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
Allocation
Asset 1
%
Asset 2
%
Asset 3
%
Asset 4
%
Asset 5
%
Asset 6
%
Asset 7
%
Asset 8
%
Asset 9
%
Asset 10
%
Total
%

Factor Analysis Results

Portfolio Regression Results

Factor regression results for the portfolio
Portfolio 11.00% iShares MSCI USA Momentum Factor ETF (MTUM)
15.00% Vanguard Mid-Cap Value ETF (VOE)
25.00% Schwab Fundamental US Small Company ETF (FNDA)
22.00% Schwab Fundamental Intl Lg Co ETF (FNDF)
14.00% Schwab Fundamental Intl Sm Co ETF (FNDC)
13.00% Schwab Fundamental Emerg Mkts Lg Co ETF (FNDE)
Time Period Sep 2013 - Jan 2016
Regression Basis 29 monthly samples
Coefficient of Determination (R2) 96.6%
Adjusted R2 96.1%
Regression F statistic 171.65 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.717 with p-value 0.979)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 6.617 with p-value 0.158)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.03 0.042 24.266 0.000 0.940...1.114
Size (SMB) 0.15 0.088 1.684 0.105 -0.034...0.331
Value (HML) 0.19 0.135 1.433 0.165 -0.085...0.472
Momentum (MOM) 0.06 0.075 0.833 0.413 -0.092...0.217
Alpha (α) -1.89bps 0.002 -0.123 0.903 -0.33%...0.30%
Annualized Alpha (α) -0.23%  
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:
    Ra
    Asset return
    Rrf
    Risk free return
    Bmkt
    Market loading factor (exposure to market risk, different from CAPM beta)
    Rmkt
    Market return
    Bsmb
    Size loading factor (the level of exposure to size risk)
    SMB
    Small Minus Big: The size premium
    Bhml
    Value loading factor (the level of exposure to value risk)
    HML
    High Minus Low: The value premium
    Bmom
    Momentum loading factor (the level of exposure to momentum)
    MOM
    Up Minus Down: The momentum 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
    R2
    Coefficient of determination

Factor Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 33.27 -23.85 -53.05 130.57  
Name Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
Portfolio Sep 2013 Jan 2016 -0.23% 34.17 -3.55 -10.25 8.13 26.62 96.6%
Regression residuals
MonthPortfolio
Sep 20130.0042
Oct 20130.0018
Nov 2013-0.0022
Dec 20130.0002
Jan 2014-0.0119
Feb 20140.0028
Mar 20140.0022
Apr 2014-0.0000
May 20140.0022
Jun 2014-0.0001
Jul 2014-0.0059
Aug 20140.0051
Sep 2014-0.0075
Oct 20140.0159
Nov 2014-0.0032
Dec 2014-0.0010
Jan 20150.0035
Feb 20150.0048
Mar 20150.0005
Apr 2015-0.0108
May 2015-0.0052
Jun 20150.0022
Jul 2015-0.0063
Aug 20150.0062
Sep 2015-0.0023
Oct 2015-0.0019
Nov 20150.0065
Dec 2015-0.0120
Jan 20160.0123