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# Calculating expected return and standard deviation

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1. Buxton Corporation is planning to invest in a security that has several potential rates of return. Using the following probability distribution of returns during different states of the economy, what is the expected rate of return on this investment? In addition, compute the standard deviation of the returns. Finally, briefly explain what these numbers represent.

Probability Expected Return
0.10 -10%
0.20 5%
0.30 10%
0.40 25%

2. Using the capital asset pricing model (CAPM), estimate the appropriate required rate of return for the following three stocks, assuming that the risk-free rate (rRF) is 5 percent and the expected return for the market (rM) is 17 percent.

Stock Beta
A 0.75
B 0.90
C 1.40

3. Based on the following table of actual (or ex post) returns for both Inquiry Corporation and the market from 2007 through 2010, calculate the average return and the standard deviation for both Inquiry and the market (keep in mind that this data is historical and not based on a probability distribution, so be sure to use the correct formulas).

Year Inquiry Corporation Market
2007 4% 2%
2008 6% 3%
2009 0% 1%
2010 2% -1%

4. (a) Derive the expected return (rP) and beta (?P) for a portfolio based on the following information:

Stock Percentage of Portfolio Beta Expected Return
1 40% 1.00 12%
2 25% 0.75 11%
3 35% 1.30 15%

(b) Given the information in the table above, present the equation for the security market line and explain where the return for this specific portfolio would lie (plot) relative to the SML (i.e., below or above the line). Assume that the risk-free rate (rRF) is 8 percent and that the expected return on the market portfolio (rM) is 12 percent.

5. Reliable Printing is evaluating a security. One-year Treasury bills (rRF) are currently paying 3.1 percent. Calculate the following investment's expected return and its standard deviation. Should Reliable Printing invest in this security? Briefly explain.

Probability Expected Return
0.15 -1%
0.30 2%
0.40 3%
0.15 8%