and especially in the lowest quantile 0.1. Specifically, BBVA shows the maximum adjusted R

^{2}value in the full period for both models. Finally, this comparison between Models A and B in both panels of this figure confirms that Model B has higher values both in average and for the maximum adjusted R

^{2}. Therefore, Model B is more effective in explaining the Spanish IBEX-35 companies’ returns to changes in explanatory risk factors.

#### 4.2. Robustness Test

#### 4.2.1. Precrisis Subperiod (January 2000–January 2008)

^{2}coefficients in the precrisis subperiod. In this subperiod, Model B explains, better than Model A does, the Spanish companies’ returns throughout the selected explanatory factors. We emphasize that the average and the maximum adjusted R

^{2}coefficients are higher in the extreme quantiles, and are the highest at quantile 0.1, according to the full sample period. Thus, both panels show a U-shaped evolution along with theta values. Additionally, the maximum explanatory power corresponds to BBVA, coinciding with the full period.

^{2}of both models are, respectively, over 33% (vs. 29% in the full period) and over 67% (vs. 64% in the full period).

#### 4.2.2. Crisis Subperiod (February 2008–January 2014)

^{2}coefficients across quantiles, presenting a U-shaped evolution. Thus, the explanatory power of both models in both panels is higher in the extreme quantiles, especially at quantile 0.1, and, in general, Model B explains the Spanish companies’ returns (except for theta 0.5) better than Model A does. Moreover, BBVA has the maximum adjusted R

^{2}value, according to the full period and the precrisis subperiod. On the other hand, this crisis subperiod is better explained with both models than the whole sample period is. For example, the average and the maximum adjusted R

^{2}s of Model B in this subperiod are, respectively, close to 34% and 68%, while in the full period, they are close to 29% and 64%, respectively, at quantile 0.1.

#### 4.2.3. Postcrisis Subperiod (February 2014–December 2018)

^{2}coefficients for the postcrisis subperiod. The best results are in the extreme quantiles, specifically, in quantile 0.1. In this subperiod, Model B explains the IBEX-35 companies’ returns better than Model A does in all of the quantiles, with the largest difference between models in all periods. For example, in the extreme quantile 0.1, Model B reaches a mean adjusted R

^{2}of 34% (vs. 31% in Model A) and a maximum adjusted R

^{2}of 64% (vs. 61% for Model A). Additionally, this postcrisis subperiod is better explained with both models than the entire sample period, especially in the highest quantiles. As an example, the maximum adjusted R

^{2}of Model B at quantile 0.9 in this subperiod is close to 63%, while in the full period, it is close to 59%. The maximum adjusted R

^{2}values in this postcrisis subsample at quantile 0.1 are slightly superior to those in the full sample (63.99% vs. 63.86%, respectively). Additionally, in this subperiod, the maximum explanatory power corresponds to Santander, in contrast to previous periods, where the maximum adjusted R

^{2}corresponded to BBVA. However, this result is in line with those obtained in the rest of the periods because both companies belong to the same banking sector.

^{2}coefficients as the values of theta increase. Therefore, these models may have a greater explanatory power in the extreme quantiles in all periods, confirming the suitability of using this methodology of regression by quantiles in this kind of research. Moreover, this research concludes that the best result of the adjusted R

^{2}corresponds to the lowest quantile, 0.1. Thus, this result, which is consistent in all subperiods, coincides with [3,4,18,29], among others.

## 5. Conclusions

^{2}. Thus, these models have the greatest explanatory power in the extreme quantile and, specifically, in the lowest quantile, 0.1, in line with previous studies such as [3]. Second, Model B explains the Spanish companies’ returns better than Model A does in the full period and in the three subsample periods. Third, BBVA has the maximum adjusted R

^{2}value in all periods, except for the postcrisis subperiod, where the maximum explanatory power corresponds to Santander. Thus, Models A and B best explain stock returns for companies that belong to the same banking sector. Fourth, the crisis subperiod is the economic stage with the highest values of this coefficient (adjusted R

^{2}) in all of the quantiles. Therefore, the proposed factor models and, in particular, the second model, explain the variations in Spanish companies’ returns the best in crisis stages.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Components of the Spanish IBEX-35 index in 2019: company (code) (x-axis) and weight (y-axis). Source: BME (Spanish Stock Exchanges and Markets).

