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
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Asset 2
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Asset 3
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Asset 4
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Asset 5
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Asset 6
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Asset 7
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Asset 8
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Asset 9
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Asset 10
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Total
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Factor Analysis Results

RPAR Risk Parity ETF

Ticker RPAR
Time Period Jan 2020 - Apr 2023
Regression Basis 40 monthly samples
Coefficient of Determination (R2) 72.6%
Adjusted R2 68.6%
Regression F statistic 18.05 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.962 with p-value 0.425)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 0.987 with p-value 0.964)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.63 0.074 8.413 0.000 0.474...0.776
Size (SMB) -0.14 0.165 -0.858 0.397 -0.478...0.194
Value (HML) -0.14 0.122 -1.172 0.249 -0.390...0.105
Profitability (RMW) -0.02 0.174 -0.093 0.926 -0.370...0.338
Investment (CMA) 0.09 0.175 0.506 0.616 -0.267...0.445
Alpha (α) -40.82bps 0.004 -0.976 0.336 -1.26%...0.44%
Annualized Alpha (α) -4.90%  
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.
  • 5-factor model: Ra = Rrf + Bmkt × ( Rmkt - Rrf ) + Bsmb × SMB + Bhml × HML + Brmw × RMW + Bcma × CMA + 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
    Brmw
    Profitability loading factor
    RMW
    Robust Minus Weak: The profitability premium
    Bcma
    Investment loading factor
    CMA
    Conservative Minus Aggressive: The conservative investment 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 Returns

Monthly Factor Premiums (BPS) 81.45 -0.48 6.55 77.72 56.03  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
RPAR Risk Parity ETF RPAR Jan 2020 Apr 2023 -4.90% 50.93 0.07 -0.93 -1.26 4.97 12.95 72.6%

Risk and Return Attribution

NameStart DateEnd DateCumulative ReturnAnnualized ReturnAnnualized Standard DeviationCumulative ReturnReturn ContributionRisk Contribution
MarketSMBHMLRMWCMAAlphaMarketSMBHMLRMWCMAAlphaMarketSMBHMLRMWCMAAlpha
RPAR Risk Parity ETFJan 2020Apr 20234.89%1.44%15.02%20.23%0.07%-0.49%-0.55%2.13%-16.50%50.62%0.16%-1.22%-1.39%5.34%-41.27%72.54%-0.98%2.77%-0.20%-1.59%27.46%

RPAR Risk Parity ETF Cumulative Return

Residuals

MonthRPAR
Jan 20201.58%
Feb 20204.46%
Mar 2020-0.59%
Apr 2020-2.19%
May 2020-1.11%
Jun 20200.97%
Jul 20202.39%
Aug 2020-4.17%
Sep 20200.68%
Oct 20200.71%
Nov 2020-0.16%
Dec 20201.71%
Jan 20210.11%
Feb 2021-1.32%
Mar 2021-2.19%
Apr 2021-0.12%
May 20214.16%
Jun 2021-0.65%
Jul 20211.21%
Aug 2021-1.14%
Sep 20210.57%
Oct 2021-0.36%
Nov 20211.15%
Dec 2021-0.26%
Jan 20221.02%
Feb 20222.34%
Mar 2022-3.63%
Apr 2022-1.74%
May 2022-0.40%
Jun 2022-1.51%
Jul 20221.00%
Aug 2022-2.23%
Sep 2022-4.98%
Oct 2022-2.22%
Nov 20225.68%
Dec 20221.49%
Jan 20233.07%
Feb 2023-3.12%
Mar 20230.29%
Apr 2023-0.55%

RPAR Risk Parity ETF

RPAR Risk Parity ETF