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) 95.8%
Adjusted R2 95.7%
Regression F statistic 800.24 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.935 with p-value 0.359)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 9.879 with p-value 0.020)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.09 0.031 35.086 0.000 1.027...1.151
Size (SMB) 0.86 0.061 13.986 0.000 0.735...0.978
Value (HML) 0.32 0.053 6.106 0.000 0.217...0.426
Alpha (α) 12.83bps 0.001 0.975 0.332 -0.13%...0.39%
Annualized Alpha (α) 1.54%  
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
    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 7.90 -27.56  
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 1.54% 63.68 6.77 -8.85 74.42 95.8%
Regression residuals
MonthPRFZ
Jan 2007-0.0009
Feb 20070.0026
Mar 2007-0.0027
Apr 20070.0033
May 20070.0015
Jun 2007-0.0013
Jul 20070.0094
Aug 20070.0072
Sep 2007-0.0020
Oct 20070.0078
Nov 20070.0040
Dec 20070.0044
Jan 2008-0.0121
Feb 20080.0258
Mar 2008-0.0066
Apr 2008-0.0007
May 2008-0.0050
Jun 2008-0.0081
Jul 2008-0.0178
Aug 2008-0.0183
Sep 2008-0.0225
Oct 20080.0136
Nov 20080.0090
Dec 2008-0.0079
Jan 20090.0130
Feb 20090.0081
Mar 2009-0.0230
Apr 20090.0995
May 20090.0277
Jun 2009-0.0104
Jul 20090.0143
Aug 20090.0286
Sep 20090.0142
Oct 2009-0.0087
Nov 2009-0.0167
Dec 20090.0123
Jan 20100.0002
Feb 2010-0.0063
Mar 2010-0.0094
Apr 2010-0.0027
May 20100.0103
Jun 2010-0.0018
Jul 2010-0.0028
Aug 20100.0076
Sep 2010-0.0064
Oct 2010-0.0057
Nov 20100.0016
Dec 2010-0.0115
Jan 2011-0.0029
Feb 20110.0020
Mar 2011-0.0101
Apr 2011-0.0008
May 20110.0051
Jun 20110.0011
Jul 20110.0058
Aug 20110.0022
Sep 20110.0029
Oct 20110.0000
Nov 2011-0.0065
Dec 2011-0.0033
Jan 20120.0042
Feb 2012-0.0044
Mar 2012-0.0077
Apr 2012-0.0029
May 2012-0.0083
Jun 2012-0.0053
Jul 2012-0.0044
Aug 20120.0034
Sep 2012-0.0095
Oct 20120.0007
Nov 20120.0044
Dec 2012-0.0024
Jan 2013-0.0050
Feb 2013-0.0022
Mar 2013-0.0078
Apr 2013-0.0007
May 20130.0008
Jun 2013-0.0051
Jul 2013-0.0082
Aug 20130.0024
Sep 20130.0032
Oct 2013-0.0101
Nov 2013-0.0029
Dec 2013-0.0054
Jan 2014-0.0067
Feb 2014-0.0022
Mar 20140.0011
Apr 20140.0054
May 2014-0.0007
Jun 2014-0.0114
Jul 20140.0079
Aug 2014-0.0046
Sep 2014-0.0013
Oct 2014-0.0055
Nov 20140.0008
Dec 2014-0.0101
Jan 20150.0129
Feb 2015-0.0069
Mar 2015-0.0012
Apr 20150.0065
May 2015-0.0157
Jun 2015-0.0052
Jul 20150.0034
Aug 20150.0064
Sep 20150.0055
Oct 2015-0.0073
Nov 2015-0.0116
Dec 20150.0035