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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

Note: The time period was constrained by the available data for Invesco S&P SmallCap 600 Pure Value ETF (RZV) [Apr 2006 - Sep 2026] and Vanguard MStar Small Cap Value ETF (VBR) [Feb 2004 - Sep 2026].

Factor Regression Summary

Name Ticker Start Date End Date Rm-Rf SMB HML MOM Alpha Annual Alpha R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Jun 2026 0.96 0.86 0.52 -0.02 -0.01% -0.07% 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Jun 2026 0.97 0.82 0.53 0.01 -0.09% -1.05% 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Jun 2026 1.12 1.04 0.78 -0.37 0.08% 0.90% 91.3%
Vanguard MStar Small Cap Value ETF VBR Apr 2006 Jun 2026 0.99 0.55 0.45 -0.05 -0.04% -0.50% 97.1%
Statistically significant factor exposures in bold

iShares S&P Small-Cap 600 Value ETF

Ticker IJS
Time Period Apr 2006 - Jun 2026
Regression Basis 243 monthly samples
Coefficient of Determination (R2) 97.4%
Adjusted R2 97.3%
Regression F statistic 2,206.02 (p-value = 0.000)
Autocorrelation Autocorrelation confirmed (Durbin-Watson test value is 1.791 with p-value 0.049)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 15.570 with p-value 0.004)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.96 0.015 62.281 0.000 0.931...0.992
Size (SMB) 0.86 0.027 31.812 0.000 0.811...0.918
Value (HML) 0.52 0.021 25.224 0.000 0.479...0.561
Momentum (MOM) -0.02 0.016 -1.153 0.250 -0.050...0.013
Alpha (α) -0.60bps 0.001 -0.092 0.927 -0.13%...0.12%
Annualized Alpha (α) -0.07%  

iShares Russell 2000 Value ETF

Ticker IWN
Time Period Apr 2006 - Jun 2026
Regression Basis 243 monthly samples
Coefficient of Determination (R2) 98.1%
Adjusted R2 98.0%
Regression F statistic 3,003.14 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.040 with p-value 0.617)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 10.108 with p-value 0.039)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.97 0.013 74.298 0.000 0.940...0.992
Size (SMB) 0.82 0.023 35.607 0.000 0.770...0.860
Value (HML) 0.53 0.017 30.340 0.000 0.493...0.561
Momentum (MOM) 0.01 0.013 0.688 0.492 -0.017...0.036
Alpha (α) -8.74bps 0.001 -1.599 0.111 -0.20%...0.02%
Annualized Alpha (α) -1.05%  

Invesco S&P SmallCap 600 Pure Value ETF

Ticker RZV
Time Period Apr 2006 - Jun 2026
Regression Basis 243 monthly samples
Coefficient of Determination (R2) 91.3%
Adjusted R2 91.2%
Regression F statistic 625.42 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.923 with p-value 0.267)
Heteroscedasticity Heteroscedasticity confirmed (Breusch-Pagan test value is 56.250 with p-value 0.000)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 1.12 0.039 28.511 0.000 1.044...1.199
Size (SMB) 1.04 0.069 15.072 0.000 0.907...1.180
Value (HML) 0.78 0.053 14.925 0.000 0.680...0.887
Momentum (MOM) -0.37 0.041 -9.024 0.000 -0.449...-0.288
Alpha (α) 7.52bps 0.002 0.454 0.650 -0.25%...0.40%
Annualized Alpha (α) 0.90%  

Vanguard MStar Small Cap Value ETF

Ticker VBR
Time Period Apr 2006 - Jun 2026
Regression Basis 243 monthly samples
Coefficient of Determination (R2) 97.1%
Adjusted R2 97.0%
Regression F statistic 1,958.96 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 2.174 with p-value 0.911)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 3.148 with p-value 0.533)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.99 0.015 64.599 0.000 0.963...1.024
Size (SMB) 0.55 0.027 20.391 0.000 0.499...0.606
Value (HML) 0.45 0.021 21.736 0.000 0.406...0.487
Momentum (MOM) -0.05 0.016 -3.032 0.003 -0.080...-0.017
Alpha (α) -4.18bps 0.001 -0.646 0.519 -0.17%...0.09%
Annualized Alpha (α) -0.50%  

Factor Returns

Monthly Factor Premiums (BPS) 85.33 -6.45 -6.17 14.77  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML MOM Total R2
iShares S&P Small-Cap 600 Value ETF IJS Apr 2006 Jun 2026 -0.07% 82.05 -5.58 -3.21 -0.27 72.39 97.4%
iShares Russell 2000 Value ETF IWN Apr 2006 Jun 2026 -1.05% 82.43 -5.26 -3.25 0.14 65.32 98.1%
Invesco S&P SmallCap 600 Pure Value ETF RZV Apr 2006 Jun 2026 0.90% 95.69 -6.73 -4.84 -5.44 86.20 91.3%
Vanguard MStar Small Cap Value ETF VBR Apr 2006 Jun 2026 -0.50% 84.80 -3.56 -2.75 -0.72 73.59 97.1%

Risk and Return Attribution

NameStart DateEnd DateCumulative ReturnAnnualized ReturnAnnualized Standard DeviationCumulative ReturnReturn ContributionRisk Contribution
MarketSMBHMLMOMAlphaMarketSMBHMLMOMAlphaMarketSMBHMLMOMAlpha
iShares S&P Small-Cap 600 Value ETFApr 2006Jun 2026413.21%8.41%20.88%510.27%-58.47%-33.01%-2.31%-3.27%84.02%-9.63%-5.44%-0.38%-0.54%62.98%22.17%11.62%0.59%2.63%
iShares Russell 2000 Value ETFApr 2006Jun 2026339.33%7.58%20.46%466.18%-49.28%-30.22%1.07%-48.42%78.33%-8.28%-5.08%0.18%-8.13%65.30%20.94%12.11%-0.30%1.95%
Invesco S&P SmallCap 600 Pure Value ETFApr 2006Jun 2026378.97%8.04%29.27%548.15%-75.76%-59.46%-53.20%19.24%72.52%-10.02%-7.87%-7.04%2.55%48.02%17.79%14.38%11.10%8.71%
Vanguard MStar Small Cap Value ETFApr 2006Jun 2026453.90%8.82%19.65%554.15%-36.11%-28.52%-6.34%-29.27%84.68%-5.52%-4.36%-0.97%-4.47%72.38%12.90%10.05%1.71%2.96%

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

iShares Russell 2000 Value ETF Cumulative Return

Invesco S&P SmallCap 600 Pure Value ETF Cumulative Return

Vanguard MStar Small Cap Value ETF Cumulative Return

Residuals

iShares S&P Small-Cap 600 Value ETF

iShares Russell 2000 Value ETF

Invesco S&P SmallCap 600 Pure Value ETF

Vanguard MStar Small Cap Value ETF

iShares S&P Small-Cap 600 Value ETF

iShares Russell 2000 Value ETF

Invesco S&P SmallCap 600 Pure Value ETF

Vanguard MStar Small Cap Value ETF

  • 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. Other investments not considered may have characteristics similar or superior to those being analyzed.
  • 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
    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