**Figure 2.**Adjusted R

^{2}by quantile for Models A (dark) and B (light): whole sample period. (

**A**): Mean Adj. R

^{2}. (

**B**): Maximum Adj. R

^{2}. Source: Own elaboration from Eviews data.

**Figure 3.**Adjusted R

^{2}by quantile for Models A (dark) and B (light): precrisis subperiod. (

**A**): Mean Adj. R

^{2}. (

**B**): Maximum Adj. R

^{2}. Source: Own elaboration from Eviews data.

**Figure 4.**Adjusted R

^{2}by quantile for Models A (dark) and B (light): crisis subperiod. (

**A**): Mean Adj. R

^{2}. (

**B**): Maximum Adj. R

^{2}. Source: Own elaboration from Eviews data.

**Figure 5.**Adjusted R

^{2}by quantile for Models A (dark) and B (light): postcrisis subperiod. (

**A**): Mean Adj. R

^{2}. (

**B**): Maximum Adj. R

^{2}. Source: Own elaboration from Eviews data.

**Table 1.**Descriptive statistics of companies’ and market returns and the rest of the explanatory factors.

Mean | Median | Max. | Min. | Std. Dev. | Asymmetry | Kurtosis | Jarque-Bera | ADF | PP | KPSS | |
---|---|---|---|---|---|---|---|---|---|---|---|

SAN | −0.0029 | 0.0073 | 0.3368 | −0.2768 | 0.0872 | −0.3309 | 4.3761 | 22.4401 *** | −14.3487 *** | −14.3383 *** | 0.0276 |

IBE | 0.0040 | 0.0074 | 0.1931 | −0.2384 | 0.0649 | −0.3228 | 4.5243 | 22.3852 *** | −14.3115 *** | −14.3118 *** | 0.1269 |

ITX | 0.0085 | 0.0086 | 0.1990 | −0.2314 | 0.0652 | −0.6686 | 4.8968 | 44.4357 *** | −13.2154 *** | −13.1967 *** | 0.1049 |

TLF | −0.0059 | −0.0038 | 0.2381 | −0.2887 | 0.0721 | −0.3345 | 4.2811 | 20.1040 *** | −16.8957 *** | −16.8957 *** | 0.0976 |

BBVA | −0.0043 | −0.0009 | 0.3040 | −0.2821 | 0.0875 | −0.01194 | 4.4542 | 18.2436 *** | −14.5442 *** | −14.5441 *** | 0.0443 |

AMS | 0.0160 | 0.0147 | 0.1250 | −0.1474 | 0.0566 | −0.56023 | 3.2120 | 5.79886 ** | −12.0383 *** | −12.0720 *** | 0.0641 |

REP | 0.0006 | 0.0072 | 0.1732 | −0.3433 | 0.0711 | −1.0725 | 6.000 | 112.2299 *** | −12.8049 *** | −12.8049 *** | 0.0666 |

CABK | −0.0033 | 0 | 0.2373 | −0.2934 | 0.0931 | −0.1482 | 3.8182 | 4.32276 * | −11.2153 *** | −11.2367 *** | 0.0772 |

FER | 0.0056 | 0.0079 | 0.3171 | −0.3187 | 0.0792 | −0.300 | 6.0634 | 80.3935 *** | −12.6804 *** | −12.8467 *** | 0.0947 |

NTGY | 0.0016 | 0.0055 | 0.1631 | −0.2756 | 0.0678 | −0.5076 | 4.292 | 22.5083 *** | −12.6054 *** | −12.7113 *** | 0.0983 |

AENA | 0.0109 | 0.0101 | 0.1283 | −0.1083 | 0.0537 | 0.1916 | 2.3912 | 1.0566 | −7.3471 *** | −7.31476 *** | 0.1492 |

IAG | 0.0085 | 0.0228 | 0.2022 | −0.4624 | 0.0935 | −1.7909 | 9.4368 | 221.5685 *** | −9.9676 *** | −10.013 *** | 0.1221 |

