Portfolio Return and Risk Metrics Quiz
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Questions and Answers

Which term contributes the most to the portfolio variance?

  • $2(0.50)(0.25)(45)$
  • $2(400)$
  • $2(0.50)(0.25)(189)$ (correct)
  • $2(0.25)(0.25)(38)$

    • What is the standard deviation of return for the portfolio?

  • 11.75%
  • 195.8751/2
  • 11.52%
  • 14% (correct)

    • What is the expected annual return of the portfolio?

  • 195.8751/2
  • 132.625
  • 14%
  • 11.75% (correct)

    • What is the sum of the first three terms in the calculation?

    <p>132.625</p> Signup and view all the answers

    If the returns on the three assets were independent, what would be the standard deviation of portfolio return?

    <p>11.52%</p> Signup and view all the answers

    What is the risk reduction benefit from holding a portfolio of assets called?

    <p>Diversification benefit</p> Signup and view all the answers

    What is the key insight of modern portfolio theory?

    <p>Diversification benefit</p> Signup and view all the answers

    What would happen to portfolio variance and risk if the covariance terms were negative?

    <p>They would decrease</p> Signup and view all the answers

    What does the diversification benefit increase with?

    <p>Decreasing covariance</p> Signup and view all the answers

    What concept is even more intuitively stated when discussing the diversification benefit?

    <p>Correlation benefit</p> Signup and view all the answers

    Which of the following is used as a measure of reward in modern portfolio theory?

    <p>Expected return</p> Signup and view all the answers

    What is the expected return on a portfolio?

    <p>A weighted average of the expected returns on the securities in the portfolio</p> Signup and view all the answers

    Which equation represents the calculation of portfolio expected return?

    <p>$E(Rp) = w1E(R1) + w2E(R2) + …+wnE(Rn)$</p> Signup and view all the answers

    What is the formula for portfolio variance of return?

    <p>$σ2(Rp) = E{[RpE(Rp)]2}$</p> Signup and view all the answers

    Which equation is used to calculate the expected return on the portfolio in the given example?

    <p>$E(Rp) = 0.50(13%) + 0.25(6%) + 0.25(15%)$</p> Signup and view all the answers

    What is used as a measure of investment risk in modern portfolio theory?

    <p>Portfolio variance of return</p> Signup and view all the answers

    What is the formula for portfolio variance in a forward-looking sense?

    <p>$σ2(Rp) = E{[RpE(Rp)]2}$</p> Signup and view all the answers

    What are the weights used in the calculation of portfolio expected return?

    <p>The respective proportions of the portfolio in currency units</p> Signup and view all the answers

    What is the measure of risk used in modern portfolio theory?

    <p>Variance of return</p> Signup and view all the answers

    What is the equation for portfolio expected return?

    <p>$E(Rp) = w1E(R1) + w2E(R2) + …+wnE(Rn)$</p> Signup and view all the answers

    Which equation represents the covariance between two random variables Ri and Rj?

    <p>Cov(Ri ,Rj) = E[(Ri − ERi)(Rj − ERj)]</p> Signup and view all the answers

    What is the formula for the sample covariance between two random variables Ri and Rj?

    <p>Cov(Ri ,Rj) = ∑n=1 n (Ri,t , _ R i)(Rj,t − E _ R j) ⁄ (n − 1)</p> Signup and view all the answers

    What is the equation for the variance of a three-asset portfolio?

    <p>σ2(Rp) = w12σ2(R1) + w1w2Cov(R1,R2) + w1w3Cov(R1,R3) +w1w2Cov(R1,R2) + w22σ2(R2) + w2w3Cov(R2,R3) +w1w3Cov(R1,R3) + w2w3Cov(R2,R3) + w23σ2(R3)</p> Signup and view all the answers

    What is the most compact way to state Equation 5, which represents the variance of a portfolio?

    <p>σ2(Rp) = ∑i=1 3 ∑j=1 3 wiwjCov(Ri ,Rj)</p> Signup and view all the answers

    What is the general equation for the variance of a portfolio of any size n?

    <p>σ2(Rp) = ∑i=1 n ∑j=1 n wiwjCov(Ri ,Rj)</p> Signup and view all the answers

    What does covariance measure?

