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 Betting 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 | Alpha | Annual Alpha | R^{2} |
---|---|---|---|---|---|---|---|---|---|

Schwab International Equity ETF | SCHF | Sep 2013 | Dec 2018 | 0.98 | -0.15 | -0.10 | -0.03% | -0.40% | 97.2% |

Schwab Emerging Markets Equity ETF | SCHE | Sep 2013 | Dec 2018 | 1.06 | 0.31 | 0.12 | -0.03% | -0.31% | 62.0% |

Schwab Fundamental Intl Sm Co ETF | FNDC | Sep 2013 | Dec 2018 | 1.00 | 0.32 | -0.14 | 0.05% | 0.65% | 94.6% |

Vanguard FTSE All-Wld ex-US SmCp ETF | VSS | Sep 2013 | Dec 2018 | 1.03 | 0.48 | -0.11 | -0.10% | -1.21% | 93.0% |

Schwab International Small-Cap Eq ETF | SCHC | Sep 2013 | Dec 2018 | 1.05 | 0.43 | -0.16 | -0.12% | -1.48% | 94.7% |

Ticker | SCHF | ||||
---|---|---|---|---|---|

Time Period | Sep 2013 - Dec 2018 | ||||

Coefficient of Determination (R^{2}) |
97.2% | ||||

Adjusted R^{2} |
97.0% | ||||

Regression F statistic | 688.93 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.755 with p-value 0.999) | ||||

Heteroskedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 3.804 with p-value 0.283) | ||||

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

Market (Rm-Rf) | 0.98 | 0.022 | 44.161 | 0.000 | 0.939...1.028 |

Size (SMB) | -0.15 | 0.049 | -2.981 | 0.004 | -0.245...-0.048 |

Value (HML) | -0.10 | 0.045 | -2.249 | 0.028 | -0.189...-0.011 |

Alpha (α) | -3.36bps | 0.001 | -0.463 | 0.645 | -0.18%...0.11% |

Annualized Alpha (α) | -0.40% |

Ticker | SCHE | ||||
---|---|---|---|---|---|

Time Period | Sep 2013 - Dec 2018 | ||||

Coefficient of Determination (R^{2}) |
62.0% | ||||

Adjusted R^{2} |
60.1% | ||||

Regression F statistic | 32.57 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 1.969 with p-value 0.446) | ||||

Heteroskedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 1.993 with p-value 0.574) | ||||

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

Market (Rm-Rf) | 1.06 | 0.110 | 9.627 | 0.000 | 0.840...1.281 |

Size (SMB) | 0.31 | 0.243 | 1.294 | 0.201 | -0.172...0.801 |

Value (HML) | 0.12 | 0.221 | 0.565 | 0.575 | -0.317...0.566 |

Alpha (α) | -2.57bps | 0.004 | -0.072 | 0.943 | -0.74%...0.69% |

Annualized Alpha (α) | -0.31% |

Ticker | FNDC | ||||
---|---|---|---|---|---|

Time Period | Sep 2013 - Dec 2018 | ||||

Coefficient of Determination (R^{2}) |
94.6% | ||||

Adjusted R^{2} |
94.3% | ||||

Regression F statistic | 350.18 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.574 with p-value 0.991) | ||||

Heteroskedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 1.445 with p-value 0.695) | ||||

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

Market (Rm-Rf) | 1.00 | 0.031 | 32.238 | 0.000 | 0.942...1.066 |

Size (SMB) | 0.32 | 0.069 | 4.679 | 0.000 | 0.184...0.459 |

Value (HML) | -0.14 | 0.062 | -2.177 | 0.033 | -0.260...-0.011 |

Alpha (α) | 5.45bps | 0.001 | 0.537 | 0.593 | -0.15%...0.26% |

Annualized Alpha (α) | 0.65% |

Ticker | VSS | ||||
---|---|---|---|---|---|

Time Period | Sep 2013 - Dec 2018 | ||||

Coefficient of Determination (R^{2}) |
93.0% | ||||

Adjusted R^{2} |
92.6% | ||||

Regression F statistic | 264.70 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.609 with p-value 0.994) | ||||

Heteroskedasticity | Heteroscedasticity confirmed (Breusch-Pagan test value is 13.383 with p-value 0.004) | ||||

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

Market (Rm-Rf) | 1.03 | 0.037 | 27.923 | 0.000 | 0.955...1.102 |

Size (SMB) | 0.48 | 0.081 | 5.851 | 0.000 | 0.313...0.638 |

Value (HML) | -0.11 | 0.074 | -1.532 | 0.131 | -0.261...0.035 |

Alpha (α) | -10.04bps | 0.001 | -0.838 | 0.406 | -0.34%...0.14% |

Annualized Alpha (α) | -1.21% |

Ticker | SCHC | ||||
---|---|---|---|---|---|

Time Period | Sep 2013 - Dec 2018 | ||||

Coefficient of Determination (R^{2}) |
94.7% | ||||

Adjusted R^{2} |
94.4% | ||||

Regression F statistic | 356.95 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 3.054 with p-value 1.000) | ||||

Heteroskedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 2.305 with p-value 0.512) | ||||

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

Market (Rm-Rf) | 1.05 | 0.032 | 32.542 | 0.000 | 0.989...1.119 |

Size (SMB) | 0.43 | 0.071 | 6.009 | 0.000 | 0.287...0.573 |

Value (HML) | -0.16 | 0.065 | -2.487 | 0.016 | -0.291...-0.032 |

Alpha (α) | -12.31bps | 0.001 | -1.168 | 0.248 | -0.33%...0.09% |

Annualized Alpha (α) | -1.48% |

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.
- 3-factor model: R
_{a}= R_{rf}+ B_{mkt}× ( R_{mkt}- R_{rf}) + B_{smb}× SMB + B_{hml}× HML + 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
- 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) | 30.98 | 14.89 | -0.16 | ||||||
---|---|---|---|---|---|---|---|---|---|

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

Schwab International Equity ETF | SCHF | Sep 2013 | Dec 2018 | -0.40% | 30.46 | -2.18 | 0.02 | 24.94 | 97.2% |

Schwab Emerging Markets Equity ETF | SCHE | Sep 2013 | Dec 2018 | -0.31% | 32.87 | 4.69 | -0.02 | 34.96 | 62.0% |

Schwab Fundamental Intl Sm Co ETF | FNDC | Sep 2013 | Dec 2018 | 0.65% | 31.10 | 4.79 | 0.02 | 41.36 | 94.6% |

Vanguard FTSE All-Wld ex-US SmCp ETF | VSS | Sep 2013 | Dec 2018 | -1.21% | 31.87 | 7.08 | 0.02 | 28.93 | 93.0% |

Schwab International Small-Cap Eq ETF | SCHC | Sep 2013 | Dec 2018 | -1.48% | 32.66 | 6.40 | 0.03 | 26.77 | 94.7% |

