# Question

In the book Foundations of Financial Management ( 7th ed.), Stanley B. Block and Geoffrey A. Hirt discuss risk measurement for investments. Block and Hirt present an investment with the possible outcomes and associated probabilities given in Table 5.2. The authors go on to say that the probabilities may be based on past experience, industry ratios and trends, interviews with company executives, and sophisticated simulation techniques. The probability values may be easy to determine for the introduction of a mechanical stamping process in which the manufacturer has 10 years of past data, but difficult to assess for a new product in a foreign market.

a. Use the probability distribution in Table 5.2 to calculate the expected value ( mean) and the standard deviation of the investment outcomes. Interpret the expected value. DS

b. Block and Hirt interpret the standard deviation of the investment outcomes as follows: “Generally, the larger the standard deviation ( or spread of outcomes), the greater is the risk.” Explain why this makes sense. Use Chebyshev’s Theorem to illustrate your point.

c. Block and Hirt compare three investments having the following means and standard deviations of the investment outcomes:

Which of these investments involves the most risk? The least risk? Explain why by using Chebyshev’s Theorem to compute an interval for each investment that will contain at least 8 9 of the investment outcomes.

d. Block and Hirt continue by comparing two more investments:

Investment A Investment B

µ$ 6,000....... µ $ 600

σ $ 600....... σ $ 190

The authors explain that Investment

A appears to have a high standard deviation, but not when related to the expected value of the distribution. A standard deviation of $ 600 on an investment with an expected value of $ 6,000 may indicate less risk than a standard deviation of $ 190 on an investment with an expected value of only $ 600. We can eliminate the size difficulty by developing a third measure, the coefficient of variation (V). This term calls for nothing more difficult than dividing the standard deviation of an investment by the expected value. Generally, the larger the coefficient of variation, the greater is the risk.

Coefficient of variation (V) = σ/ µ

Calculate the coefficient of variation for investments A and B. Which investment carries the greater risk?

e. Calculate the coefficient of variation for investments 1, 2, and 3 in part c. Based on the coefficient of variation, which investment involves the most risk? The least risk? Do we obtain the same results as we did by comparing standard deviations ( in part c)? Why?

a. Use the probability distribution in Table 5.2 to calculate the expected value ( mean) and the standard deviation of the investment outcomes. Interpret the expected value. DS

b. Block and Hirt interpret the standard deviation of the investment outcomes as follows: “Generally, the larger the standard deviation ( or spread of outcomes), the greater is the risk.” Explain why this makes sense. Use Chebyshev’s Theorem to illustrate your point.

c. Block and Hirt compare three investments having the following means and standard deviations of the investment outcomes:

Which of these investments involves the most risk? The least risk? Explain why by using Chebyshev’s Theorem to compute an interval for each investment that will contain at least 8 9 of the investment outcomes.

d. Block and Hirt continue by comparing two more investments:

Investment A Investment B

µ$ 6,000....... µ $ 600

σ $ 600....... σ $ 190

The authors explain that Investment

A appears to have a high standard deviation, but not when related to the expected value of the distribution. A standard deviation of $ 600 on an investment with an expected value of $ 6,000 may indicate less risk than a standard deviation of $ 190 on an investment with an expected value of only $ 600. We can eliminate the size difficulty by developing a third measure, the coefficient of variation (V). This term calls for nothing more difficult than dividing the standard deviation of an investment by the expected value. Generally, the larger the coefficient of variation, the greater is the risk.

Coefficient of variation (V) = σ/ µ

Calculate the coefficient of variation for investments A and B. Which investment carries the greater risk?

e. Calculate the coefficient of variation for investments 1, 2, and 3 in part c. Based on the coefficient of variation, which investment involves the most risk? The least risk? Do we obtain the same results as we did by comparing standard deviations ( in part c)? Why?

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