Factor Regression Analysis

Factor Regression Overview

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:

  • The capital asset pricing model (CAPM) with market factor (MKT)
  • The Fama-French three factor model with market, size, and value factors (MKT, SMB, HML)
  • The Carhart four-factor model with market, size, value, and momentum factors (MKT, SMB, HML, MOM)
  • The Fama-French five factor model with market, size, value, profitability, and investment factors (MKT, SMB, HML, RMW, CMA)
  • The q-factor model with market, size, investment, return on equity, and expected growth factors (MKT, ME, I/A, ROE, EG)

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.

Additionally you can freely construct the factor model using any combination of existing factors or other time series under the custom factor returns model.

Regression Model

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

iShares Core S&P Small-Cap ETF

Ticker IJR
Time Period Jun 2000 - Jan 2023
Regression Basis 272 monthly samples
Coefficient of Determination (R2) 94.9%
Adjusted R2 94.8%
Regression F statistic 981.35 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.180 with p-value 0.929)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 6.072 with p-value 0.299)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.07 0.023 47.284 0.000 1.026...1.115
Size (SMB) 0.84 0.038 22.279 0.000 0.767...0.915
Value (HML) 0.32 0.025 12.468 0.000 0.267...0.367
Momentum (MOM) 0.05 0.018 2.728 0.007 0.013...0.083
Quality (QMJ) 0.29 0.041 7.089 0.000 0.211...0.374
Alpha (α) -11.87bps 0.001 -1.413 0.159 -0.28%...0.05%
Annualized Alpha (α) -1.42%  
Notes and Disclosures
  • IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
  • 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. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
  • Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
  • Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
  • 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.
  • Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • Refer to the documentation 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
    Bqmj
    Quality loading factor
    QMJ
    Quality Minus Junk 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 Returns

Monthly Factor Premiums (BPS) 54.78 17.54 17.60 26.14 44.66  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM QMJ Total R2
iShares Core S&P Small-Cap ETF IJR Jun 2000 Jan 2023 -1.42% 58.64 14.75 5.58 1.27 13.07 81.45 94.9%

Risk and Return Attribution

NameStart DateEnd DateCumulative ReturnAnnualized ReturnAnnualized Standard DeviationCumulative ReturnReturn ContributionRisk Contribution
MarketSMBHMLMOMQMJAlphaMarketSMBHMLMOMQMJAlphaMarketSMBHMLMOMQMJAlpha
iShares Core S&P Small-Cap ETFJun 2000Jan 2023717.46%9.71%19.53%540.25%103.01%47.81%14.42%135.25%-123.28%56.04%10.69%4.96%1.50%14.03%-12.79%80.87%22.72%2.44%-1.77%-9.41%5.15%

