Portfolio Theory and Risk Management
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Questions and Answers

What is the formula to calculate the expected return of a portfolio?

  • E(rA + B) = wA E(rA) / wB E(rB)
  • E(rA + B) = wA E(rB) + wB E(rA)
  • E(rA + B) = wA E(rA) - wB E(rB)
  • E(rA + B) = wA E(rA) + wB E(rB) (correct)

    • The variance of a portfolio is linear.

    False

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

    cov(A, B) = E(rA - rĀ )(rB - rB̄ )

    Correlations are measured on a scale from ______________ to +1.

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

    What is the goal of the two-step procedure in constructing portfolios?

    <p>Maximize expected return given risk</p> Signup and view all the answers

    Match the following portfolio theory concepts with their definitions:

    <p>Diversification = Reducing risk by combining assets with low correlation Efficient Frontier = A set of optimal portfolios that maximize return given risk Co-movement = The correlation between two assets</p> Signup and view all the answers

    An efficient frontier is a set of portfolios that minimize risk given expected return.

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

    What is the purpose of diversification in portfolio management?

    <p>Reducing risk by combining assets with low correlation</p> Signup and view all the answers

    What is the formula for estimating expected returns under a simplified model for the returns?

    <p>E(r̃) = r̄ = ∑(ri · p(ri))</p> Signup and view all the answers

    The standard deviation of the monthly returns on AAPL is 0.05.

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

    What is the mean monthly return on AAPL?

    <p>0.02402937</p> Signup and view all the answers

    The mean absolute deviation of returns is denoted by ______________.

    <p>MAD(r)</p> Signup and view all the answers

    Match the following measures of risk with their definitions:

    <p>Range = Maximum - minimum Interquartile Range = Q 0.75 - Q 0.25 Mean Absolute Deviation = E |r - E(r)| Variance = E [r - E(r)]2</p> Signup and view all the answers

    Standard deviations are expressed in a different unit of measurement than the returns.

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

    What is the probability that a value will be within 2 standard deviations of the mean?

    <p>95%</p> Signup and view all the answers

    What is a characteristic of expected returns on a portfolio level?

    <p>They are linear.</p> Signup and view all the answers

    What is the Italian word for "to dare"?

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

    The word "feng xian" in Chinese refers to opportunity and danger.

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

    What is key in business according to the provided content?

    <p>Taking risk in an intelligent way</p> Signup and view all the answers

    The price plot of Apple (AAPL) shows the distribution of the returns of an _______________

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

    What is the volume of AAPL in millions on the given plot?

    <p>116,868,600</p> Signup and view all the answers

    The plot shows the returns of AAPL from January 2010 to February 2023.

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

    Match the following risk management strategies with their descriptions:

    <p>Risk avoidance = Eliminating the risk entirely Risk mitigation = Reducing the likelihood of a risk Risk transfer = Transferring the risk to another party Risk retention = Accepting the risk and doing nothing</p> Signup and view all the answers

    What is the concept that deals with the probability of different outcomes of an investment?

    <p>Probability distribution</p> Signup and view all the answers

    Study Notes

    Portfolio Theory

    • The expected return of a portfolio is the weighted average of the expected returns on the individual assets: E(rA + B) = wA E(rA) + wB E(rB)
    • The variance of a portfolio is nonlinear, considering the co-movements between the assets: σ²A + B = wA σ²A + wB σ²B + 2wA wB cov(rA, rB)

    Co-movement

    • Co-movement can be measured using covariances: cov(A, B) = E(rA - rĀ)(rB - rB̄)
    • Co-movement can also be measured using correlations (standardized covariances): ρA,B = covA,B / σAσB

    Efficient Frontier

    • An efficient frontier is a set of portfolios that maximize expected return for a given level of risk or minimize risk for a given level of expected return
    • To construct an efficient frontier, follow a two-step procedure:
    • Build an efficient frontier by maximizing expected return given risk or minimizing risk given expected return
    • Choose one portfolio based on the investor's risk aversion

    Diversification

    • Diversification aims to reduce risk without sacrificing return

    Risk and Return

    • Risk refers to the uncertainty of an investment's outcome
    • In business, taking risk in an intelligent way is key

    Distribution of Returns

    • The distribution of returns of an asset can be illustrated using a price plot
    • The mean monthly return on AAPL is 0.02402937

    Expected Returns

    • An estimator of expected returns is: E(r̃) = r̄ = ∑(ri * p(ri)) / N
    • The mean monthly return on AAPL is 0.02402937

    Measures of Risk

    • Range: maximum - minimum
    • Interquartile range (IQR): Q0.75 - Q0.25
    • Mean Absolute Deviation (MAD): E |r - E(r)|
    • Mean Squared Deviation or Variance: var(r) = E [r - E(r)]²
    • Standard deviation: std(r) = √var(r)
    • The standard deviation of the monthly returns on AAPL is 0.07967378

    Standard Deviation

    • Standard deviations are expressed in the same unit of measurement as the returns
    • Assuming normality, probability statements can be made based on the mean and standard deviation
    • Rules of thumb:
    • Prob(E(X̃) ≠ 1σ < x < E(X̃) + 1σ) ≈ 2/3
    • Prob(E(X̃) ≠ 2σ < x < E(X̃) + 2σ) ≈ 95%
    • Prob(E(X̃) ≠ 3σ < x < E(X̃) + 3σ) ≈ 99%

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    Description

    This quiz covers portfolio theory, including the calculation of expected returns and variances, and the importance of co-movements between assets. It's a part of the Introduction to Financial Markets course.

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