This online Fama-French factor regression analysis tool supports regression analysis for individual assets or a portfolio of assets using the capital asset pricing model (CAPM), Fama-French three-factor model, the Carhart four-factor model, or the new Fama-French five-factor model. You can also run market model regression for beta analysis based on selected assets or imported benchmarks. The analysis is based on asset returns for the entered mutual funds and ETFs, and the factor returns published on Kenneth French's web site and AQR's web site. The multiple linear regression indicates how well the returns of the given assets or a portfolio are explained by the Fama-French three-factor model based on market, size and value loading factors. Carhart four-factor model adds momentum as the fourth factor for explaining asset returns, and the Fama-French five-factor model extends the three-factor model with profitability (RMW) and investment (CMA) factors. The tool also supports the use of other factor models including Quality Minus Junk (QMJ) and Bet Against Beta (BAB) factors as described in Asness-Frazzini-Pedersen papers. For bond funds and balanced funds you can include the fixed income factor model to explain returns based on term risk (interest rate risk) and credit risk exposure. The fixed income factors can be further adjusted to account for the yield curve and to add high yield credit risk as an additional factor. You can also view the table of mutual fund and ETF factor regressions.

Name | Ticker | Start Date | End Date | Rm-Rf | SMB | HML-DEV | MOM | QMJ | BAB | Alpha | Annual Alpha | R^{2} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Vanguard PRIMECAP Adm | VPMAX | Dec 2013 | Dec 2017 | 0.97 | -0.04 | -0.33 | -0.17 | -0.13 | 0.14 | 0.25% | 2.98% | 90.5% |

AQR Style Premia Alternative I | QSPIX | Dec 2013 | Dec 2017 | 0.15 | -0.32 | 0.38 | 0.31 | 0.20 | 0.25 | 0.03% | 0.30% | 47.3% |

iShares Edge MSCI USA Momentum Fctr ETF | MTUM | Dec 2013 | Dec 2017 | 0.98 | -0.26 | -0.32 | 0.19 | -0.06 | -0.21 | 0.41% | 4.87% | 89.6% |

Ticker | VPMAX | ||||
---|---|---|---|---|---|

Time Period | Dec 2013 - Dec 2017 | ||||

Coefficient of Determination (R^{2}) |
90.5% | ||||

Adjusted R^{2} |
89.2% | ||||

Regression F statistic | 66.82 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.204 with p-value 0.788) | ||||

Heteroskedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 1.067 with p-value 0.983) | ||||

Factor | Loading | Standard Error | t-stat | p-value | 95% Confidence Interval |

Market (Rm-Rf) | 0.97 | 0.057 | 16.951 | 0.000 | 0.855...1.086 |

Size (SMB) | -0.04 | 0.080 | -0.559 | 0.579 | -0.205...0.116 |

Value (HML-DEV) | -0.33 | 0.081 | -4.015 | 0.000 | -0.491...-0.162 |

Momentum (MOM) | -0.17 | 0.073 | -2.320 | 0.025 | -0.316...-0.022 |

Quality (QMJ) | -0.13 | 0.076 | -1.665 | 0.103 | -0.281...0.027 |

Low Beta (BAB) | 0.14 | 0.128 | 1.076 | 0.288 | -0.121...0.397 |

Alpha (α) | 24.82bps | 0.002 | 1.365 | 0.180 | -0.12%...0.62% |

Annualized Alpha (α) | 2.98% |

Ticker | QSPIX | ||||
---|---|---|---|---|---|

Time Period | Dec 2013 - Dec 2017 | ||||

Coefficient of Determination (R^{2}) |
47.3% | ||||

Adjusted R^{2} |
39.8% | ||||

Regression F statistic | 6.29 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.184 with p-value 0.768) | ||||

Heteroskedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 7.669 with p-value 0.263) | ||||