ACS | 0.0058 | 0.0139 | 0.2297 | −0.3263 | 0.0753 | −0.6443 | 5.5534 | 63.3956 *** | −13.5608 *** | −13.5608 *** | 0.1538 |

REE | 0.0102 | 0.0149 | 0.1396 | −0.1234 | 0.0571 | −0.2423 | 2.5804 | 3.3725 | −14.5302 *** | −14.5883 *** | 0.3751 |

GRF | 0.0131 | 0.0135 | 0.2371 | −0.2685 | 0.0842 | −0.2103 | 3.1875 | 1.3606 | −13.5848 *** | −13.5294 *** | 0.1294 |

ELE | 0.0025 | 0.0054 | 0.2174 | −0.6365 | 0.0822 | −2.3378 | 21.070 | 2758.109 *** | −14.8538 *** | −14.8254 *** | 0.1240 |

CLNX | 0.0135 | 0.0195 | 0.1985 | −0.1237 | 0.0655 | 0.3726 | 3.1877 | 1.13176 | −7.9627 *** | −7.9627 *** | 0.1698 |

BKT | 0.0023 | 0.0012 | 0.3344 | −0.3088 | 0.0910 | 0.0102 | 4.3854 | 14.8771 *** | −10.9469 *** | −12.5371 *** | 0.1168 |

ENG | 0.0055 | 0.0069 | 0.2150 | −0.1791 | 0.0582 | −0.0471 | 3.7962 | 5.088 *** | −15.1887 *** | −15.1956 *** | 0.1563 |

SGRE | 0.0047 | 0.0197 | 0.3985 | −0.6342 | 0.1192 | −0.8461 | 6.9777 | 155.717 *** | −11.5790 *** | −12.1744 *** | 0.1180 |

MRL | 0.0070 | 0.0119 | 0.1220 | −0.1016 | 0.0484 | −0.1338 | 2.6442 | 0.4708 | −6.9510 *** | −6.9296 *** | 0.1108 |

SAB | 0.0040 | 0.0057 | 0.1374 | −0.2206 | 0.0523 | −0.5533 | 4.4449 | 31.7431 *** | −13.8173 *** | −13.8334 *** | 0.0904 |

MAP | 0.0036 | −0.0015 | 0.2740 | −0.3323 | 0.0811 | −0.3577 | 5.4651 | 54.6291 *** | −13.0419 *** | −13.0208 *** | 0.1490 |

BKIA | −0.0213 | −0.0126 | 0.689 | −0.6779 | 0.1821 | −0.1008 | 8.4696 | 112.3409 *** | −9.65057 *** | −9.6848 *** | 0.0987 |

ANA | 0.0034 | 0.0067 | 0.2267 | −0.3664 | 0.0914 | −0.6702 | 4.5620 | 32.8351 *** | −10.6089 *** | −11.7138 *** | 0.1627 |

MTS | −0.0079 | −0.0067 | 0.3719 | −0.5600 | 0.1260 | −0.6491 | 6.1944 | 74.8059 *** | −9.8659 *** | −9.8665 *** | 0.0487 |

COL | −0.0191 | −0.0033 | 0.3895 | −0.5946 | 0.1445 | −0.8613 | 6.2437 | 103.4151 *** | −10.2469 *** | −10.9179 *** | 0.2115 |

VIS | 0.0090 | 0.0149 | 0.2076 | −0.1753 | 0.0566 | −0.1165 | 4.2459 | 13.1874 *** | −15.1747 *** | −152872 *** | 0.1126 |

CIE | 0.0133 | 0.0074 | 0.3885 | −0.3539 | 0.0914 | −0.1628 | 6.7286 | 117.3224 *** | −14.4300 *** | −14.4800 *** | 0.0886 |

ACX | −0.0004 | 0.0004 | 0.0302 | −0.0532 | 0.0113 | −1.2179 | 7.4188 | 197.3044 *** | −11.9968 *** | −12.0519 *** | 0.3937 |

