Regression Analysis and CAPM Quiz
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Questions and Answers

What does the R-squared value in regression analysis specifically measure?

  • The significance of regression coefficients
  • The fixed effects in a model
  • The explained variation in dependent variable Y (correct)
  • The degree of relationship between X and Y
  • In the CAPM equation, how is the systematic risk component determined?

  • By the product of beta and the stock's unique risk
  • By the square of beta multiplied by market variance (correct)
  • By covariances of the stock with market returns
  • By the total market returns divided by stock returns
  • What is a key implication of the Capital Asset Pricing Model (CAPM) regarding expected returns?

  • Only the risk-free rate influences expected returns
  • Linear relationship exists between expected returns and beta (correct)
  • Expected returns are based on total market returns only
  • Expected returns are non-linear with respect to risk
  • What is a major concern raised by Roll's critique of the CAPM?

    <p>The difficulty in determining the true market portfolio</p> Signup and view all the answers

    Which of the following is a reason for the rejection of CAPM according to empirical evidence?

    <p>High-beta stocks yielding lower than predicted returns</p> Signup and view all the answers

    What does the Fama-French Three-Factor Model add to the traditional CAPM framework?

    <p>Size and value factors</p> Signup and view all the answers

    Which of the following best describes the primary assumption of the Arbitrage Pricing Theory (APT)?

    <p>Multiple factors affect asset returns without arbitrage opportunities.</p> Signup and view all the answers

    What effect is observed with smaller firms compared to larger firms?

    <p>They tend to earn higher returns.</p> Signup and view all the answers

    What additional risk factors are included in the Fama-French Five-Factor Model compared to the Three-Factor Model?

    <p>Profitability and investment factors</p> Signup and view all the answers

    What critique is commonly associated with empirically motivated factors in financial models?

    <p>Data-snooping concerns may invalidate findings.</p> Signup and view all the answers

    Study Notes

    Regression Analysis

    • The fundamental relationship between a dependent variable (Y) and an independent variable (X) is expressed through the equation: Y = α + βX + ε.
    • The coefficient β quantifies the change in Y for every unit change in X, calculated as the covariance of X and Y divided by the variance of X.
    • The R-squared value indicates the proportion of variation in the dependent variable (Y) that is explained by the independent variable (X).

    CAPM and Asset Returns

    • The Capital Asset Pricing Model (CAPM) describes the expected return of a stock as a function of its beta: (r_it - r_f) = α_i + β_i(r_Mt - r_f) + ε_it
    • This model breaks down the total risk of a stock into two components: systematic (β_i^2 * σ_M^2) and idiosyncratic (σ_ε^2) risk.

    Estimating Expected Returns

    • The expected return of an asset (E(r_j)) is estimated using CAPM: E(r_j) = r_f + β_j[E(r_M) - r_f].
    • This calculation relies on the risk-free rate (r_f), the market risk premium (E(r_M) - r_f), and the asset's beta (β_j).

    CAPM Implications

    • CAPM suggests a linear relationship between expected excess returns and an asset's beta.
    • The market risk premium serves as the slope of the Security Market Line (SML), depicting the relationship between expected return and risk.
    • The expected return of an asset depends solely on its beta, implying that the asset's specific risk is not rewarded.

    Testing CAPM

    • Time-series analysis investigates whether the alpha (α_i) for all assets is zero, as CAPM predicts.
    • The two-pass approach involves:
      • Estimating betas for each stock individually.
      • Running a cross-sectional regression: (r_it - r_ft) = γ_0 + γ_1β_i + ε_i
    • CAPM should hold if the intercept (γ_0) equals zero and the slope (γ_1) is equivalent to the market risk premium (r_Mt - r_ft).

    Empirical Evidence

    • The Fama-MacBeth (1973) method is widely used to test CAPM. This approach involves creating portfolios based on betas, calculating rolling betas, and conducting cross-sectional regressions.
    • The research findings highlight:
      • An approximately linear relationship between returns and betas.
      • A flatter risk-return relationship than predicted by CAPM.
      • Lower returns for high-beta stocks than anticipated by CAPM.
      • Higher returns for low-beta stocks than predicted by CAPM.

    Roll's Critique

    • Empirically testing CAPM using market proxies might not be a true test of the model.
    • Only the true market portfolio, encompassing all assets, can offer a legitimate validation of CAPM.
    • CAPM may be inherently untestable due to the inability to observe the true market portfolio.

    Reasons for CAPM Rejection

    • Errors in beta estimation can impact the validity of CAPM results.
    • The use of market proxies rather than the true market portfolio can lead to inaccurate conclusions.
    • The market representation might be incomplete, as it typically excludes assets like bonds, real estate, foreign investments, and human capital.

    CAPM Tests

    • Standard CAPM tests have been challenged by adding factors like squared beta and idiosyncratic risk.
    • Empirical evidence indicates that the Security Market Line (SML) is flatter than predicted by theory.
    • Introducing firm size and book-to-market ratio as variables into the model leads to rejection of CAPM, as these factors prove significant while beta does not.

    Size and Book-to-Market Effects

    • Small firms tend to earn higher returns compared to large firms, known as the size effect.
    • Stocks with a high book-to-market ratio, often referred to as value stocks, generally earn higher returns than stocks with a low book-to-market ratio, known as growth stocks.
    • These effects have been observed consistently across various countries.

    Multifactor Models

    • Multifactor models were developed to account for multiple risk factors beyond market risk.
    • Examples of such factors include GDP, interest rates, and expected inflation.

    Arbitrage Pricing Theory (APT)

    • Proposed by Ross in 1976, APT provides an alternative to CAPM.
    • It assumes that returns can be explained by multiple factors, and ultimately, no risk-free arbitrage opportunities exist.
    • APT distinguishes between systematic (factor) risk and diversifiable idiosyncratic risk.

    Fama-French Three-Factor Model

    • Developed as an extension of CAPM, it includes three factors: market excess return, SMB (Small Minus Big), and HML (High Minus Low book-to-market).
    • This model has proven more successful than CAPM in explaining the cross-sectional variation in returns.

    Fama-French Five-Factor Model

    • This model expands upon the three-factor model by incorporating two additional factors: profitability (RMW) and investment (CMA).

    Limitations and Considerations

    • There are concerns regarding data-snooping when it comes to empirically motivated factors.
    • There is ongoing debate surrounding whether these factors act as proxies for unknown risk factors.

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    Description

    Test your understanding of regression analysis and the Capital Asset Pricing Model (CAPM). This quiz covers key concepts such as the relationship between dependent and independent variables, the calculation of expected returns, and the components of stock risk. Challenge yourself and see how well you grasp these fundamental topics in finance.

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