Factor | Loading | Standard Error | t-stat | p-value | 95% Confidence Interval |

Market (Rm-Rf) | 0.15 | 0.086 | 1.765 | 0.085 | -0.022...0.326 |

Size (SMB) | -0.32 | 0.120 | -2.629 | 0.012 | -0.557...-0.073 |

Value (HML-DEV) | 0.38 | 0.123 | 3.109 | 0.003 | 0.134...0.628 |

Momentum (MOM) | 0.31 | 0.110 | 2.854 | 0.007 | 0.092...0.535 |

Quality (QMJ) | 0.20 | 0.115 | 1.742 | 0.089 | -0.032...0.432 |

Low Beta (BAB) | 0.25 | 0.193 | 1.311 | 0.197 | -0.137...0.644 |

Alpha (α) | 2.53bps | 0.003 | 0.092 | 0.927 | -0.53%...0.58% |

Annualized Alpha (α) | 0.30% |

Ticker | MTUM | ||||
---|---|---|---|---|---|

Time Period | Dec 2013 - Dec 2017 | ||||

Coefficient of Determination (R^{2}) |
89.6% | ||||

Adjusted R^{2} |
88.1% | ||||

Regression F statistic | 60.09 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.211 with p-value 0.796) | ||||

Heteroskedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 9.004 with p-value 0.173) | ||||

Factor | Loading | Standard Error | t-stat | p-value | 95% Confidence Interval |

Market (Rm-Rf) | 0.98 | 0.057 | 16.995 | 0.000 | 0.860...1.092 |

Size (SMB) | -0.26 | 0.080 | -3.222 | 0.002 | -0.418...-0.096 |

Value (HML-DEV) | -0.32 | 0.082 | -3.901 | 0.000 | -0.483...-0.154 |

Momentum (MOM) | 0.19 | 0.073 | 2.633 | 0.012 | 0.045...0.340 |

Quality (QMJ) | -0.06 | 0.076 | -0.743 | 0.462 | -0.211...0.097 |

Low Beta (BAB) | -0.21 | 0.129 | -1.651 | 0.106 | -0.472...0.047 |

Alpha (α) | 40.62bps | 0.002 | 2.226 | 0.031 | 0.04%...0.77% |

Annualized Alpha (α) | 4.87% |

Notes on results:

- Time frame for factor analysis is the full available data range unless a specific date interval is specified.
- Results are based on multiple linear regression against monthly factor returns.
- 4-factor model: R
_{a}= R_{rf}+ B_{mkt}× ( R_{mkt}- R_{rf}) + B_{smb}× SMB + B_{hml}× HML + B_{mom}× UMD + α - Symbols:
- R
_{a} - Asset return
- R
_{rf} - Risk free return
- B
_{mkt} - Market loading factor (exposure to market risk, different from CAPM beta)
- R
_{mkt} - Market return
- B
_{smb} - Size loading factor (the level of exposure to size risk)
- SMB
- Small Minus Big: The size premium
- B
_{hml} - Value loading factor (the level of exposure to value risk)
- HML
- High Minus Low: The value premium
- B
_{mom} - Momentum loading factor (the level of exposure to momentum)
- MOM
- Up Minus Down: The momentum premium
- B
_{qmj} - Quality loading factor
- QMJ
- Quality Minus Junk factor. See QMJ paper by Asness-Frazzini-Pedersen
- B
_{bab} - Low Beta loading factor
- BAB
- Bet Against Beta factor. See BAB paper by Frazzini-Pedersen
- Alpha
- Excess return over the benchmark
- t-stat
- t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error
- p-value
- p-value measures the statistical significance of the estimated parameter
- R
^{2} - Coefficient of determination

- R
- Resources:

Monthly Factor Premiums (BPS) | 88.30 | -26.73 | -30.02 | 38.63 | 59.34 | 91.73 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Name | Ticker | Start Date | End Date | Annual Alpha | Rm-Rf | SMB | HML-DEV | MOM | QMJ | BAB | Total | R^{2} |

Vanguard PRIMECAP Adm | VPMAX | Dec 2013 | Dec 2017 | 2.98% | 85.67 | 1.19 | 9.80 | -6.53 | -7.53 | 12.66 | 120.09 | 90.5% |

