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

Invesco FTSE RAFI US 1500 Small-Mid ETF

Factor regression results for Invesco FTSE RAFI US 1500 Small-Mid ETF
Ticker PRFZ
Time Period Jan 2007 - Dec 2015
Regression Basis 108 monthly samples
Coefficient of Determination (R2) 95.9%
Adjusted R2 95.8%
Regression F statistic 809.10 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.942 with p-value 0.373)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 10.219 with p-value 0.017)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.09 0.031 35.047 0.000 1.025...1.148
Size (SMB) 0.86 0.061 14.055 0.000 0.736...0.978
Value (HML) 0.33 0.052 6.236 0.000 0.223...0.431
Alpha (α) 12.91bps 0.001 0.986 0.327 -0.13%...0.39%
Annualized Alpha (α) 1.55%  
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
    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) 58.47 8.51 -28.47  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML Total R2
Invesco FTSE RAFI US 1500 Small-Mid ETF PRFZ Jan 2007 Dec 2015 1.55% 63.52 7.29 -9.30 74.42 95.9%
Regression residuals
MonthPRFZ
Jan 2007-0.07%
Feb 20070.28%
Mar 2007-0.24%
Apr 20070.34%
May 20070.16%
Jun 2007-0.14%
Jul 20070.92%
Aug 20070.71%
Sep 2007-0.23%
Oct 20070.81%
Nov 20070.39%
Dec 20070.42%
Jan 2008-1.20%
Feb 20082.57%
Mar 2008-0.68%
Apr 2008-0.07%
May 2008-0.46%
Jun 2008-0.86%
Jul 2008-1.78%
Aug 2008-1.82%
Sep 2008-2.27%
Oct 20081.35%
Nov 20080.96%
Dec 2008-0.76%
Jan 20091.39%
Feb 20090.87%
Mar 2009-2.35%
Apr 20099.85%
May 20092.78%
Jun 2009-1.07%
Jul 20091.44%
Aug 20092.84%
Sep 20091.42%
Oct 2009-0.86%
Nov 2009-1.67%
Dec 20091.23%
Jan 2010-0.00%
Feb 2010-0.65%
Mar 2010-0.93%
Apr 2010-0.27%
May 20101.03%
Jun 2010-0.17%
Jul 2010-0.26%
Aug 20100.74%
Sep 2010-0.60%
Oct 2010-0.59%
Nov 20100.13%
Dec 2010-1.13%
Jan 2011-0.32%
Feb 20110.23%
Mar 2011-0.98%
Apr 2011-0.07%
May 20110.49%
Jun 20110.07%
Jul 20110.56%
Aug 20110.21%
Sep 20110.29%
Oct 20110.07%
Nov 2011-0.59%
Dec 2011-0.30%
Jan 20120.38%
Feb 2012-0.47%
Mar 2012-0.80%
Apr 2012-0.28%
May 2012-0.82%
Jun 2012-0.51%
Jul 2012-0.45%
Aug 20120.33%
Sep 2012-0.96%
Oct 20120.04%
Nov 20120.42%
Dec 2012-0.26%
Jan 2013-0.51%
Feb 2013-0.23%
Mar 2013-0.76%
Apr 2013-0.08%
May 20130.05%
Jun 2013-0.50%
Jul 2013-0.80%
Aug 20130.25%
Sep 20130.33%
Oct 2013-1.01%
Nov 2013-0.28%
Dec 2013-0.53%
Jan 2014-0.67%
Feb 2014-0.21%
Mar 20140.09%
Apr 20140.53%
May 2014-0.08%
Jun 2014-1.13%
Jul 20140.78%
Aug 2014-0.48%
Sep 2014-0.15%
Oct 2014-0.54%
Nov 20140.12%
Dec 2014-1.00%
Jan 20151.28%
Feb 2015-0.68%
Mar 2015-0.13%
Apr 20150.65%
May 2015-1.56%
Jun 2015-0.54%
Jul 20150.37%
Aug 20150.61%
Sep 20150.58%
Oct 2015-0.70%
Nov 2015-1.17%
Dec 20150.35%