iShares Core S&P Small-Cap ETF Cumulative Return

Residuals

MonthIJR
Jun 2000-3.73%
Jul 2000-0.91%
Aug 20003.02%
Sep 20000.26%
Oct 20004.48%
Nov 2000-2.41%
Dec 20007.80%
Jan 2001-2.60%
Feb 2001-0.65%
Mar 20010.94%
Apr 2001-0.21%
May 2001-2.86%
Jun 20010.46%
Jul 20011.38%
Aug 20010.47%
Sep 2001-1.94%
Oct 2001-0.73%
Nov 2001-1.33%
Dec 20010.05%
Jan 2002-0.84%
Feb 2002-0.40%
Mar 2002-0.02%
Apr 20021.62%
May 2002-1.97%
Jun 2002-1.95%
Jul 2002-3.21%
Aug 20020.97%
Sep 20020.79%
Oct 20020.03%
Nov 20020.12%
Dec 2002-1.00%
Jan 2003-1.54%
Feb 2003-1.52%
Mar 2003-0.55%
Apr 20031.68%
May 2003-0.80%
Jun 2003-0.60%
Jul 2003-0.49%
Aug 20030.49%
Sep 2003-3.60%
Oct 2003-0.72%
Nov 2003-0.69%
Dec 2003-1.15%
Jan 2004-1.59%
Feb 20040.71%
Mar 20040.66%
Apr 20040.94%
May 20040.77%
Jun 20041.20%
Jul 2004-0.89%
Aug 2004-0.41%
Sep 20040.76%
Oct 20040.24%
Nov 20040.09%
Dec 2004-1.91%
Jan 20050.64%
Feb 20050.16%
Mar 2005-0.38%
Apr 2005-0.07%
May 20050.80%
Jun 2005-0.45%
Jul 20050.38%
Aug 2005-0.17%
Sep 20050.23%
Oct 2005-0.22%
Nov 20050.77%
Dec 2005-1.05%
Jan 20060.35%
Feb 20060.49%
Mar 20060.53%
Apr 2006-0.52%
May 2006-0.10%
Jun 2006-0.22%
Jul 2006-1.28%
Aug 2006-0.55%
Sep 2006-0.32%
Oct 20060.10%
Nov 2006-0.40%
Dec 2006-0.98%
Jan 20070.04%
Feb 2007-0.14%
Mar 20070.66%
Apr 20070.08%
May 20070.39%
Jun 2007-0.64%
Jul 20071.04%
Aug 20071.65%
Sep 2007-0.10%
Oct 2007-0.36%
Nov 20070.25%
Dec 2007-1.05%
Jan 20081.22%
Feb 2008-0.34%
Mar 20080.58%
Apr 20081.24%
May 2008-0.52%
Jun 20080.67%
Jul 20080.76%
Aug 20080.25%
Sep 20081.78%
Oct 20080.88%
Nov 2008-0.09%
Dec 20080.80%
Jan 2009-3.71%
Feb 2009-0.46%
Mar 2009-1.43%
Apr 20093.76%
May 2009-2.93%
Jun 2009-0.56%
Jul 2009-0.19%
Aug 2009-0.81%
Sep 2009-1.54%
Oct 2009-0.34%
Nov 2009-0.80%
Dec 20090.79%
Jan 20100.27%
Feb 2010-1.09%
Mar 2010-0.19%
Apr 2010-0.11%
May 20101.79%
Jun 20101.13%
Jul 2010-0.40%
Aug 2010-0.64%
Sep 2010-0.26%
Oct 2010-0.12%
Nov 20100.56%
Dec 20100.04%
Jan 2011-0.38%
Feb 2011-0.62%
Mar 20111.10%
Apr 20110.29%
May 20111.03%
Jun 20110.12%
Jul 20110.30%
Aug 2011-0.17%
Sep 2011-0.54%
Oct 20112.01%
Nov 20110.55%
Dec 20110.29%
Jan 20120.75%
Feb 2012-1.05%
Mar 20120.26%
Apr 2012-0.26%
May 2012-0.26%
Jun 2012-0.32%
Jul 2012-0.25%
Aug 20120.73%
Sep 2012-0.88%
Oct 2012-0.12%
Nov 20120.37%
Dec 20120.61%
Jan 2013-0.31%
Feb 20130.34%
Mar 2013-0.24%
Apr 20130.15%
May 20130.20%
Jun 20130.06%
Jul 2013-0.01%
Aug 20131.01%
Sep 20130.45%
Oct 2013-0.11%
Nov 20130.53%
Dec 2013-0.97%
Jan 20140.17%
Feb 2014-0.24%
Mar 2014-0.37%
Apr 20140.02%
May 2014-0.72%
Jun 2014-0.02%
Jul 2014-0.54%
Aug 20140.00%
Sep 20140.65%
Oct 20142.72%
Nov 2014-0.34%
Dec 20141.73%
Jan 20150.60%
Feb 2015-0.25%
Mar 20151.48%
Apr 2015-2.02%
May 20150.62%
Jun 20151.46%
Jul 20151.71%
Aug 2015-0.20%
Sep 20151.41%
Oct 2015-0.29%
Nov 20151.42%
Dec 20150.27%
Jan 20160.57%
Feb 2016-0.11%
Mar 2016-0.31%
Apr 2016-1.48%
May 20161.29%
Jun 2016-0.33%
Jul 2016-0.17%
Aug 20160.10%
Sep 20160.01%
Oct 2016-0.46%
Nov 20163.05%
Dec 20160.16%
Jan 2017-1.47%
Feb 20170.48%
Mar 2017-0.21%
Apr 20170.28%
May 2017-0.10%
Jun 20170.43%
Jul 20170.28%
Aug 2017-0.92%
Sep 20172.20%
Oct 2017-0.26%
Nov 20170.14%
Dec 2017-0.64%
Jan 2018-0.17%
Feb 20180.62%
Mar 20181.43%
Apr 2018-0.26%
May 20181.12%
Jun 20180.02%
Jul 20181.50%
Aug 20181.70%
Sep 2018-1.32%
Oct 2018-1.77%
Nov 20180.83%
Dec 2018-0.23%
Jan 20190.23%
Feb 2019-0.22%
Mar 2019-1.05%
Apr 20190.50%
May 2019-0.36%
Jun 20190.88%
Jul 20190.46%
Aug 20191.16%
Sep 2019-0.45%
Oct 20190.96%
Nov 20190.12%
Dec 2019-1.24%
Jan 20201.21%
Feb 20200.30%
Mar 20201.48%
Apr 2020-5.35%
May 2020-0.75%
Jun 2020-0.61%
Jul 2020-0.15%
Aug 2020-3.14%
Sep 2020-0.89%
Oct 20201.73%
Nov 20201.61%
Dec 20201.12%
Jan 20212.44%
Feb 20210.17%
Mar 2021-1.02%
Apr 2021-1.28%
May 2021-1.05%
Jun 2021-1.31%
Jul 2021-1.24%
Aug 2021-0.34%
Sep 2021-0.33%
Oct 2021-1.90%
Nov 2021-0.03%
Dec 20210.59%
Jan 2022-0.03%
Feb 20221.59%
Mar 2022-2.23%
Apr 2022-0.95%
May 20220.97%
Jun 2022-0.30%
Jul 20222.10%
Aug 2022-0.81%
Sep 2022-0.23%
Oct 20220.13%
Nov 20220.32%
Dec 2022-1.17%
Jan 20232.19%

iShares Core S&P Small-Cap ETF

iShares Core S&P Small-Cap ETF