TL5 | −0.0041 | −0.0018 | 0.3173 | −0.3012 | 0.0949 | −0.1100 | 4.3697 | 14.1924 *** | −6.9540 *** | −12.7180 *** | 0.0906 |

IDR | 0.0022 | 0.0032 | 0.2296 | −0.2322 | 0.0704 | −0.1108 | 3.8179 | 5.9542 ** | −14.0872 *** | −14.0852 *** | 0.3156 |

MELL | 0.0026 | 0.0069 | 0.5629 | −0.5138 | 0.1089 | −0.1358 | 8.6414 | 263.1685 *** | −13.5509 *** | −13.6310 *** | 0.0801 |

TRE | 0.0012 | 0.0092 | 0.1944 | −0.4167 | 0.0884 | −0.9057 | 5.8000 | 70.9006 *** | −8.4232 *** | −8.4212 *** | 0.0997 |

ENC | 0.0030 | 0.0159 | 0.2517 | −0.3628 | 0.1026 | −0.5536 | 3.7719 | 15.0312 *** | −12.1922 *** | −12.3068 *** | 0.0938 |

R_{M} (IBEX_35) | −0.0019 | 0.003 | 0.1537 | −0.1882 | 0.0571 | −0.3596 | 3.8029 | 11.1842 *** | −14.7357 *** | −14.7399 *** | 0.0767 |

SMB | 0.0011 | 0.0016 | 0.0486 | −0.0693 | 0.0202 | −0.4976 | 3.8788 | 16.9641 *** | −14.9194 *** | −14.9219 *** | 0.0659 |

HML | 0.0046 | 0.0038 | 0.1132 | −0.0954 | 0.0260 | 0.5372 | 5.1836 | 56.7537 *** | −6.0685 *** | −12.6196 *** | 0.9778 |

RMW | 0.0030 | 0.0037 | 0.0638 | −0.0488 | 0.0169 | −0.2251 | 3.8279 | 8.5101 *** | −13.3470 *** | −13.3158 *** | 0.1140 |

CMA | 0.0035 | 0.0017 | 0.0875 | −0.0725 | 0.0186 | 0.6950 | 6.6439 | 145.7634 *** | −12.0046 *** | −12.3646 *** | 0.7803 |

MOM | 0.0018 | 0.0037 | 0.1836 | −0.3439 | 0.0534 | −1.5054 | 12.6213 | 974.0149 *** | −15.0872 *** | −15.0921 *** | 0.0591 |

LTREV | 0.0029 | 0.0009 | 0.1621 | −0.1461 | 0.0388 | 0.3938 | 7.0261 | 161.2873 *** | −16.7516 *** | −17.5382 *** | 0.2151 |

LIQV | 0.0046 | 0.0046 | 0.1119 | −0.1278 | 0.0362 | −0.2499 | 4.2180 | 16.3959 *** | −13.3194 *** | −13.2245 *** | 0.6740 |

I | 0.0376 | 0.0406 | 0.0676 | 0.0088 | 0.0147 | −0.4528 | 2.1551 | 14.7636 *** | −1.0484 | −1.0484 | 1.0198 |

**Table 2.**Sensitivity of companies’ returns to variations in explanatory factors: Model A (extension of the Fama and French three-factor model) for the whole sample period.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 33 | 0 | 33 | 34 | 0 | 34 | 34 | 0 | 34 | 33 | 0 | 33 | 30 | 0 | 30 |

