Investment Portfolio Diversification Quiz
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Questions and Answers

What is the expected return for a portfolio with 40% in Umbrella and 60% in Resort?

  • 14% (correct)
  • 20%
  • 8%
  • 10%

    • Which of the following values corresponds to the standard deviation of the portfolio?

  • 8%
  • 6% (correct)
  • 10%
  • 14%

    • What is the Sharpe Ratio for the complete portfolio with 40% in Umbrella and 60% in Resort?

  • 2
  • 1
  • 0.75
  • 1.5 (correct)

    • How is the covariance between the returns of Umbrella and Resort calculated?

    <p>Using probabilities and variations from expected returns</p> Signup and view all the answers

    With a correlation coefficient of -1, what does this imply about the relationship between two stocks?

    <p>One stock's return varies perfectly inversely with the other's.</p> Signup and view all the answers

    Why is the complete portfolio better than investing 100% in either stock?

    <p>It has a smaller standard deviation.</p> Signup and view all the answers

    What does a correlation of +1 indicate?

    <p>Perfect positive correlation</p> Signup and view all the answers

    What is the value of the covariance calculated for the returns of Umbrella and Resort?

    <p>-0.13125</p> Signup and view all the answers

    What is the expected return of Umbrella stock?

    <p>12.5%</p> Signup and view all the answers

    What is the Sharpe ratio for Resort stock?

    <p>0.29</p> Signup and view all the answers

    Which formula correctly calculates the variance of Umbrella stock based on its expected return?

    <p>$0.5 × (0.5 − 0.125)^2 + 0.5 × (−0.25 − 0.125)^2$</p> Signup and view all the answers

    What weight is allocated to Resort stock in the complete portfolio?

    <p>60%</p> Signup and view all the answers

    How do you calculate the expected return of the complete portfolio?

    <p>By multiplying the probability of each scenario with the return of each asset.</p> Signup and view all the answers

    What is the standard deviation of Resort stock?

    <p>35%</p> Signup and view all the answers

    What is the purpose of calculating the Sharpe ratio in a portfolio?

    <p>To measure the risk-adjusted return of the portfolio.</p> Signup and view all the answers

    What is the risk-free rate used in the Sharpe ratio calculations?

    <p>5%</p> Signup and view all the answers

    What is the primary consideration when evaluating the risk-minimizing portfolio versus a stock portfolio that is 100% in stock?

    <p>The risk-minimizing portfolio has lower risk but also lower expected return.</p> Signup and view all the answers

    What condition indicates that portfolio A dominates portfolio B according to the mean-variance criterion?

    <p>Portfolio A has higher expected return and lower variance.</p> Signup and view all the answers

    What is the benefit of having two assets that are perfectly negatively correlated?

    <p>Reduced standard deviation to zero</p> Signup and view all the answers

    In the context of the mean-variance criterion, what does it mean when a portfolio lies below the minimum-variance portfolio?

    <p>It is considered inefficient and can be rejected.</p> Signup and view all the answers

    What impact does a correlation coefficient of 0 (ρSB = 0) have on the minimum variance portfolio allocation?

    <p>It signifies no interaction between stock and bond returns.</p> Signup and view all the answers

    Which of the following statements is true regarding diversification benefits?

    <p>Greater negative correlation increases diversification benefits.</p> Signup and view all the answers

    What is the expected return for the minimum variance portfolio with perfect negative correlation?

    <p>6.48%</p> Signup and view all the answers

    Which statement best characterizes portfolios that are rejected due to inefficiency on the downward-sloping portion of the curve?

    <p>They are dominated by portfolios with higher expected returns and equal risk.</p> Signup and view all the answers

    In the calculation of portfolio standard deviation, what does a negative correlation coefficient imply?

    <p>Reduced portfolio volatility</p> Signup and view all the answers

    What is the implication of having a minimum variance portfolio with 9.2% in stock and 90.8% in bond?

    <p>The expected return is lower compared to portfolios with higher stock allocation.</p> Signup and view all the answers

    What does the capital allocation line (CAL) represent in a portfolio including a risk-free asset?

    <p>The optimal allocation between risk-free and risky assets</p> Signup and view all the answers

    What directly influences an investor's decision between a risk-minimizing portfolio and a stock portfolio?

    <p>The investor's personal risk aversion levels.</p> Signup and view all the answers

    How can portfolios positioned directly above an inefficient portfolio on the curve be described?

    <p>They provide a better risk-return profile than the inefficient one below.</p> Signup and view all the answers

    When constructing a minimum variance portfolio, what mathematical relationship is utilized?

