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    Portfolio Risk and Return, Beta, Standard deviation

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    1) Consider the following three investments:

    Security Expected return Standard deviation
    J 0.12 0.4
    K 0.14 0.4
    L 0.13 0.5
    M 0.12 0.3

    Using the mean-variance criteria, identify whether one security dominates or whether there is no dominance for each pssible pair of securities

    2) Tor Johnson has identified the following securities for a portfolio:

    Security Amount invested Expected Return Beta
    A $1,000 0.10 0.75
    B 5000 0.15 1.20
    C 1500 0.12 0.90
    D 2500 0.16 1.30

    Compute the expected return of the portfolio. Compute the beta of the portfolio.

    3) Stock X has a standard deviation of return of 0.6 and stock Y has a standard deviation of 0.4. The correlation of the two stocks is 0.5. Compute the standard deviation of a portfolio invested half in X and half in Y.
    4) The expected standard deviation of market returns is 0.20. Maria Houseman has the following four stocks:
    Standard deviation of market returns= 0.20

    Security Standard deviation Correlation with market
    A 0.30 0.70
    B 0.75 0.30
    C 0.45 0.50
    D 0.50 0.16

    Compute the beta of each stock

    5) The rate of treasury bills is 4% and the equity risk premium is 10%. Use the SML to estimate the return on each of the stocks in problem 4.

    6) Maria has decided to invest $5,000 in each of the stocks in 4). Compute the expected return on the portfolio and the portfolio beta.

    Please see attached file

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    https://brainmass.com/business/capital-asset-pricing-model/portfolio-risk-and-return-beta-standard-deviation-71458

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    Solution Preview

    Please see the attached file.
    1 Standard deviation Expected return
    J 0.4 0.12
    K 0.4 0.14
    L 0.5 0.13
    M 0.3 0.12

    If we plot the expected return against the standard devition we see that
    J has a standard deviation of 0.4 and expected return of 0.12
    K has a standard deviation of 0.4 and expected return of 0.14

    Thus K has a higher return for the same risk (standard deviation)
    K dominates J

    2 Amount invested Expected Return Beta
    A $1,000 0.10 0.75
    B 5000 0.15 1.20
    C 1500 0.12 0.90
    D 2500 0.16 1.30

    Return of portfolio
    r p=summation of wi* ri = w1* r1 + w2*r2+w3r3+w4r4+---
    Beta of portfolio
    beta p=summation of wi* beta i= w1* beta 1 + w2*beta 2+ w3beta 3 + w4beta 4+---

    Amount invested Expected Return Beta
    A $1,000 0.10 0.75
    B 5000 0.15 1.20
    C 1500 0.12 0.90
    D 2500 0.16 1.30

    Amount invested "weights
    (wi)" "Expected Return
    (ri)" wi* ri "Beta ...

    Solution Summary

    Calculates Portfolio return, Portfolio beta, Portfolio standard deviation, Beta of stock etc.

    $2.19

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