Portfolio Management: Efficient Frontier
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Questions and Answers

What happens to the efficient frontier when the correlation between two assets in a portfolio is reduced?

  • The efficient frontier extends to the left and possibly upward (correct)
  • The efficient frontier shifts to the right
  • The efficient frontier remains unchanged
  • The efficient frontier extends to the upper left

    • What determines the optimal portfolio for an individual investor?

  • The market risk-free rate
  • The expected return on the portfolio
  • The individual's utility curve (correct)
  • The asset allocation plan

    • According to the CAPM, what is the rational investor's optimal portfolio?

  • A 100% allocation to the market portfolio
  • The global minimum variance portfolio (correct)
  • A 50% allocation to the risk-free asset
  • A portfolio with a 100% allocation to a single stock

    • What happens to the efficient frontier when the expected volatility of an asset changes?

    <p>The efficient frontier is stable</p> Signup and view all the answers

    Why does reducing correlation between assets in a portfolio reduce risk?

    <p>Because it reduces the portfolio's standard deviation</p> Signup and view all the answers

    What is the relationship between an investor's utility curve and their optimal portfolio?

    <p>The utility curve is tangent to the optimal portfolio</p> Signup and view all the answers

    What is the effect of a change in return expectations on the efficient frontier?

    <p>The efficient frontier extends to the upper right</p> Signup and view all the answers

    What is the characteristic of the optimal portfolio according to the CAPM?

    <p>It is the global minimum variance portfolio</p> Signup and view all the answers

    What are the required inputs for the model?

    <p>Expected return and variance of each security, as well as the covariance between all securities</p> Signup and view all the answers

    When does diversification provide benefits?

    <p>As long as the correlation coefficient between the assets is less than 1</p> Signup and view all the answers

    What does the efficient frontier represent?

    <p>The set of portfolios that dominate all others as to risk and return</p> Signup and view all the answers

    Which portfolio is most likely to lie on the efficient frontier?

    <p>Portfolio B with an expected return of 11% and standard deviation of 13%</p> Signup and view all the answers

    Why can Portfolio C not lie on the efficient frontier?

    <p>Because it has the same return as Portfolio D, but has more risk</p> Signup and view all the answers

    What is the main benefit of diversification?

    <p>Reduction of the overall risk of the portfolio</p> Signup and view all the answers

    What is the relationship between risk and return?

    <p>As risk increases, return increases</p> Signup and view all the answers

    What is the purpose of the efficient frontier?

    <p>To identify the set of portfolios that dominate all others as to risk and return</p> Signup and view all the answers

    Which of the following portfolios lies on the efficient frontier?

    <p>Portfolio C with an expected return of 11 and a standard deviation of 10</p> Signup and view all the answers

    What is the formula to calculate the covariance between two stocks?

    <p>cov1,2 = 0.75 × 0.16 × 0.22</p> Signup and view all the answers

    What is the benefit of diversification when the correlation between two stocks is less than +1?

    <p>Potential benefits from diversification arise</p> Signup and view all the answers

    What does a correlation coefficient of zero imply?

    <p>No relationship between the stocks' returns</p> Signup and view all the answers

    What is the characteristic of a portfolio that plots above the efficient frontier?

    <p>It is unattainable and efficient</p> Signup and view all the answers

    What is the characteristic of a portfolio that plots below the efficient frontier?

    <p>It is attainable and inefficient</p> Signup and view all the answers

    What does a correlation coefficient of -1 imply?

    <p>A perfect negative relationship between the stocks' returns</p> Signup and view all the answers

    What is the formula to calculate the correlation coefficient between two assets?

    <p>CovA,B / (SDA × SDB)</p> Signup and view all the answers

    If the covariance between the market's returns and a stock's returns is 0.008, what can be said about the relationship between the two?

    <p>The stock's returns are positively correlated with the market's returns.</p> Signup and view all the answers

    What is the condition to construct a zero variance portfolio?

    <p>A correlation coefficient of -1</p> Signup and view all the answers

    What is the effect of adding a security with a positive covariance to a portfolio?

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

    What is the formula for calculating the correlation coefficient between two assets?