Month | SCHF | SCHE | FNDC | VSS | SCHC |
---|---|---|---|---|---|

Sep 2013 | 0.0060 | 0.0061 | 0.0099 | -0.0038 | -0.0065 |

Oct 2013 | -0.0003 | 0.0062 | 0.0020 | 0.0119 | 0.0097 |

Nov 2013 | 0.0008 | -0.0134 | -0.0037 | -0.0086 | -0.0109 |

Dec 2013 | 0.0046 | -0.0221 | 0.0035 | 0.0030 | 0.0183 |

Jan 2014 | -0.0084 | -0.0692 | -0.0132 | -0.0099 | -0.0142 |

Feb 2014 | -0.0053 | -0.0161 | 0.0047 | 0.0269 | 0.0224 |

Mar 2014 | 0.0036 | 0.0494 | -0.0027 | -0.0026 | 0.0052 |

Apr 2014 | 0.0027 | 0.0020 | -0.0000 | 0.0104 | 0.0035 |

May 2014 | 0.0017 | 0.0125 | 0.0065 | 0.0021 | -0.0019 |

Jun 2014 | 0.0028 | 0.0145 | -0.0030 | -0.0010 | 0.0004 |

Jul 2014 | -0.0004 | 0.0341 | -0.0044 | -0.0124 | -0.0138 |

Aug 2014 | 0.0064 | 0.0402 | 0.0018 | 0.0171 | 0.0115 |

Sep 2014 | -0.0047 | -0.0254 | -0.0061 | -0.0118 | -0.0114 |

Oct 2014 | 0.0088 | 0.0489 | 0.0177 | 0.0107 | 0.0074 |

Nov 2014 | -0.0120 | -0.0099 | -0.0215 | -0.0188 | -0.0221 |

Dec 2014 | -0.0062 | -0.0171 | 0.0080 | 0.0013 | 0.0041 |

Jan 2015 | 0.0017 | 0.0064 | 0.0075 | -0.0005 | 0.0024 |

Feb 2015 | 0.0023 | -0.0137 | 0.0095 | 0.0133 | 0.0084 |

Mar 2015 | 0.0003 | -0.0099 | 0.0005 | -0.0041 | -0.0007 |

Apr 2015 | -0.0031 | 0.0130 | -0.0201 | -0.0044 | -0.0103 |

May 2015 | 0.0034 | -0.0354 | 0.0005 | -0.0031 | 0.0032 |

Jun 2015 | 0.0010 | -0.0053 | 0.0047 | -0.0050 | 0.0014 |

Jul 2015 | -0.0063 | -0.0604 | -0.0063 | -0.0256 | -0.0121 |

Aug 2015 | -0.0036 | -0.0284 | 0.0109 | 0.0004 | 0.0120 |

Sep 2015 | 0.0033 | 0.0141 | -0.0000 | 0.0144 | 0.0090 |

Oct 2015 | -0.0040 | -0.0106 | -0.0001 | -0.0085 | -0.0119 |

Nov 2015 | 0.0032 | -0.0123 | 0.0083 | 0.0079 | 0.0042 |

Dec 2015 | -0.0095 | -0.0315 | -0.0046 | -0.0116 | -0.0092 |

Jan 2016 | 0.0100 | 0.0214 | 0.0085 | 0.0048 | 0.0040 |

Feb 2016 | -0.0167 | 0.0035 | -0.0109 | 0.0082 | 0.0002 |

Mar 2016 | 0.0051 | 0.0500 | 0.0092 | -0.0065 | 0.0027 |

Apr 2016 | -0.0043 | -0.0289 | -0.0101 | -0.0011 | 0.0019 |

May 2016 | 0.0042 | -0.0227 | 0.0176 | 0.0024 | 0.0050 |

Jun 2016 | 0.0130 | 0.0830 | 0.0012 | 0.0074 | -0.0068 |

Jul 2016 | -0.0066 | -0.0048 | 0.0071 | 0.0009 | 0.0044 |

Aug 2016 | 0.0074 | 0.0053 | -0.0006 | -0.0013 | -0.0034 |

Sep 2016 | 0.0017 | -0.0014 | 0.0071 | 0.0027 | 0.0012 |

Oct 2016 | -0.0002 | 0.0136 | 0.0084 | -0.0071 | -0.0116 |

Nov 2016 | 0.0091 | -0.0234 | 0.0106 | 0.0062 | 0.0149 |

Dec 2016 | -0.0029 | -0.0308 | -0.0054 | -0.0101 | -0.0068 |

Jan 2017 | 0.0045 | 0.0140 | 0.0004 | 0.0069 | -0.0001 |

Feb 2017 | 0.0024 | 0.0160 | 0.0041 | 0.0054 | -0.0024 |

Mar 2017 | -0.0010 | -0.0021 | -0.0070 | -0.0007 | -0.0020 |

Apr 2017 | -0.0076 | -0.0088 | 0.0027 | 0.0019 | 0.0045 |

May 2017 | -0.0023 | -0.0222 | -0.0126 | -0.0156 | -0.0102 |

Jun 2017 | 0.0063 | -0.0041 | 0.0044 | 0.0032 | 0.0053 |

Jul 2017 | -0.0008 | 0.0191 | 0.0010 | 0.0043 | 0.0013 |

Aug 2017 | -0.0038 | 0.0244 | -0.0004 | 0.0046 | 0.0026 |

Sep 2017 | 0.0043 | -0.0285 | 0.0038 | 0.0000 | 0.0036 |

Oct 2017 | 0.0037 | 0.0076 | 0.0018 | 0.0004 | -0.0040 |

Nov 2017 | -0.0001 | -0.0081 | 0.0001 | 0.0007 | 0.0020 |

Dec 2017 | 0.0003 | 0.0134 | -0.0006 | 0.0045 | 0.0040 |

Jan 2018 | 0.0019 | 0.0424 | -0.0076 | -0.0058 | -0.0022 |

Feb 2018 | -0.0101 | -0.0172 | -0.0053 | -0.0070 | -0.0082 |

Mar 2018 | 0.0057 | 0.0120 | 0.0074 | 0.0151 | 0.0099 |

Apr 2018 | -0.0046 | -0.0455 | -0.0018 | -0.0024 | 0.0031 |

May 2018 | -0.0028 | -0.0107 | -0.0094 | 0.0022 | 0.0010 |

Jun 2018 | -0.0057 | -0.0232 | -0.0056 | -0.0082 | 0.0006 |

Jul 2018 | 0.0041 | 0.0276 | -0.0032 | 0.0038 | -0.0027 |

Aug 2018 | -0.0027 | -0.0182 | -0.0069 | -0.0041 | 0.0018 |

Sep 2018 | 0.0012 | -0.0142 | -0.0024 | -0.0188 | -0.0055 |

Oct 2018 | 0.0002 | 0.0188 | -0.0043 | -0.0045 | -0.0026 |

Nov 2018 | 0.0037 | 0.0498 | 0.0004 | 0.0101 | -0.0061 |

Dec 2018 | -0.0053 | 0.0264 | -0.0117 | 0.0100 | 0.0022 |

Rolling regressions are only shown for the first three ticker symbols entered.

Rolling returns are only shown for the first three ticker symbols entered.