Factor Regression Analysis

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:

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.

Portfolio Assets
Asset 1
Asset 2
Asset 3
Asset 4
Asset 5
Asset 6
Asset 7
Asset 8
Asset 9
Asset 10

Factor Analysis Results

Portfolio Allocation

Portfolio Allocation
Ticker Name Allocation
MTUM iShares MSCI USA Momentum Factor ETF 11.00%
VOE Vanguard Mid-Cap Value ETF 15.00%
FNDA Schwab Fundamental US Small Company ETF 25.00%
FNDF Schwab Fundamental Intl Lg Co ETF 22.00%
FNDC Schwab Fundamental Intl Sm Co ETF 14.00%
FNDE Schwab Fundamental Emerg Mkts Lg Co ETF 13.00%
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Portfolio Regression Results

Factor regression results for the portfolio
Time Period Sep 2013 - Jan 2016
Regression Basis 29 monthly samples
Coefficient of Determination (R2) 96.6%
Adjusted R2 96.0%
Regression F statistic 170.50 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.720 with p-value 0.980)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 6.479 with p-value 0.166)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.03 0.042 24.177 0.000 0.939...1.114
Size (SMB) 0.15 0.089 1.683 0.105 -0.034...0.332
Value (HML) 0.19 0.137 1.389 0.177 -0.092...0.472
Momentum (MOM) 0.06 0.075 0.828 0.416 -0.093...0.218
Alpha (α) -2.17bps 0.002 -0.141 0.889 -0.34%...0.29%
Annualized Alpha (α) -0.26%  

Equity Assets

Equity Assets
WeightRm-Rft(Rm-Rf)SMBt(SMB)HMLt(HML)MOMt(MOM)Annual Alphat(Alpha)R^2
Intl Developed100.00%0.9512.710.
iShares MSCI USA Momentum Factor ETF11.00%0.9316.12-0.14-2.01-0.27-2.350.192.772.36%1.0393.36%
Vanguard Mid-Cap Value ETF15.00%0.9521.540.162.980.080.860.000.081.11%0.6496.18%
Schwab Fundamental US Small Company ETF25.00%1.0424.790.5410.660.222.540.050.97-0.49%-0.2997.58%
Schwab Fundamental Intl Lg Co ETF22.00%1.007.30-0.19-1.14-0.13-0.48-0.17-1.09-7.99%-1.4874.85%
Schwab Fundamental Intl Sm Co ETF14.00%0.775.880.110.70-0.10-0.39-0.12-0.79-1.54%-0.2967.30%
Schwab Fundamental Emerg Mkts Lg Co ETF13.00%0.894.16-0.05-
Factor regressions from September 2013 to January 2016. Statistically significant values in bold.
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.
  • 4-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + Bmom × MOM + α
  • Symbols:
    Asset return
    Risk free return
    Market loading factor (exposure to market risk, different from CAPM beta)
    Market return
    Size loading factor (the level of exposure to size risk)
    Small Minus Big: The size premium
    Value loading factor (the level of exposure to value risk)
    High Minus Low: The value premium
    Momentum loading factor (the level of exposure to momentum)
    Up Minus Down: The momentum premium
    Excess return over the benchmark
    t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error
    p-value measures the statistical significance of the estimated parameter
    Coefficient of determination

Factor Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 33.29 -22.87 -53.49 130.66  
Name Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Portfolio Sep 2013 Jan 2016 -0.26% 34.18 -3.41 -10.15 8.17 26.62 96.6%
Regression residuals
Sep 20130.43%
Oct 20130.19%
Nov 2013-0.23%
Dec 20130.01%
Jan 2014-1.19%
Feb 20140.29%
Mar 20140.22%
Apr 2014-0.00%
May 20140.22%
Jun 2014-0.01%
Jul 2014-0.58%
Aug 20140.51%
Sep 2014-0.76%
Oct 20141.59%
Nov 2014-0.33%
Dec 2014-0.10%
Jan 20150.35%
Feb 20150.47%
Mar 20150.06%
Apr 2015-1.08%
May 2015-0.52%
Jun 20150.21%
Jul 2015-0.66%
Aug 20150.62%
Sep 2015-0.21%
Oct 2015-0.18%
Nov 20150.64%
Dec 2015-1.21%
Jan 20161.24%