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    Investment Problems

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    Textbook: Essentials of Investments

    Chapter 5 (1, 2, 13, and 19)

    1. A portfolio of nondividend-paying stocks earned a geometric mean return of 5.0%
    between January 1, 2001, and December 31, 2007. The arithmetic mean return for the
    same period was 6.0%. If the market value of the portfolio at the beginning of 2001 was
    $100,000, what was the market value of the portfolio at the end of 2007?

    2. Which of the following statements about the standard deviation is/are true? A standard
    deviation:
    i. Is the square root of the variance.
    ii. Is denominated in the same units as the original data.
    iii. Can be a positive or a negative number.

    13. An analyst estimates that a stock has the following probabilities of return depending on
    the state of the economy. What is the expected return of the stock? (See Table below)

    State of Economy Probability Return
    Good .1 15%
    Normal .6 13
    Poor .3 7

    For Problems 19-23, assume that you manage a risky portfolio with an expected rate of
    return of 17% and a standard deviation of 27%. The T-bill rate is 7%.

    19. a. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill
    money market fund. What is the expected return and standard deviation of your
    client's portfolio?
    b. Suppose your risky portfolio includes the following investments in the given
    proportions:
    Stock A 27%
    Stock B 33%
    Stock C 40%
    What are the investment proportions of your client's overall portfolio, including the
    position in T-bills?
    c. What is the reward-to-volatility ratio ( S ) of your risky portfolio and your client's
    overall portfolio?
    d. Draw the CAL of your portfolio on an expected return/standard deviation diagram.
    What is the slope of the CAL? Show the position of your client on your fund's CAL.

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    Solution Summary

    The solution explains some investment problems relating to value of portfolio, standard deviation, return on stock and CAL

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