This factor regression tool supports factor regression analysis of individual assets or a portfolio of assets using the given risk factor model. The multiple linear regression indicates how well the returns of the given assets or a portfolio are explained by the risk factor exposures. The supported equity risk factor models include:

- The capital asset pricing model (CAPM) with market factor (MKT)
- The Fama-French three factor model with market, size, and value factors (MKT, SMB, HML)
- The Carhart four-factor model with market, size, value, and momentum factors (MKT, SMB, HML, MOM)
- The Fama-French five factor model with market, size, value, profitability, and investment factors (MKT, SMB, HML, RMW, CMA)
- The q-factor model with market, size, investment, return on equity, and expected growth factors (MKT, ME, I/A, ROE, EG)

Additional supported equity factors include the short and long-term reversal factors (STREV, LTREV) based on Fama-French factor data, quality (QMJ) factor based on both AQR and Alpha Architect factor data, and bet against beta (BAB) factor based on AQR factor data.

For fixed income 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 exposures. 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.

Name | Ticker | Start Date | End Date | FF-MKT-RF | FF-SMB | FF-HML | FF-MOM | FF-RMW | Alpha | Annual Alpha | R^{2} |
---|---|---|---|---|---|---|---|---|---|---|---|

iShares S&P Small-Cap 600 Value ETF | IJS | 02/15/2018 | 11/30/2020 | 0.89 | 0.84 | 0.46 | -0.15 | 0.28 | -0.00% | -0.02% | 92.0% |

iShares Core S&P Small-Cap ETF | IJR | 02/15/2018 | 11/30/2020 | 0.99 | 0.84 | 0.36 | -0.04 | 0.21 | -0.00% | -0.23% | 97.9% |

Vanguard US Multifactor ETF | VFMF | 02/15/2018 | 11/30/2020 | 0.98 | 0.45 | 0.46 | 0.20 | 0.17 | -0.01% | -1.53% | 97.4% |

Ticker | IJS | |||||
---|---|---|---|---|---|---|

Time Period | 02/15/2018 - 11/30/2020 | |||||

Regression Basis | 703 daily samples | |||||

Coefficient of Determination (R^{2}) |
92.0% | |||||

Adjusted R^{2} |
91.9% | |||||

Regression F statistic | 1,604.44 (p-value = 0.000) | |||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.621 with p-value 1.000) | |||||

Heteroscedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 4.595 with p-value 0.467) | |||||

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

FF-MKT-RF | Market | 0.89 | 0.014 | 65.241 | 0.000 | 0.861...0.915 |

FF-SMB | Size | 0.84 | 0.033 | 25.119 | 0.000 | 0.770...0.901 |

FF-HML | Value | 0.46 | 0.032 | 14.706 | 0.000 | 0.402...0.526 |

FF-MOM | Momentum | -0.15 | 0.026 | -5.905 | 0.000 | -0.201...-0.101 |

FF-RMW | Profitability | 0.28 | 0.053 | 5.243 | 0.000 | 0.174...0.382 |

Alpha | Alpha | -0.01bps | 0.000 | -0.004 | 0.997 | -0.04%...0.04% |

Annualized Alpha | Annualized Alpha | -0.02% |

Ticker | IJR | |||||
---|---|---|---|---|---|---|

Time Period | 02/15/2018 - 11/30/2020 | |||||

Regression Basis | 703 daily samples | |||||

Coefficient of Determination (R^{2}) |
97.9% | |||||

Adjusted R^{2} |
97.9% | |||||

Regression F statistic | 6,553.06 (p-value = 0.000) | |||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.164 with p-value 0.985) | |||||

Heteroscedasticity | Heteroscedasticity confirmed (Breusch-Pagan test value is 54.881 with p-value 0.000) | |||||

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

FF-MKT-RF | Market | 0.99 | 0.007 | 146.863 | 0.000 | 0.976...1.003 |

FF-SMB | Size | 0.84 | 0.016 | 51.077 | 0.000 | 0.809...0.874 |

FF-HML | Value | 0.36 | 0.016 | 22.929 | 0.000 | 0.327...0.389 |

FF-MOM | Momentum | -0.04 | 0.013 | -3.451 | 0.001 | -0.069...-0.019 |

FF-RMW | Profitability | 0.21 | 0.026 | 8.047 | 0.000 | 0.160...0.263 |

Alpha | Alpha | -0.09bps | 0.000 | -0.090 | 0.928 | -0.02%...0.02% |

Annualized Alpha | Annualized Alpha | -0.23% |

Ticker | VFMF | |||||
---|---|---|---|---|---|---|

Time Period | 02/15/2018 - 11/30/2020 | |||||

Regression Basis | 703 daily samples | |||||

Coefficient of Determination (R^{2}) |
97.4% | |||||

Adjusted R^{2} |
97.4% | |||||

Regression F statistic | 5,242.35 (p-value = 0.000) | |||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.339 with p-value 1.000) | |||||

Heteroscedasticity | Heteroscedasticity confirmed (Breusch-Pagan test value is 34.071 with p-value 0.000) | |||||

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

FF-MKT-RF | Market | 0.98 | 0.007 | 143.880 | 0.000 | 0.963...0.990 |

FF-SMB | Size | 0.45 | 0.017 | 26.915 | 0.000 | 0.414...0.479 |

FF-HML | Value | 0.46 | 0.016 | 29.295 | 0.000 | 0.430...0.491 |

FF-MOM | Momentum | 0.20 | 0.013 | 15.615 | 0.000 | 0.174...0.224 |

FF-RMW | Profitability | 0.17 | 0.026 | 6.453 | 0.000 | 0.119...0.223 |

Alpha | Alpha | -0.61bps | 0.000 | -0.602 | 0.547 | -0.03%...0.01% |

Annualized Alpha | Annualized Alpha | -1.53% |

Notes on results:

- Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
- Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
- The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
- The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities.
- The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
- Refer to the FAQ section regarding the list of factor data sources and methodology descriptions
- Results are based on multiple linear regression against daily factor returns.
- Symbols:
- MKT-RF
- Market factor (excess return over the risk free rate)
- SMB
- Size factor (Small Minus Big)
- HML
- Value factor (High Minus Low)
- MOM
- Momentum factor (Up Minus Down)
- RMW
- Profitability factor (Robust Minus Weak)
- CMA
- Conservative investment factor (Conservative Minus Aggressive)
- ST-REV
- Short-term reversal factor
- LT-REV
- Long-term reversal factor
- QMJ
- Quality factor (Quality Minus Junk)
- BAB
- Bet Against Beta factor
- TRM
- Term factor (fixed income)
- CDT
- Credit factor (fixed income)
- 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

Daily Factor Premiums (BPS) | 5.83 | 0.19 | -7.19 | 0.61 | 0.03 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Name | Ticker | Start Date | End Date | Annual Alpha | FF-MKT-RF | FF-SMB | FF-HML | FF-MOM | FF-RMW | Total | R^{2} |

iShares S&P Small-Cap 600 Value ETF | IJS | 02/15/2018 | 11/30/2020 | -0.02% | 5.18 | 0.16 | -3.33 | -0.09 | 0.01 | 1.91 | 92.0% |

iShares Core S&P Small-Cap ETF | IJR | 02/15/2018 | 11/30/2020 | -0.23% | 5.77 | 0.16 | -2.57 | -0.03 | 0.01 | 3.25 | 97.9% |

Vanguard US Multifactor ETF | VFMF | 02/15/2018 | 11/30/2020 | -1.53% | 5.69 | 0.08 | -3.31 | 0.12 | 0.01 | 1.98 | 97.4% |

Residuals are only available for monthly regressions.