i | 5 | 3 | 8 | 5 | 2 | 7 | 3 | 2 | 5 | 5 | 5 | 10 | 3 | 4 | 7 |

SMB | 13 | 1 | 14 | 12 | 2 | 14 | 11 | 2 | 13 | 10 | 1 | 11 | 8 | 1 | 9 |

HML | 2 | 5 | 7 | 6 | 4 | 10 | 7 | 8 | 15 | 7 | 9 | 16 | 3 | 6 | 9 |

MOM | 2 | 2 | 4 | 3 | 1 | 4 | 1 | 1 | 2 | 1 | 3 | 4 | 4 | 4 | 8 |

LTREV | 6 | 2 | 8 | 2 | 1 | 3 | 2 | 1 | 3 | 4 | 3 | 7 | 2 | 1 | 3 |

LIQV | 4 | 3 | 7 | 3 | 2 | 5 | 1 | 1 | 2 | 3 | 3 | 6 | 4 | 4 | 8 |

TOTAL | 65 | 16 | 81 | 65 | 12 | 77 | 59 | 15 | 74 | 63 | 24 | 87 | 54 | 20 | 74 |

**Table 3.**Sensitivity of companies’ returns to variations in explanatory factors: Model B (extension of the Fama and French five-factor model) for the whole sample period.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 33 | 0 | 33 | 34 | 0 | 34 | 34 | 0 | 34 | 34 | 0 | 34 | 31 | 0 | 31 |

i | 4 | 1 | 5 | 3 | 2 | 5 | 2 | 3 | 5 | 4 | 5 | 9 | 3 | 5 | 8 |

SMB | 10 | 2 | 12 | 8 | 4 | 12 | 7 | 2 | 9 | 8 | 0 | 8 | 10 | 1 | 11 |

HML | 6 | 3 | 9 | 4 | 3 | 7 | 5 | 3 | 8 | 4 | 6 | 10 | 3 | 6 | 9 |

RMW | 3 | 4 | 7 | 5 | 3 | 8 | 5 | 3 | 8 | 2 | 3 | 5 | 3 | 3 | 6 |

CMA | 0 | 7 | 7 | 0 | 5 | 5 | 0 | 4 | 4 | 1 | 3 | 4 | 5 | 3 | 8 |

MOM | 2 | 1 | 3 | 2 | 1 | 3 | 2 | 1 | 3 | 0 | 2 | 2 | 1 | 1 | 2 |

LTREV | 5 | 1 | 6 | 4 | 0 | 4 | 1 | 1 | 2 | 2 | 2 | 4 | 1 | 4 | 5 |

LIQV | 2 | 3 | 5 | 2 | 2 | 4 | 1 | 2 | 3 | 3 | 4 | 7 | 2 | 5 | 7 |

TOTAL | 65 | 22 | 87 | 62 | 20 | 82 | 57 | 19 | 76 | 58 | 25 | 83 | 59 | 28 | 87 |

**Table 4.**Sensitivity of companies’ returns to variations in explanatory factors: Model A (extension of the Fama and French three-factor model) for the precrisis subperiod.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 20 | 0 | 20 | 22 | 0 | 22 | 20 | 0 | 20 | 18 | 0 | 18 | 17 | 0 | 17 |

i | 4 | 4 | 8 | 3 | 3 | 6 | 2 | 2 | 4 | 2 | 1 | 3 | 1 | 3 | 4 |

SMB | 8 | 2 | 10 | 4 | 2 | 6 | 3 | 1 | 4 | 5 | 1 | 6 | 4 | 1 | 5 |

HML | 2 | 1 | 3 | 2 | 1 | 3 | 3 | 2 | 5 | 3 | 1 | 4 | 1 | 2 | 3 |

MOM | 1 | 3 | 4 | 1 | 0 | 1 | 1 | 2 | 3 | 1 | 1 | 2 | 0 | 2 | 2 |

LTREV | 2 | 0 | 2 | 1 | 0 | 1 | 2 | 1 | 3 | 2 | 1 | 3 | 1 | 1 | 2 |

LIQV | 2 | 2 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 3 | 2 | 3 | 5 |

