Foundations of Finance: CAPM and Portfolio Risk
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What becomes difficult to solve when considering a large number of assets in portfolio selection?

  • Calculating the expected returns
  • Determining correlations
  • Finding optimal portfolio weights (correct)
  • Assessing idiosyncratic risks

    • Which risk is accounted for in the portfolio variance equation when correlation between securities equals zero?

  • Idiosyncratic risk (correct)
  • Systematic risk
  • Market risk
  • Credit risk

    • What is the implication of increasing the number of securities in a portfolio to infinity in terms of portfolio standard deviation?

  • Portfolio standard deviation increases
  • Portfolio variance remains constant
  • Portfolio variance becomes negative
  • Portfolio standard deviation approaches zero (correct)

    • Which model aims to improve upon the Capital Asset Pricing Model (CAPM)?

    <p>Fama-French 3 factor model</p> Signup and view all the answers

    What is a significant practical problem associated with the CAPM concerning inputs needed for calculations?

    <p>Inputs are complex and time-consuming to update</p> Signup and view all the answers

    In the context of portfolio theory, what does the Security Market Line represent?

    <p>The relationship between risk and return</p> Signup and view all the answers

    What is one key benefit of the Capital Asset Pricing Model (CAPM)?

    <p>It is empirically parsimonious</p> Signup and view all the answers

    What type of risk is specifically mitigated when the correlation between two securities is zero?

    <p>Idiosyncratic risk</p> Signup and view all the answers

    What does the risk contribution of security 𝑖 to portfolio risk 𝜎𝑚 primarily depend on?

    <p>The covariance of security 𝑖 with other assets</p> Signup and view all the answers

    How is the measure of risk contribution mathematically represented?

    <p>As a partial derivative</p> Signup and view all the answers

    What operation connects the derivative of the portfolio variance with respect to 𝑤𝑖 to the standard deviation?

    <p>Multiplication by 2𝜎𝑀</p> Signup and view all the answers

    Which mathematical expression represents the derivative of the portfolio standard deviation with respect to the weight of security 𝑖?

    <p>$ rac{2 ext{Cov}(R_i, R_j)}{ ext{Var}(R)}$</p> Signup and view all the answers

    In the context of portfolio risk, what does systematic risk primarily rely on?

    <p>The covariance between assets</p> Signup and view all the answers

    What is the effect of changing the portfolio weight of asset 𝑖 on market volatility?

    <p>It influences the contribution to market risk</p> Signup and view all the answers

    What does the expression $𝜕𝜎𝑀 /𝜕𝑤𝑖$ represent in portfolio management?

    <p>The sensitivity of portfolio risk to weight change</p> Signup and view all the answers

    What does the term 'infinitesimal amount' in regard to adjusting portfolio weight signify?

    <p>A very small change</p> Signup and view all the answers

    What is the primary assumption made about the assets in the diversification strategy?

    <p>Each asset is equally risky.</p> Signup and view all the answers

    What happens to the variance of the portfolio as the number of assets (N) increases?

    <p>It declines towards zero.</p> Signup and view all the answers

    Which equation correctly represents the relationship between the returns of an individual stock and the broad market index?

    <p>$R_i = eta_i R_M + u_i$</p> Signup and view all the answers

    How does the correlation of U.S. stocks affect portfolio variance according to the discussed factor model?

    <p>Higher correlation increases variance.</p> Signup and view all the answers

    What is $eta_i$ in the context of the regression model for stock returns?

    <p>The slope of the regression line indicating responsiveness to market returns.</p> Signup and view all the answers

    In a diversified portfolio, if each asset is represented by a weight of $w_i = rac{1}{N}$, what does this signify?

    <p>Wealth is equally distributed across multiple assets.</p> Signup and view all the answers

    What does the term $𝜎_p^2$ represent in portfolio theory?

    <p>The variance of the portfolio's returns.</p> Signup and view all the answers

    What does the expression $Cov(R_i, R_M)$ represent in the understanding of stock returns?

    <p>The relationship between the returns of stock $R_i$ and the market index.</p> Signup and view all the answers

    What is the primary motivation behind using a portfolio approach in investing?

    <p>To eliminate idiosyncratic risk in individual stocks.</p> Signup and view all the answers

    What does the long-short approach primarily hedge against?

    <p>Market risk exposure.</p> Signup and view all the answers

    In the FF three-factor regression model, what does the term 𝑅𝑓𝑡 represent?

    <p>The risk-free rate of return.</p> Signup and view all the answers

    What does a higher $R^2$ value in a regression indicate regarding stock returns?

    <p>The model captures a larger fraction of the variation in returns.</p> Signup and view all the answers

    As per the findings in the homework assignment related to the SMB factor, what happens to the estimated $𝛽𝑖𝑆𝑀𝐵$ as portfolios transition from small-cap to large-cap firms?

    <p>It moves from positive to negative.</p> Signup and view all the answers

    What phenomenon does the HML factor capture in the three-factor model?