    <p>Covariance of A and B / [(Standard deviation of A)(Standard Deviation of B)]</p> Signup and view all the answers

    What is the range of the correlation coefficient?

    <p>-1 to 1</p> Signup and view all the answers

    An investor's portfolio has an expected return of 10% with a variance of 0.01. If the covariance between the portfolio and a new security is 0.005, what will be the effect on the portfolio's variance?

    <p>The variance will increase.</p> Signup and view all the answers

    What is the condition for a stock to reduce the risk of a portfolio?

    <p>Correlation coefficient is less than +1</p> Signup and view all the answers

    What is the relationship between the covariance and the correlation coefficient?

    <p>The correlation coefficient is a measure of the covariance.</p> Signup and view all the answers

    What is the characteristic of the indifference curves for investors who are less risk averse?

    <p>Flatter</p> Signup and view all the answers

    A portfolio has an expected return of 12% with a variance of 0.02. If a security is added to the portfolio with a covariance of 0.007, what will be the effect on the portfolio's expected return?

    <p>The expected return will remain unchanged.</p> Signup and view all the answers

    What is the expected standard deviation of returns for Asset X?

    <p>15%</p> Signup and view all the answers

    What is the effect of adding a security with a negative covariance to a portfolio?

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

    What is the percentage of the portfolio invested in Asset X?

    <p>40%</p> Signup and view all the answers

    What is the formula for calculating the portfolio standard deviation?

    <p>[(0.4)^2(0.25) + (0.6)^2(0.4) + 2(0.4)(0.6)(1)(0.25)(0.5)(0.4)(0.5)]^0.5</p> Signup and view all the answers

    What is the characteristic of indifference curves for investors who are more risk averse?

    <p>Steeper</p> Signup and view all the answers

    What is the expected standard deviation of returns for Asset Y?

    <p>25%</p> Signup and view all the answers

    Study Notes

    Portfolio Management

    • Reducing correlation between two assets in a portfolio moves the efficient frontier to the left, possibly slightly upward, reflecting the influence of correlation on reducing portfolio risk.
    • The efficient frontier is stable unless return expectations change or asset volatility changes.

    Investor's Optimal Portfolio

    • The optimal portfolio for an investor is the highest indifference curve that is tangent to the efficient frontier, giving the investor the greatest possible utility.
    • The individual's utility curve determines the optimal portfolio.

    CAPM and Investor's Choice

    • A rational investor would be least likely to choose a 130% allocation to the market portfolio as their optimal portfolio.
    • The CAPM requires investors to know the expected return and variance of each security as well as the covariance between all securities.

    Diversification Benefits

    • There are benefits to diversification as long as the correlation coefficient between assets is less than 1.
    • Diversification reduces risk, and the benefits increase as the correlation coefficient decreases.

    Efficient Frontier

    • The efficient frontier represents the set of portfolios that dominate all others in terms of risk and return.
    • The efficient frontier is the set of portfolios with the highest expected return at each level of risk.

    Portfolio Construction

    • A portfolio with a higher return than a similar portfolio with the same risk cannot lie on the efficient frontier.
    • A portfolio with a lower return than a similar portfolio with the same risk cannot lie on the efficient frontier.

    Correlation and Covariance

    • Correlation coefficient measures the relationship between two assets, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation).
    • Covariance measures the extent to which two assets move together, calculated as the product of their standard deviations and correlation coefficient.

    Calculations and Formulas

    • Covariance formula: CovA,B = (rA,B) × (SDA) × (SDB)
    • Correlation coefficient formula: rA,B = CovA,B / (SDA × SDB)

    Risk Reduction and Diversification

    • Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than +1.
    • Diversification reduces risk and increases return, making it a key concept in portfolio management.

    Investor Risk Aversion

    • Investors who are less risk averse have flatter indifference curves, willing to take on more risk for a slightly higher return.
    • Investors who are more risk averse require a much higher return to accept more risk, producing steeper indifference curves.

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    Related Documents

    Portfolio Risk and Return Part I - Answers PDF

    Description

    This quiz assesses your understanding of the efficient frontier in a two-asset portfolio, specifically how correlation between assets affects the frontier. Test your knowledge of portfolio management and risk-return relationships.

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