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
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Factor Analysis Results

Vanguard Real Estate ETF

Factor regression results for Vanguard Real Estate ETF
Ticker VNQ
Time Period Feb 2010 - Sep 2016
Regression Basis 80 monthly samples
Coefficient of Determination (R2) 63.2%
Adjusted R2 60.7%
Regression F statistic 25.40 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.360 with p-value 0.953)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.872 with p-value 0.867)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.137 7.047 0.000 0.690...1.234
Size (SMB) 0.13 0.170 0.788 0.433 -0.205...0.474
Value (HML) 0.09 0.189 0.494 0.623 -0.283...0.470
Term Risk (TRM) 0.66 0.143 4.641 0.000 0.378...0.947
Credit Risk (CDT) 0.55 0.244 2.258 0.027 0.065...1.039
Alpha (α) -46.19bps 0.004 -1.203 0.233 -1.23%...0.30%
Annualized Alpha (α) -5.54%  
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: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + 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
    Bt
    Term risk loading factor
    Bc
    Credit risk loading factor
    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) 112.95 8.87 -12.05 76.26 36.25  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML TRM CDT Total R2
Vanguard Real Estate ETF VNQ Feb 2010 Sep 2016 -5.54% 108.67 1.19 -1.13 50.54 20.01 133.10 63.2%
Regression residuals
MonthVNQ
Feb 20102.54%
Mar 20104.63%
Apr 20101.89%
May 20101.94%
Jun 2010-2.90%
Jul 20102.26%
Aug 2010-0.95%
Sep 2010-3.36%
Oct 20103.67%
Nov 2010-1.28%
Dec 2010-0.31%
Jan 20113.87%
Feb 20110.02%
Mar 2011-1.57%
Apr 20111.36%
May 20110.73%
Jun 20110.90%
Jul 20110.40%
Aug 2011-2.65%
Sep 2011-8.62%
Oct 20112.74%
Nov 2011-1.47%
Dec 20110.94%
Jan 20120.41%
Feb 2012-4.29%
Mar 20125.74%
Apr 20121.16%
May 2012-2.55%
Jun 20122.56%
Jul 2012-2.45%
Aug 2012-1.62%
Sep 2012-3.44%
Oct 2012-0.09%
Nov 2012-0.47%
Dec 20123.51%
Jan 20131.05%
Feb 2013-0.49%
Mar 2013-0.49%
Apr 20132.36%
May 2013-3.61%
Jun 20133.43%
Jul 2013-4.15%
Aug 2013-2.44%
Sep 2013-0.52%
Oct 2013-0.72%
Nov 2013-6.45%
Dec 2013-1.13%
Jan 20143.16%
Feb 2014-0.15%
Mar 2014-0.26%
Apr 20142.45%
May 2014-1.20%
Jun 2014-1.34%
Jul 20142.70%
Aug 2014-3.98%
Sep 2014-0.76%
Oct 20145.67%
Nov 2014-1.32%
Dec 20140.18%
Jan 20153.91%
Feb 2015-5.32%
Mar 20152.37%
Apr 2015-3.26%
May 20150.94%
Jun 20150.29%
Jul 20152.92%
Aug 20151.02%
Sep 20155.36%
Oct 2015-1.23%
Nov 2015-0.61%
Dec 20155.96%
Jan 20160.59%
Feb 2016-1.75%
Mar 20161.07%
Apr 2016-4.38%
May 20161.03%
Jun 20162.54%
Jul 2016-1.83%
Aug 2016-4.07%
Sep 2016-0.80%