manchester88

The mean monthly return on U.S. Treasury bills (T-bills) is 0.42%. The mean monthly return for an index of small stocks is 4.56%, with a standard deviation of 3.56%. What is the Sharpe measure for the index of small stocks?

A) 1.16%.

B) 16.56%.

C) 10.60%.

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The Sharpe ratio measures excess return per unit of risk. (4.56 – 0.42) / 3.56 = 1.16%.

manchester88

Portfolio A earned a return of 10.23% and had a standard deviation of returns of 6.22%. If the return over the same period on Treasury bills (T-bills) was 0.52% and the return to Treasury bonds (T-bonds) was 4.56%, what is the Sharpe ratio of the portfolio?

A) 1.56.

B) 0.56.

C) 0.91.

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Sharpe ratio = (Rp – Rf) / σp, where (Rp – Rf) is the difference between the portfolio return and the risk free rate, and σp is the standard deviation of portfolio returns. Thus, the Sharpe ratio is: (10.23 – 0.52) / 6.22 = 1.56. Note, the T-bill rate is used for the risk free rate.

manchester88

A portfolio has a return of 14.2% and a Sharpe’s measure of 3.52. If the risk-free rate is 4.7%, what is the standard deviation of returns?

A) 3.9%.

B) 2.6%.

C) 2.7%.

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Standard Deviation of Returns = (14.2% – 4.7%) / 3.52 = 2.6988.

manchester88

Given a population of 200, 100, and 300, the coefficient of variation is closest to:

A) 30%.

B) 40%.

C) 100%.

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CV = (σ/mean)
mean = (200 + 100 + 300)/3 = 200
σ = √[(200 - 200)2 + (100 - 200)2 + (300 - 200)2 / 3] = √6666.67 = 81.65
(81.65/200) = 40.82%

manchester88

The mean monthly return on (U.S. Treasury bills) T-bills is 0.42% with a standard deviation of 0.25%. What is the coefficient of variation?

A) 60%.

B) 84%.

C) 168%.

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The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean, or 0.25 / 0.42 = 0.595, or 60%.

manchester88

An investor is considering two investments. Stock A has a mean annual return of 16% and a standard deviation of 14%. Stock B has a mean annual return of 20% and a standard deviation of 30%. Calculate the coefficient of variation (CV) of each stock and determine if Stock A has less dispersion or more dispersion relative to B. Stock A's CV is:

A) 1.14, and thus has more dispersion relative to the mean than Stock B.

B) 1.14, and thus has less dispersion relative to the mean than Stock B.

C) 0.875, and thus has less dispersion relative to the mean than Stock B.

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CV stock A = 0.14 / 0.16 = 0.875
CV stock B = 0.30 / 0.20 = 1.5
Stock A has less dispersion relative to the mean than Stock B.

manchester88

The mean monthly return on a sample of small stocks is 4.56% with a standard deviation of 3.56%. What is the coefficient of variation?

A) 78%.

B) 128%.

C) 84%.

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The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean. 3.56 / 4.56 = 0.781, or 78%.

manchester88

If stock X's expected return is 30% and its expected standard deviation is 5%, Stock X's expected coefficient of variation is:

A) 0.167.

B) 6.0.

C) 1.20.

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The coefficient of variation is the standard deviation divided by the mean: 5 / 30 = 0.167.

manchester88

What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?

A) 40%.

B) 25%.

C) 20%.

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Coefficient of variation, CV = standard deviation / mean. The standard deviation is the square root of the variance, or 4½ = 2. So, CV = 2 / 10 = 20%.

manchester88

If the historical mean return on an investment is 2.0% and the standard deviation is 8.8%, what is the coefficient of variation (CV)?

A) 1.76.

B) 6.80.

C) 4.40.

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The CV = the standard deviation of returns / mean return or 8.8% / 2.0% = 4.4.