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Range of Returns

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a) Explain why the geometric and arithmetic mean returns are not equal and whether one or the other may be more useful for investment decision making.

b) For the time period indicated, rank these investments on a risk-adjusted basis from most to least desirable. Explain your rationale.

c) Assume the returns in these series are normally distributed.

1. Calculate the range of returns that an investor would have expected to achieve 95 percent of the time holding common stocks.

2. Suppose an investor holds real estate for this time period. Determine the probability of at least breaking even on this investment.

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Expected returns Stocks X and Y have the following probability distributions of expected future returns

Please assist me in accurately answering the following questions. I am having a difficult time solving the questions.

8-6 Expected returns Stocks X and Y have the following probability distributions of
expected future returns:

Probability X Y

0.1 (10%) (35%)
0.2 2 0
0.4 12 20
0.2 20 25
0.1 38 45

a. Calculate the expected rate of return, r?Y, for Stock Y. (r?X _ 12%.)
b. Calculate the standard deviation of expected returns, _X , for Stock X. (_Y _ 20.35%.)Now calculate the coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than Stock X? Explain.

8-20 Realized rates of return Stocks A and B have the following historical returns:

Year Stock A's Returns, rA Stock B's Returns, rB

2001 (18.00%) (14.50%)
2002 33.00 21.80
2003 15.00 30.50
2004 (0.50) (7.60)
2005 27.00 26.30

a. Calculate the average rate of return for each stock during the period 2001 through 2005.
b. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would the realized rate of return on the portfolio have been in each year? What would the average return on the portfolio have been during this period?
c. Calculate the standard deviation of returns for each stock and for the portfolio.
d. Calculate the coefficient of variation for each stock and for the portfolio.
e. Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

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