    <p>How the co-movements of returns affect aggregate portfolio variance</p> Signup and view all the answers

    Which equation represents the calculation of portfolio variance in a forward-looking sense?

    <p>$\sigma^2(R_p) = \sum_{i=1}^3 \sum_{j=1}^3 w_i w_j Cov(R_i, R_j)$</p> Signup and view all the answers

    Which term contributes the most to the portfolio variance?

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

    What is the measure of risk used in modern portfolio theory?

    <p>Standard deviation</p> Signup and view all the answers

    What is the expected annual return of the portfolio?

    <p>$E(R_p)$</p> Signup and view all the answers

    What are the weights used in the calculation of portfolio expected return?

    <p>$w_1, w_2, w_3$</p> Signup and view all the answers

    What is the key insight of modern portfolio theory?

    <p>Diversification can reduce risk</p> Signup and view all the answers

    What is the formula for portfolio variance of return?

    <p>$\sigma^2(R_p) = \sum_{i=1}^3 \sum_{j=1}^3 w_i w_j Cov(R_i, R_j)$</p> Signup and view all the answers

    What is used as a measure of investment risk in modern portfolio theory?

    <p>Standard deviation</p> Signup and view all the answers

    What is the standard deviation of return for the portfolio?

    <p>$\sigma(R_p)$</p> Signup and view all the answers

    What is the equation for portfolio expected return?

    <p>$E(R_p) = w_1 E(R_1) + w_2 E(R_2) + w_3 E(R_3)$</p> Signup and view all the answers

    Study Notes

    Portfolio Variance and Risk

    • The covariance term contributes the most to the portfolio variance.
    • The standard deviation of return for the portfolio is a measure of investment risk.
    • The expected annual return of the portfolio is the sum of the weighted returns of individual assets.

    Modern Portfolio Theory

    • The key insight of modern portfolio theory is that the risk of a portfolio can be reduced through diversification.
    • Diversification benefit increases with the number of assets in the portfolio.
    • The concept of diversification benefit is more intuitively stated when discussing the risk reduction benefit of holding a portfolio.

    Portfolio Return and Variance

    • The expected return on a portfolio is the sum of the weighted returns of individual assets.
    • The formula for portfolio variance of return is: variance = w1^2 * σ1^2 + w2^2 * σ2^2 + w3^2 * σ3^2 + 2 * w1 * w2 * σ1 * σ2 + 2 * w1 * w3 * σ1 * σ3 + 2 * w2 * w3 * σ2 * σ3.
    • The formula for portfolio variance in a forward-looking sense is: variance = w1^2 * σ1^2 + w2^2 * σ2^2 + w3^2 * σ3^2 + 2 * w1 * w2 * σ1 * σ2 + 2 * w1 * w3 * σ1 * σ3 + 2 * w2 * w3 * σ2 * σ3.
    • The equation for portfolio expected return is: E(Rp) = w1 * E(R1) + w2 * E(R2) + w3 * E(R3).
    • The weights used in the calculation of portfolio expected return are the proportions of each asset in the portfolio.

    Covariance and Risk

    • Covariance measures the linear relationship between two random variables.
    • The formula for the sample covariance between two random variables Ri and Rj is: cov(Ri, Rj) = Σ{(Ri - E(Ri)) * (Rj - E(Rj))} / (n - 1).
    • The equation for the variance of a three-asset portfolio is: variance = w1^2 * σ1^2 + w2^2 * σ2^2 + w3^2 * σ3^2 + 2 * w1 * w2 * σ1 * σ2 + 2 * w1 * w3 * σ1 * σ3 + 2 * w2 * w3 * σ2 * σ3.
    • The general equation for the variance of a portfolio of any size n is: variance = Σ{wi^2 * σi^2} + 2 * Σ{wi * wj * σi * σj}.

    Risk Reduction

    • If the returns on the three assets were independent, the standard deviation of portfolio return would be lower.
    • If the covariance terms were negative, portfolio variance and risk would decrease.
    • The measure of risk used in modern portfolio theory is standard deviation.

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    Test your knowledge of portfolio return and risk metrics with this quiz. Explore the concepts of expected return and variance of return in modern portfolio theory.

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