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# Standard Deviation of Stock Returns & Market Return

1. The standard deviation of stock returns for Stock A is 30%. The standard deviation of the market return is 20% and the correlation between Stock A and the market is 0.75.

a. Calculate Stock A's beta.
b. In a bull market with rapidly increasing stock prices, will Stock A likely outperform or underperform the average stock? Why?
c. Is the beta of a diversified portfolio less stable or more stable than the beta of a single security? Why?

2. How might a large retailer take advantage of each of the following (Do not merely provide a definition. Provide a specific example of each.):
a. Flexibility option
b. Growth option
c. Investment timing option
d. Abandonment option
e. Decision-tree analysis

#### Solution Preview

1. The standard deviation of stock returns for Stock A is 30%. The standard deviation of the market return is 20% and the correlation between Stock A and the market is 0.75.

a. Calculate Stock A's beta.
Stock Beta = Correlation (A,Market)*Standard Deviation (A)/Standard deviation(Market)
Correlation (A,Market)=0.75
Standard Deviation (A)=30%
Standard deviation(Market)=20%

Stock Beta = 0.75*30%/20%=1.125

b. In a bull market with rapidly increasing stock prices, will Stock A likely outperform or underperform the average stock? Why?
Since the beta of stock A is more than 1, the price of A will increase faster than the average stock in a bull market. Hence, Stock A will outperform.

c. Is the beta of a diversified portfolio less stable or more stable than the beta of a single security? Why?

Beta of a diversified portfolio is more stable than the beta of a single stock. A single security's beta changes over ...

#### Solution Summary

This post answer two questions: stock beta and its behavior; how various capital investment options be used for different purposes.

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