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.

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Factor Analysis Results

RPAR Risk Parity ETF

Factor regression results for RPAR Risk Parity ETF
Ticker RPAR
Time Period Jan 2020 - Apr 2022
Regression Basis 28 monthly samples
Coefficient of Determination (R2) 73.2%
Adjusted R2 67.1%
Regression F statistic 12.00 (p-value = 0.000)
Autocorrelation No autocorrelation confirmed (Durbin-Watson test value is 1.886 with p-value 0.322)
Heteroscedasticity No heteroscedasticity confirmed (Breusch-Pagan test value is 1.269 with p-value 0.938)
Factor Loading Standard Error t-stat p-value 95% Confidence Interval
Market (Rm-Rf) 0.49 0.079 6.242 0.000 0.329...0.656
Size (SMB) -0.12 0.154 -0.806 0.429 -0.445...0.196
Value (HML) -0.05 0.108 -0.472 0.641 -0.275...0.173
Profitability (RMW) -0.14 0.168 -0.833 0.414 -0.488...0.208
Investment (CMA) -0.10 0.184 -0.524 0.606 -0.479...0.286
Alpha (α) 7.47bps 0.004 0.177 0.861 -0.80%...0.95%
Annualized Alpha (α) 0.90%  
Notes on results:
  • 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 Performance Attribution in Basis Points

Factor regression results
Monthly Factor Premiums (BPS) 113.36 5.36 25.46 76.50 74.07  
Name Ticker Start Date End Date Annual Alpha Rm-Rf SMB HML RMW CMA Total R2
RPAR Risk Parity ETF RPAR Jan 2020 Apr 2022 0.90% 55.81 -0.67 -1.30 -10.69 -7.15 43.46 73.2%
Regression residuals
MonthRPAR
Jan 20201.15%
Feb 20202.60%
Mar 2020-1.39%
Apr 2020-0.63%
May 2020-0.92%
Jun 20201.09%
Jul 20203.07%
Aug 2020-3.05%
Sep 2020-0.55%
Oct 2020-0.78%
Nov 20200.68%
Dec 20201.64%
Jan 2021-0.33%
Feb 2021-2.46%
Mar 2021-1.51%
Apr 2021-0.03%
May 20213.89%
Jun 2021-0.49%
Jul 20211.72%
Aug 2021-1.57%
Sep 2021-0.83%
Oct 20210.07%
Nov 20211.76%
Dec 20210.79%
Jan 20220.14%
Feb 20221.52%
Mar 2022-3.07%
Apr 2022-2.51%