AQR Style Premia Alternative I | QSPIX | Dec 2013 | Dec 2017 | 0.30% | 13.44 | 8.42 | -11.43 | 12.11 | 11.87 | 23.25 | 60.18 | 47.3% |

iShares Edge MSCI USA Momentum Fctr ETF | MTUM | Dec 2013 | Dec 2017 | 4.87% | 86.16 | 6.88 | 9.55 | 7.44 | -3.37 | -19.50 | 127.78 | 89.6% |

Month | VPMAX | QSPIX | MTUM |
---|---|---|---|

Dec 2013 | -0.0136 | -0.0062 | -0.0080 |

Jan 2014 | 0.0101 | -0.0143 | 0.0018 |

Feb 2014 | 0.0092 | -0.0041 | 0.0117 |

Mar 2014 | 0.0009 | 0.0125 | -0.0254 |

Apr 2014 | -0.0191 | 0.0047 | -0.0076 |

May 2014 | 0.0133 | -0.0003 | 0.0120 |

Jun 2014 | -0.0064 | -0.0073 | -0.0081 |

Jul 2014 | 0.0085 | 0.0109 | -0.0002 |

Aug 2014 | -0.0077 | -0.0132 | 0.0012 |

Sep 2014 | 0.0117 | -0.0163 | 0.0007 |

Oct 2014 | -0.0067 | 0.0299 | 0.0017 |

Nov 2014 | 0.0005 | 0.0263 | 0.0003 |

Dec 2014 | -0.0009 | 0.0005 | -0.0066 |

Jan 2015 | 0.0016 | -0.0143 | -0.0013 |

Feb 2015 | -0.0088 | -0.0294 | -0.0018 |

Mar 2015 | -0.0074 | 0.0268 | -0.0107 |

Apr 2015 | -0.0121 | -0.0051 | -0.0023 |

May 2015 | -0.0010 | 0.0167 | 0.0015 |

Jun 2015 | -0.0130 | -0.0097 | 0.0062 |

Jul 2015 | -0.0057 | -0.0195 | -0.0138 |

Aug 2015 | 0.0067 | 0.0043 | 0.0047 |

Sep 2015 | 0.0123 | 0.0120 | -0.0051 |

Oct 2015 | 0.0118 | 0.0052 | -0.0013 |

Nov 2015 | -0.0051 | -0.0138 | -0.0080 |

Dec 2015 | 0.0079 | 0.0157 | -0.0031 |

Jan 2016 | -0.0011 | -0.0077 | 0.0058 |

Feb 2016 | -0.0115 | -0.0138 | 0.0004 |

Mar 2016 | 0.0049 | -0.0104 | 0.0086 |

Apr 2016 | -0.0023 | 0.0107 | 0.0128 |

May 2016 | 0.0032 | -0.0199 | -0.0080 |

Jun 2016 | -0.0254 | -0.0114 | 0.0181 |

Jul 2016 | 0.0125 | 0.0066 | -0.0059 |

Aug 2016 | 0.0092 | -0.0126 | -0.0123 |

Sep 2016 | 0.0076 | 0.0171 | -0.0008 |

Oct 2016 | -0.0011 | -0.0121 | 0.0007 |

Nov 2016 | 0.0088 | 0.0048 | -0.0211 |

Dec 2016 | 0.0011 | -0.0199 | 0.0080 |

Jan 2017 | 0.0015 | 0.0060 | 0.0019 |

Feb 2017 | -0.0023 | 0.0206 | -0.0006 |

Mar 2017 | -0.0076 | -0.0110 | 0.0132 |

Apr 2017 | -0.0041 | -0.0065 | 0.0105 |

May 2017 | 0.0050 | -0.0056 | 0.0156 |

Jun 2017 | 0.0038 | 0.0035 | 0.0001 |

Jul 2017 | -0.0124 | 0.0171 | 0.0036 |

Aug 2017 | -0.0005 | 0.0077 | -0.0091 |

Sep 2017 | 0.0174 | 0.0075 | 0.0183 |

Oct 2017 | 0.0079 | 0.0094 | 0.0068 |

Nov 2017 | 0.0022 | -0.0009 | 0.0009 |

Dec 2017 | -0.0034 | 0.0088 | -0.0062 |