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 S&P Small-Cap 600 Value ETF

Ticker IJS
Time Period Aug 2000 - Jul 2023
Regression Basis 276 monthly samples
Coefficient of Determination (R2) 75.2%
Adjusted R2 75.2%
Regression F statistic 832.86 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.850 with p-value 0.105)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.213 with p-value 0.073)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.11 0.039 28.859 0.000 1.037...1.189
Alpha (α) 17.13bps 0.002 0.957 0.339 -0.18%...0.52%
Annualized Alpha (α) 2.06%  
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.
  • CAPM: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + α
  • Symbols:
    Ra
    Asset return
    Rrf
    Risk free return
    Bmkt
    Market loading factor (exposure to market risk, CAPM beta)
    Rmkt
    Market return
    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) 58.55  
Name Ticker Start Date End Date Annual Alpha Rm-Rf Total R2
iShares S&P Small-Cap 600 Value ETF IJS Aug 2000 Jul 2023 2.06% 65.16 82.29 75.2%

Risk and Return Attribution

NameStart DateEnd DateCumulative ReturnAnnualized ReturnAnnualized Standard DeviationCumulative ReturnReturn ContributionRisk Contribution
MarketAlphaMarketAlphaMarketAlpha
iShares S&P Small-Cap 600 Value ETFAug 2000Jul 2023725.71%9.61%20.48%619.39%106.32%85.35%14.65%75.20%24.80%

