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 | Rm-Rf | SMB | HML | Alpha | Annual Alpha | R^{2} |
---|---|---|---|---|---|---|---|---|---|

Vanguard US Value Factor ETF | VFVA | Mar 2018 | May 2020 | 1.20 | 0.41 | 0.70 | 0.08% | 1.02% | 98.6% |

DFA Tax-Managed US Marketwide Value II | DFMVX | Mar 2018 | May 2020 | 1.03 | 0.03 | 0.38 | -0.05% | -0.58% | 99.3% |

DFA Tax-Managed US Targeted Value | DTMVX | Mar 2018 | May 2020 | 1.06 | 0.64 | 0.62 | -0.13% | -1.58% | 99.3% |

Ticker | VFVA | ||||
---|---|---|---|---|---|

Time Period | Mar 2018 - May 2020 | ||||

Regression Basis | 27 monthly samples | ||||

Coefficient of Determination (R^{2}) |
98.6% | ||||

Adjusted R^{2} |
98.4% | ||||

Regression F statistic | 540.37 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 2.183 with p-value 0.681) | ||||

Heteroscedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 2.352 with p-value 0.503) | ||||

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

Market (Rm-Rf) | 1.20 | 0.048 | 25.116 | 0.000 | 1.104...1.302 |

Size (SMB) | 0.41 | 0.102 | 4.073 | 0.000 | 0.204...0.625 |

Value (HML) | 0.70 | 0.062 | 11.242 | 0.000 | 0.571...0.828 |

Alpha (α) | 8.48bps | 0.003 | 0.339 | 0.738 | -0.43%...0.60% |

Annualized Alpha (α) | 1.02% |

Ticker | DFMVX | ||||
---|---|---|---|---|---|

Time Period | Mar 2018 - May 2020 | ||||

Regression Basis | 27 monthly samples | ||||

Coefficient of Determination (R^{2}) |
99.3% | ||||

Adjusted R^{2} |
99.2% | ||||

Regression F statistic | 1,024.55 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 1.771 with p-value 0.254) | ||||

Heteroscedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 1.060 with p-value 0.787) | ||||

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

Market (Rm-Rf) | 1.03 | 0.026 | 39.453 | 0.000 | 0.980...1.088 |

Size (SMB) | 0.03 | 0.056 | 0.512 | 0.613 | -0.087...0.144 |

Value (HML) | 0.38 | 0.034 | 11.296 | 0.000 | 0.314...0.455 |

Alpha (α) | -4.80bps | 0.001 | -0.351 | 0.729 | -0.33%...0.24% |

Annualized Alpha (α) | -0.58% |

Ticker | DTMVX | ||||
---|---|---|---|---|---|

Time Period | Mar 2018 - May 2020 | ||||

Regression Basis | 27 monthly samples | ||||

Coefficient of Determination (R^{2}) |
99.3% | ||||

Adjusted R^{2} |
99.2% | ||||

Regression F statistic | 1,126.56 (p-value = 0.000) | ||||

Autocorrelation | No autocorrelation confirmed (Durbin-Watson test value is 1.681 with p-value 0.181) | ||||

Heteroscedasticity | No heteroscedasticity confirmed (Breusch-Pagan test value is 7.202 with p-value 0.066) | ||||

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

Market (Rm-Rf) | 1.06 | 0.031 | 34.223 | 0.000 | 0.996...1.124 |

Size (SMB) | 0.64 | 0.066 | 9.783 | 0.000 | 0.508...0.780 |

Value (HML) | 0.62 | 0.040 | 15.339 | 0.000 | 0.534...0.701 |

Alpha (α) | -13.21bps | 0.002 | -0.816 | 0.423 | -0.47%...0.20% |

Annualized Alpha (α) | -1.58% |

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 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

Monthly Factor Premiums (BPS) | 57.15 | -23.63 | -177.33 | ||||||
---|---|---|---|---|---|---|---|---|---|

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

Vanguard US Value Factor ETF | VFVA | Mar 2018 | May 2020 | 1.02% | 68.76 | -9.80 | -124.05 | -56.62 | 98.6% |

DFA Tax-Managed US Marketwide Value II | DFMVX | Mar 2018 | May 2020 | -0.58% | 59.08 | -0.67 | -68.18 | -14.58 | 99.3% |

DFA Tax-Managed US Targeted Value | DTMVX | Mar 2018 | May 2020 | -1.58% | 60.59 | -15.22 | -109.47 | -77.30 | 99.3% |

Month | VFVA | DFMVX | DTMVX |
---|---|---|---|

Mar 2018 | 0.0052 | 0.0022 | 0.0074 |

Apr 2018 | 0.0025 | -0.0017 | -0.0102 |

May 2018 | -0.0154 | -0.0074 | 0.0042 |

Jun 2018 | 0.0125 | 0.0018 | -0.0007 |

Jul 2018 | -0.0120 | 0.0063 | -0.0015 |

Aug 2018 | -0.0069 | -0.0023 | 0.0032 |

Sep 2018 | 0.0012 | 0.0059 | -0.0061 |

Oct 2018 | 0.0130 | 0.0032 | -0.0061 |

Nov 2018 | -0.0202 | 0.0026 | -0.0026 |

Dec 2018 | 0.0002 | -0.0046 | 0.0039 |

Jan 2019 | 0.0216 | 0.0058 | 0.0061 |

Feb 2019 | -0.0024 | 0.0042 | 0.0077 |

Mar 2019 | -0.0027 | -0.0036 | 0.0007 |

Apr 2019 | -0.0019 | -0.0090 | 0.0047 |

May 2019 | -0.0132 | 0.0076 | -0.0079 |

Jun 2019 | 0.0022 | 0.0044 | 0.0098 |

Jul 2019 | -0.0017 | -0.0005 | 0.0093 |

Aug 2019 | 0.0013 | -0.0007 | 0.0030 |

Sep 2019 | 0.0073 | -0.0022 | 0.0076 |

Oct 2019 | -0.0028 | 0.0116 | 0.0059 |

Nov 2019 | -0.0048 | 0.0003 | -0.0053 |

Dec 2019 | -0.0058 | -0.0073 | -0.0121 |

Jan 2020 | -0.0110 | -0.0134 | 0.0043 |

Feb 2020 | 0.0044 | -0.0067 | -0.0039 |

Mar 2020 | 0.0154 | 0.0033 | -0.0002 |

Apr 2020 | 0.0214 | -0.0035 | -0.0132 |

May 2020 | -0.0074 | 0.0035 | -0.0083 |

The selected date range contains insufficient data for rolling regression analysis