    <p>Co-movement differences between value and growth stocks.</p> Signup and view all the answers

    What does the term 'long-short approach' imply in the context of investment strategies?

    <p>Simultaneously holding long and short positions in securities.</p> Signup and view all the answers

    Which of the following statements is true about the Fama-French three-factor model?

    <p>It accounts for size and value dimensions in asset pricing.</p> Signup and view all the answers

    What does CAPM primarily explain about stock returns?

    <p>Returns purely based on aggregate stock market exposure</p> Signup and view all the answers

    What is the systematic risk factor identified in the CAPM?

    <p>Market excess return, $E[R_M] - R_f$</p> Signup and view all the answers

    In which step of the Fama-MacBeth procedure do we run a time-series regression for each stock?

    <p>Step 1</p> Signup and view all the answers

    What does 𝛽𝑖 measure in the context of asset pricing?

    <p>Systematic risk of security i</p> Signup and view all the answers

    What is estimated in Step 2 of the Fama-MacBeth procedure?

    <p>A cross-sectional regression for expected returns</p> Signup and view all the answers

    Which equations represents the Security Characteristic Line (SCL)?

    <p>$R_{it} - R_f = a_i + \beta_i \times (R_{Mt} - R_f) + \epsilon_{it}$</p> Signup and view all the answers

    Which equation represents the relationship between expected return and risk in asset pricing?

    <p>𝐸 [𝑅𝑖 ] − 𝑅 𝑓 = 𝜆 𝑗 𝛽𝑖</p> Signup and view all the answers

    What is the purpose of the coefficients $\beta_i$ in the CAPM framework?

    <p>To determine the stock's sensitivity to the market risk factor</p> Signup and view all the answers

    What is the purpose of the Fama-MacBeth approach in asset pricing?

    <p>To jointly estimate market price of risk and asset exposure</p> Signup and view all the answers

    The market price of risk factor 𝑗, denoted by 𝜆 𝑗, indicates what?

    <p>The excess return demanded for exposure to a risk factor</p> Signup and view all the answers

    How is the cross-sectional regression in Step 2 structured?

    <p>It investigates whether higher $\beta$ results in higher expected returns.</p> Signup and view all the answers

    What risk factors did Fama-MacBeth identify in the asset pricing tests conducted in class?

    <p>Value-Growth factor and Small-Large factor</p> Signup and view all the answers

    What data is collected first in the Fama-MacBeth procedure?

    <p>Panel dataset of historical asset excess returns</p> Signup and view all the answers

    How is systematic risk quantified in the context of security pricing?

    <p>Via covariance with all other securities</p> Signup and view all the answers

    What does the expected risk premium for a stock represent?

    <p>The return an investor expects above the risk-free rate</p> Signup and view all the answers

    When is the Fama-MacBeth procedure particularly useful?

    <p>For testing if CAPM holds and other risk factors explain returns</p> Signup and view all the answers

    Study Notes

    Foundations of Finance: CAPM and Empirical Asset Pricing

    • The quadratic programming problem for optimal portfolio selection becomes difficult with many assets.
    • The Capital Asset Pricing Model (CAPM) offers a simplified and empirically sound method.
    • It calculates expected returns by accounting for risk-free rate and market risk.

    Portfolio Variance with Many Risky Securities: Idiosyncratic and Systematic Risk

    • Case 1: Non-systematic risk only: Portfolio variance is the sum of individual asset variances when correlations are zero.
    • Case 2: Systematic and non-systematic risk: US stock correlations are not zero.
    • Portfolio variance decreases with more assets; it approaches zero with many assets.
    • Systematic risk, captured by Beta, is the sensitivity of a stock's return compared to the overall market.
    • Idiosyncratic risk is the unique risk of an asset, not related to the market.
    • Total risk= systematic risk + idiosyncratic risk

    Risk-Reward Relationship and Security Market Line

    • A First Risk-Reward Relationship: The expected return of a security should be influenced by its systematic risk (beta) and the risk-free rate.
    • A Second Risk-Reward Relationship (Security Market Line): The expected return of an asset equals the risk-free return plus the systematic risk compensation, calculated through its beta.
      • Expected return = risk-free rate + beta * (market risk premium)

    Testing CAPM: The Fama-French Approach

    • The Fama-MacBeth procedure estimates market risk prices (lambda) and beta measures of factors in asset returns.
    • It tests whether a portfolio's returns can be explained by changes in the factors.

    Improving CAPM: Fama-French Three-Factor Model

    • Includes size (SMB) and value (HML) factors beyond market risk, offering a more comprehensive understanding of returns.
    • These factors represent the systematic risk of small minus big (SMB) and high minus low (HML) portfolios.
    • The Fama-French model assesses expected returns considering these three factors (market, size, value).

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    Foundations of Finance Notes on CAPM and Empirical Asset Pricing PDF

    Description

    Explore the principles of the Capital Asset Pricing Model (CAPM) and learn how it simplifies portfolio selection. This quiz examines the concepts of systematic and idiosyncratic risk, variance in portfolios, and the risk-reward relationship in asset pricing.

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