iShares S&P Small-Cap 600 Value ETF Cumulative Return

Residuals

MonthIJS
Aug 2000-1.11%
Sep 20005.20%
Oct 20001.45%
Nov 20007.15%
Dec 200010.87%
Jan 20013.66%
Feb 20016.42%
Mar 20012.54%
Apr 2001-2.58%
May 20011.62%
Jun 20013.72%
Jul 20011.67%
Aug 20015.75%
Sep 2001-4.69%
Oct 20011.37%
Nov 2001-1.18%
Dec 20014.73%
Jan 20023.44%
Feb 20021.82%
Mar 20023.70%
Apr 20029.50%
May 2002-2.41%
Jun 20023.10%
Jul 2002-7.00%
Aug 2002-1.29%
Sep 20023.30%
Oct 2002-6.45%
Nov 2002-1.42%
Dec 20023.39%
Jan 2003-1.47%
Feb 2003-2.22%
Mar 2003-1.63%
Apr 2003-0.61%
May 20032.43%
Jun 20031.00%
Jul 20032.05%
Aug 20032.11%
Sep 2003-2.38%
Oct 20032.08%
Nov 20032.55%
Dec 2003-2.32%
Jan 2004-0.47%
Feb 20040.71%
Mar 20043.03%
Apr 2004-2.15%
May 20040.04%
Jun 20043.03%
Jul 2004-0.50%
Aug 2004-0.13%
Sep 20042.63%
Oct 2004-0.92%
Nov 20043.74%
Dec 2004-2.58%
Jan 2005-0.51%
Feb 20050.47%
Mar 2005-0.55%
Apr 2005-2.60%
May 20051.68%
Jun 20052.88%
Jul 20051.07%
Aug 2005-0.98%
Sep 2005-0.96%
Oct 2005-1.60%
Nov 20050.41%
Dec 2005-1.27%
Jan 20064.85%
Feb 20060.10%
Mar 20062.69%
Apr 2006-1.17%
May 2006-1.18%
Jun 2006-0.14%
Jul 2006-2.80%
Aug 2006-0.15%
Sep 2006-1.44%
Oct 20061.34%
Nov 2006-0.12%
Dec 2006-1.22%
Jan 2007-0.03%
Feb 20070.71%
Mar 2007-0.45%
Apr 2007-2.66%
May 20070.45%
Jun 2007-0.63%
Jul 2007-2.68%
Aug 2007-0.29%
Sep 2007-3.76%
Oct 2007-1.43%
Nov 2007-2.28%
Dec 2007-0.18%
Jan 20082.70%
Feb 2008-0.23%
Mar 20081.52%
Apr 2008-2.83%
May 20081.49%
Jun 20080.64%
Jul 20083.41%
Aug 20082.76%
Sep 20085.14%
Oct 2008-0.94%
Nov 2008-3.25%
Dec 20084.47%
Jan 2009-5.08%
Feb 2009-1.97%
Mar 2009-2.57%
Apr 20097.38%
May 2009-5.30%
Jun 20090.86%
Jul 20092.23%
Aug 2009-0.40%
Sep 2009-0.52%
Oct 2009-3.36%
Nov 2009-3.46%
Dec 20094.86%
Jan 20101.03%
Feb 20100.81%
Mar 20100.59%
Apr 20104.22%
May 20100.06%
Jun 2010-2.26%
Jul 2010-1.18%
Aug 2010-2.78%
Sep 20100.13%
Oct 2010-0.46%
Nov 20101.62%
Dec 20101.20%
Jan 2011-2.63%
Feb 20110.15%
Mar 20111.51%
Apr 2011-2.34%
May 2011-0.52%
Jun 20110.18%
Jul 2011-0.33%
Aug 2011-1.49%
Sep 2011-2.29%
Oct 20112.54%
Nov 20110.77%
Dec 20111.02%
Jan 20122.11%
Feb 2012-3.38%
Mar 2012-0.74%
Apr 2012-1.13%
May 2012-0.47%
Jun 20120.04%
Jul 2012-1.74%
Aug 20121.06%
Sep 2012-0.08%
Oct 2012-0.18%
Nov 20120.60%
Dec 20122.06%
Jan 2013-1.02%
Feb 20130.02%
Mar 2013-0.55%
Apr 2013-1.77%
May 20131.00%
Jun 20131.02%
Jul 20130.10%
Aug 2013-0.57%
Sep 20132.23%
Oct 2013-1.34%
Nov 20130.60%
Dec 2013-2.00%
Jan 20140.01%
Feb 2014-0.72%
Mar 20140.69%
Apr 2014-2.25%
May 2014-1.84%
Jun 20140.77%
Jul 2014-2.97%
Aug 2014-0.43%
Sep 2014-3.92%
Oct 20144.15%
Nov 2014-2.53%
Dec 20142.46%
Jan 2015-2.03%
Feb 2015-1.14%
Mar 20152.10%
Apr 2015-2.65%
May 2015-0.93%
Jun 20151.95%
Jul 2015-4.59%
Aug 20151.93%
Sep 2015-0.53%
Oct 2015-2.23%
Nov 20151.68%
Dec 2015-2.85%
Jan 20160.39%
Feb 20161.97%
Mar 20161.48%
Apr 20160.93%
May 2016-1.72%
Jun 20160.70%
Jul 20160.47%
Aug 20160.40%
Sep 20160.40%
Oct 2016-1.69%
Nov 20167.75%
Dec 20160.99%
Jan 2017-3.58%
Feb 2017-2.83%
Mar 2017-1.04%
Apr 2017-0.92%
May 2017-3.67%
Jun 20171.86%
Jul 2017-1.57%
Aug 2017-3.16%
Sep 20175.52%
Oct 2017-2.17%
Nov 20170.04%
Dec 2017-1.81%
Jan 2018-5.16%
Feb 2018-0.26%
Mar 20183.70%
Apr 20181.14%
May 20182.61%
Jun 2018-0.05%
Jul 2018-1.27%
Aug 2018-1.02%
Sep 2018-3.44%
Oct 2018-1.75%
Nov 2018-1.66%
Dec 2018-2.10%
Jan 20192.53%
Feb 2019-0.00%
Mar 2019-5.50%
Apr 2019-0.48%
May 2019-2.64%
Jun 2019-0.40%
Jul 2019-0.39%
Aug 2019-2.60%
Sep 20193.63%
Oct 2019-0.62%
Nov 2019-1.89%
Dec 2019-0.56%
Jan 2020-6.48%
Feb 2020-1.39%
Mar 2020-11.16%
Apr 2020-1.47%
May 2020-3.84%
Jun 20200.66%
Jul 2020-4.03%
Aug 2020-3.60%
Sep 2020-1.32%
Oct 20205.82%
Nov 20205.15%
Dec 20202.16%
Jan 20216.10%
Feb 20217.53%
Mar 20212.01%
Apr 2021-3.97%
May 20213.40%
Jun 2021-3.94%
Jul 2021-5.95%
Aug 2021-1.58%
Sep 20213.24%
Oct 2021-4.71%
Nov 2021-1.06%
Dec 20210.49%
Jan 20222.38%
Feb 20224.66%
Mar 2022-3.08%
Apr 20223.97%
May 20222.49%
Jun 20220.19%
Jul 2022-2.38%
Aug 2022-0.33%
Sep 2022-0.37%
Oct 20225.28%
Nov 2022-1.77%
Dec 20220.15%
Jan 20234.03%
Feb 20230.63%
Mar 2023-9.81%
Apr 2023-3.59%
May 2023-4.58%
Jun 20230.73%
Jul 20231.83%

iShares S&P Small-Cap 600 Value ETF

iShares S&P Small-Cap 600 Value ETF