TOTAL | 39 | 12 | 51 | 33 | 6 | 39 | 31 | 8 | 39 | 33 | 6 | 39 | 26 | 12 | 38 |

**Table 5.**Sensitivity of companies’ returns to variations in explanatory factors: Model B (extension of the Fama and French five-factor model) for the precrisis subperiod.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 22 | 0 | 22 | 22 | 0 | 22 | 19 | 0 | 19 | 20 | 0 | 20 | 19 | 0 | 19 |

i | 5 | 3 | 8 | 2 | 4 | 6 | 1 | 2 | 3 | 3 | 1 | 4 | 3 | 3 | 6 |

SMB | 5 | 3 | 8 | 2 | 2 | 4 | 3 | 1 | 4 | 5 | 1 | 6 | 4 | 2 | 6 |

HML | 2 | 0 | 2 | 2 | 0 | 2 | 2 | 1 | 3 | 2 | 1 | 3 | 3 | 1 | 4 |

RMW | 1 | 1 | 2 | 3 | 1 | 4 | 2 | 1 | 3 | 3 | 3 | 6 | 2 | 5 | 7 |

CMA | 1 | 1 | 2 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 3 |

MOM | 1 | 2 | 3 | 2 | 1 | 3 | 0 | 1 | 1 | 1 | 4 | 5 | 1 | 2 | 3 |

LTREV | 2 | 1 | 3 | 1 | 0 | 1 | 1 | 0 | 1 | 2 | 0 | 2 | 2 | 0 | 2 |

LIQV | 0 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 3 | 2 | 5 | 3 | 3 | 6 |

TOTAL | 39 | 13 | 52 | 35 | 9 | 44 | 29 | 8 | 37 | 40 | 13 | 53 | 39 | 17 | 56 |

**Table 6.**Sensitivity of companies’ returns to variations in explanatory factors: Model A (extension of the Fama and French three-factor model) for the crisis subperiod.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 16 | 0 | 16 | 19 | 0 | 19 | 22 | 0 | 22 | 19 | 0 | 19 | 18 | 0 | 18 |

i | 4 | 3 | 7 | 3 | 0 | 3 | 3 | 1 | 4 | 3 | 1 | 4 | 4 | 1 | 5 |

SMB | 4 | 0 | 4 | 5 | 1 | 6 | 4 | 0 | 4 | 3 | 1 | 4 | 3 | 1 | 4 |

HML | 4 | 2 | 6 | 1 | 2 | 3 | 0 | 2 | 2 | 3 | 1 | 4 | 2 | 0 | 2 |

MOM | 2 | 3 | 5 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 4 | 6 | 2 | 2 | 4 |

LTREV | 2 | 0 | 2 | 4 | 2 | 6 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 4 | 4 |

LIQV | 5 | 1 | 6 | 2 | 1 | 3 | 4 | 1 | 5 | 1 | 2 | 3 | 1 | 2 | 3 |

TOTAL | 37 | 9 | 46 | 35 | 7 | 42 | 35 | 6 | 41 | 32 | 9 | 41 | 30 | 10 | 40 |

**Table 7.**Sensitivity of companies’ returns to variations in explanatory factors: Model B (extension of the Fama and French five-factor model) for the crisis subperiod.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 18 | 0 | 18 | 21 | 0 | 21 | 22 | 0 | 22 | 21 | 0 | 21 | 21 | 0 | 21 |

i | 4 | 3 | 7 | 3 | 0 | 3 | 2 | 1 | 3 | 2 | 3 | 5 | 4 | 1 | 5 |

SMB | 5 | 0 | 5 | 6 | 0 | 6 | 8 | 0 | 8 | 3 | 2 | 5 | 2 | 1 | 3 |

HML | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 3 | 1 | 4 | 5 | 1 | 6 |

RMW | 0 | 0 | 0 | 2 | 1 | 3 | 0 | 1 | 1 | 0 | 0 | 0 | 3 | 0 | 3 |

CMA | 1 | 4 | 5 | 0 | 3 | 3 | 0 | 2 | 2 | 1 | 2 | 3 | 3 | 3 | 6 |

MOM | 1 | 1 | 2 | 2 | 1 | 3 | 3 | 1 | 4 | 2 | 1 | 3 | 2 | 2 | 4 |

LTREV | 2 | 0 | 2 | 2 | 2 | 4 | 0 | 0 | 0 | 2 | 1 | 3 | 0 | 2 | 2 |

LIQV | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 2 | 3 | 1 | 2 | 3 |

TOTAL | 33 | 9 | 42 | 38 | 8 | 46 | 36 | 7 | 43 | 35 | 12 | 47 | 41 | 12 | 53 |

**Table 8.**Sensitivity of companies’ returns to variations in explanatory factors: Model A (extension of the Fama and French three-factor model) for the postcrisis subperiod.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 29 | 0 | 29 | 29 | 0 | 29 | 29 | 0 | 29 | 27 | 0 | 27 | 24 | 0 | 24 |

