burning0spear

A portfolio of options had a return of 22% with a standard deviation of 20%. If the risk-free rate is 7.5%, what is the Sharpe ratio for the portfolio?

A) 0.725.

B) 0.568.

C) 0.147.

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Sharpe ratio = (22% – 7.50%) / 20% = 0.725.

burning0spear

Johnson Inc. manages a growth portfolio of equity securities that has had a mean monthly return of 1.4% and a standard deviation of returns of 10.8%. Smith Inc. manages a blended equity and fixed income portfolio that has had a mean monthly return of 1.2% and a standard deviation of returns of 6.8%. The mean monthly return on Treasury bills has been 0.3%. Based on the Sharpe ratio, the:

A) performance of the Smith portfolio is preferable to the performance of the Johnson portfolio.

B) Johnson and Smith portfolios have exhibited the same risk-adjusted performance.

C) performance of the Johnson portfolio is preferable to the performance of the Smith portfolio.

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The Sharpe ratio for the Johnson portfolio is (1.4 − 0.3)/10.8 = 0.1019.

The Sharpe ratio for the Smith portfolio is (1.2 − 0.3)/6.8 = 0.1324.

The Smith portfolio has the higher Sharpe ratio, or greater excess return per unit of risk.

burning0spear

Portfolio A earned an annual return of 15% with a standard deviation of 28%. If the mean return on Treasury bills (T-bills) is 4%, the Sharpe ratio for the portfolio is:

A) 0.54.

B) 1.87.

C) 0.39.

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(15 − 4) / 28 = 0.39

burning0spear

Which of the following statements regarding the Sharpe ratio is most accurate? The Sharpe ratio measures:

A) excess return per unit of risk.

B) peakedness of a return distrubtion.

C) total return per unit of risk.

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The Sharpe ratio measures excess return per unit of risk. Remember that the numerator of the Sharpe ratio is (portfolio return − risk free rate), hence the importance of excess return. Note that peakedness of a return distribution is measured by kurtosis.

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.