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 80.00% AGFiQ US Market Neutral Anti-Beta (BTAL)
20.00% ProShares UltraPro S&P500 (UPRO)
Time Period Oct 2011 - Oct 2020
Regression Basis 109 monthly samples
Coefficient of Determination (R2) 48.9%
Adjusted R2 46.9%
Regression F statistic 24.85 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.979 with p-value 0.460)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 9.977 with p-value 0.041)
Factor Description Loading Standard Error t-stat p-value 95% Confidence Interval
AQR-MKT-RF Market 0.26 0.049 5.380 0.000 0.167...0.362
AQR-SMB Size -0.43 0.094 -4.525 0.000 -0.613...-0.239
AQR-QMJ Quality 0.25 0.098 2.582 0.011 0.059...0.448
AQR-BAB Bet Against Beta 0.44 0.072 6.183 0.000 0.301...0.585
Alpha Alpha -16.09bps 0.002 -0.877 0.382 -0.52%...0.20%
Annualized Alpha Annualized Alpha -1.93%  
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.
  • Symbols:
    MKT-RF
    Market factor (excess return over the risk free rate)
    SMB
    Size factor (Small Minus Big)
    HML
    Value factor (High Minus Low)
    MOM
    Momentum factor (Up Minus Down)
    RMW
    Profitability factor (Robust Minus Weak)
    CMA
    Conservative investment factor (Conservative Minus Aggressive)
    ST-REV
    Short-term reversal factor
    LT-REV
    Long-term reversal factor
    QMJ
    Quality factor (Quality Minus Junk)
    BAB
    Bet Against Beta factor
    TRM
    Term factor (fixed income)
    CDT
    Credit factor (fixed income)
    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) 109.81 -8.17 28.87 74.33  
Name Start Date End Date Annual Alpha AQR-MKT-RF AQR-SMB AQR-QMJ AQR-BAB Total R2
Portfolio Oct 2011 Oct 2020 -1.93% 29.02 3.48 7.31 32.94 56.66 48.9%
Regression residuals
MonthPortfolio
Oct 2011-0.0263
Nov 20110.0201
Dec 20110.0214
Jan 2012-0.0304
Feb 2012-0.0105
Mar 2012-0.0116
Apr 20120.0045
May 20120.0250
Jun 20120.0169
Jul 2012-0.0010
Aug 2012-0.0130
Sep 20120.0101
Oct 2012-0.0201
Nov 20120.0059
Dec 2012-0.0069
Jan 2013-0.0313
Feb 20130.0232
Mar 20130.0021
Apr 20130.0082
May 2013-0.0153
Jun 2013-0.0075
Jul 20130.0001
Aug 2013-0.0234
Sep 2013-0.0020
Oct 2013-0.0000
Nov 20130.0005
Dec 2013-0.0106
Jan 2014-0.0148
Feb 20140.0116
Mar 20140.0135
Apr 20140.0061
May 2014-0.0061
Jun 20140.0114
Jul 2014-0.0044
Aug 2014-0.0118
Sep 2014-0.0257
Oct 20140.0028
Nov 20140.0026
Dec 20140.0278
Jan 20150.0056
Feb 2015-0.0113
Mar 2015-0.0048
Apr 2015-0.0208
May 2015-0.0104
Jun 2015-0.0257
Jul 20150.0090
Aug 20150.0056
Sep 2015-0.0282
Oct 2015-0.0087
Nov 2015-0.0038
Dec 2015-0.0045
Jan 20160.0240
Feb 2016-0.0037
Mar 20160.0287
Apr 20160.0069
May 2016-0.0064
Jun 20160.0531
Jul 2016-0.0349
Aug 2016-0.0053
Sep 20160.0018
Oct 2016-0.0187
Nov 2016-0.0366
Dec 20160.0006
Jan 2017-0.0071
Feb 2017-0.0004
Mar 20170.0118
Apr 2017-0.0006
May 20170.0092
Jun 2017-0.0151
Jul 20170.0009
Aug 2017-0.0004
Sep 2017-0.0098
Oct 20170.0016
Nov 2017-0.0121
Dec 20170.0088
Jan 2018-0.0163
Feb 2018-0.0098
Mar 20180.0211
Apr 20180.0053
May 20180.0197
Jun 20180.0246
Jul 2018-0.0042
Aug 20180.0268
Sep 2018-0.0014
Oct 2018-0.0088
Nov 2018-0.0100
Dec 2018-0.0066
Jan 20190.0154
Feb 20190.0133
Mar 20190.0147
Apr 2019-0.0085
May 20190.0091
Jun 2019-0.0058
Jul 2019-0.0003
Aug 20190.0387
Sep 2019-0.0106
Oct 20190.0026
Nov 20190.0105
Dec 20190.0043
Jan 20200.0171
Feb 2020-0.0005
Mar 20200.0104
Apr 20200.0538
May 20200.0170
Jun 2020-0.0295
Jul 20200.0051
Aug 2020-0.0005
Sep 2020-0.0191
Oct 2020-0.0163