i | 5 | 4 | 9 | 4 | 2 | 6 | 3 | 1 | 4 | 2 | 3 | 5 | 6 | 2 | 8 |

SMB | 5 | 3 | 8 | 4 | 3 | 7 | 3 | 4 | 7 | 3 | 2 | 5 | 3 | 3 | 6 |

HML | 4 | 7 | 11 | 3 | 5 | 8 | 5 | 7 | 12 | 5 | 11 | 16 | 4 | 8 | 12 |

MOM | 6 | 2 | 8 | 6 | 1 | 7 | 6 | 1 | 7 | 3 | 2 | 5 | 3 | 5 | 8 |

LTREV | 4 | 2 | 6 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 0 | 3 | 3 |

LIQV | 0 | 2 | 2 | 0 | 0 | 0 | 1 | 0 | 1 | 2 | 1 | 3 | 2 | 2 | 4 |

TOTAL | 53 | 20 | 73 | 46 | 11 | 57 | 47 | 14 | 61 | 43 | 20 | 63 | 42 | 23 | 65 |

**Table 9.**Sensitivity of companies’ returns to variations in explanatory factors: Model B (extension of the Fama and French five-factor model) for the postcrisis subperiod.

Theta = 0.1 | Theta = 0.25 | Theta = 0.5 | Theta = 0.75 | Theta = 0.9 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | POS | NEG | TOTAL | |

R_{M} | 31 | 0 | 31 | 31 | 0 | 31 | 31 | 0 | 31 | 29 | 0 | 29 | 27 | 0 | 27 |

i | 0 | 4 | 4 | 1 | 2 | 3 | 0 | 1 | 1 | 0 | 2 | 2 | 1 | 2 | 3 |

SMB | 6 | 3 | 9 | 4 | 1 | 5 | 5 | 2 | 7 | 4 | 2 | 6 | 7 | 3 | 10 |

HML | 5 | 3 | 8 | 2 | 1 | 3 | 3 | 2 | 5 | 1 | 6 | 7 | 2 | 5 | 7 |

RMW | 6 | 3 | 9 | 4 | 3 | 7 | 3 | 3 | 6 | 3 | 3 | 6 | 2 | 5 | 7 |

CMA | 1 | 3 | 4 | 0 | 3 | 3 | 0 | 3 | 3 | 1 | 1 | 2 | 2 | 0 | 2 |

MOM | 5 | 3 | 8 | 3 | 0 | 3 | 2 | 1 | 3 | 1 | 3 | 4 | 4 | 3 | 7 |

LTREV | 1 | 1 | 2 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 2 | 3 | 0 | 3 | 3 |

LIQV | 1 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | 2 | 1 | 3 |

TOTAL | 56 | 21 | 77 | 46 | 10 | 56 | 44 | 12 | 56 | 42 | 19 | 61 | 47 | 22 | 69 |

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## Share and Cite

**MDPI and ACS Style**

Jareño, F.; González, M.d.l.O.; Munera, L.
Analysis of the Spanish IBEX-35 Companies’ Returns Using Extensions of the Fama and French Factor Models. *Symmetry* **2020**, *12*, 295.
https://doi.org/10.3390/sym12020295

**AMA Style**

Jareño F, González MdlO, Munera L.
Analysis of the Spanish IBEX-35 Companies’ Returns Using Extensions of the Fama and French Factor Models. *Symmetry*. 2020; 12(2):295.
https://doi.org/10.3390/sym12020295

**Chicago/Turabian Style**

Jareño, Francisco, María de la O González, and Laura Munera.
2020. "Analysis of the Spanish IBEX-35 Companies’ Returns Using Extensions of the Fama and French Factor Models" *Symmetry* 12, no. 2: 295.
https://doi.org/10.3390/sym12020295