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

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

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%.

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.

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

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

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

A higher Sharpe ratio indicates:

A) a higher excess return per unit of risk.

B) lower volatility of returns.

C) a lower risk per unit of return.

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The Sharpe ratio is excess return (return − Rf) per unit of risk (defined as the standard deviation of returns).

burning0spear

Which of the following statements about statistical concepts is least accurate?

A) The coefficient of variation is useful when comparing dispersion of data measured in different units or having large differences in their means.

B) For a normal distribution, only 95% of the observations lie within ±3 standard deviations from the mean.

C) For any distribution, based on Chebyshev’s Inequality, 75% of the observations lie within ±2 standard deviations from the mean.

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For a normal distribution, 95% of the observations lie within ±2 standard deviations of the mean while 99% of the observations lie within plus or minus three standard deviations of the mean. Both remaining statements are true. Note that 75% of observations for any distribution lie within ±2 standard deviations of the mean using Chebyshev’s inequality.

burning0spear

According to Chebyshev’s Inequality, for any distribution, what is the minimum percentage of observations that lie within three standard deviations of the mean?

A) 94%.

B) 89%.

C) 75%.

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According to Chebyshev’s Inequality, for any distribution, the minimum percentage of observations that lie within k standard deviations of the distribution mean is equal to: 1 – (1 / k2). If k = 3, then the percentage of distributions is equal to 1 – (1 / 9) = 89%.