    <p>$ ext{Std. Dev.}(P) = |w_S imes ext{Std. Dev.}(S) - w_B imes ext{Std. Dev.}(B)|$</p> Signup and view all the answers

    Which factor is critical for selecting the optimal risky portfolio that maximizes returns per unit of risk?

    <p>Sharpe ratio</p> Signup and view all the answers

    What is the weight of asset S in the minimum variance portfolio with the provided conditions?

    <p>0.2963</p> Signup and view all the answers

    What does the optimal risky portfolio represent in asset allocation?

    <p>The portfolio at the tangent point of the efficient frontier.</p> Signup and view all the answers

    Which of the following is an essential task in asset allocation with a risk-free asset and multiple risky assets?

    <p>Selecting an optimal risky portfolio.</p> Signup and view all the answers

    What is the role of the Capital Allocation Line (CAL) in asset allocation?

    <p>It shows the trade-off between risk-free assets and optimal risky portfolios.</p> Signup and view all the answers

    Which statement describes a complete portfolio?

    <p>A mix of risk-free assets and an optimal risky portfolio.</p> Signup and view all the answers

    What does the Sharpe Ratio measure in the context of investment portfolios?

    <p>The risk-adjusted performance of a portfolio.</p> Signup and view all the answers

    Study Notes

    Diversification

    • Umbrella Stock Expected Return: 12.5%
    • Umbrella Stock Standard Deviation: 37.5%
    • Umbrella Stock Sharpe Ratio: 0.2

    Diversification

    • Resort Stock Expected Return: 15%
    • Resort Stock Standard Deviation: 35%
    • Resort Stock Sharpe Ratio: 0.29

    Diversification with Two Risky Assets

    • Portfolio with 40% Umbrella & 60% Resort
      • Rainy Scenario Return: 8%
      • Sunny Scenario Return: 20%
    • Expected Return: 14%
    • Portfolio Standard Deviation: 6%
    • Portfolio Sharpe Ratio: 1.5

    Covariance and Correlation

    • Umbrella Stock - Resort Stock Correlation: -1

    Minimum Variance Portfolio

    • Minimum Variance Portfolio: 9.2% Stocks, 90.8% Bonds
    • This portfolio has a lower risk and lower expected return than a portfolio with only stocks.
    • Which portfolio is preferable depends on the investor's risk aversion.

    Mean-Variance Criterion

    • Investors prefer portfolios with high expected returns and low volatility.
    • Portfolio A dominates portfolio B if portfolio A has higher expected return and lower standard deviation than Portfolio B.
    • The minimum variance portfolio is the point where portfolio volatility starts to increase again.
    • Portfolios on the downward sloping portion of the mean variance curve can be rejected as inefficient.
    • Perfectly negatively correlated assets will have maximum diversification benefits, as the portfolio standard deviation can be reduced to zero.
    • With perfect negative correlation, the portfolio with the lowest risk will have an expected return of 6.48% and a standard deviation of 0.
    • Any portfolio expected return below 6.48% can be rejected as inefficient.

    Asset Allocation with a Risk-Free Asset and Two Risky Assets

    • Investors want the risky portfolio that offers the highest Sharpe Ratio.
    • Combining a risk-free asset with a risky portfolio produces a Capital Allocation Line (CAL).
    • The CAL connects the risk-free asset with the risky portfolio.
    • The optimal risky portfolio is the one that is the tangent point on the CAL, as it offers the highest Sharpe Ratio.

    Asset Allocation with a Risk-Free Asset and Many Risky Assets

    • The asset allocation problem with a risk-free asset and many risky assets is similar to the problem with two risky assets.
    • The problem can be broken down into two tasks:
      • Determining the optimal risky portfolio: the portfolio that maximises the Sharpe ratio
      • Allocating assets between the risk-free asset and the optimal risky portfolio.
    • The optimal risky portfolio is the tangent point on the upward sloping efficient frontier.
    • Investors will choose the highest Sharpe Ratio portfolio and then allocate assets between the risk-free asset and the optimal risky portfolio based on their individual risk tolerance.

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    Related Documents

    MFIN1151 Lecture Notes - Topic 3 - Portfolio Diversification PDF

    Description

    Test your understanding of investment portfolio diversification, including concepts like expected return, standard deviation, and Sharpe ratio. Explore the implications of covariance and the mean-variance criterion to grasp how to assess different investment strategies. This quiz will enhance your awareness of portfolio composition and risk management.

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