Reading 7: Statistical Concepts and Market Returns-LOS i, (P class, div, interpret, standard, return

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Session 2: Quantitative Methods: Basic Concepts
Reading 7: Statistical Concepts and Market Returns

LOS i, (Part 2): Define, calculate, and interpret the Sharpe ratio.

 

 

 

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) 0.568.

B) 0.725.

C) 0.147.

bmaggie

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) 0.568.

B) 0.725.

C) 0.147.

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

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A higher Sharpe ratio indicates:

A) lower volatility of returns.

B) a lower risk per unit of return.

C) a higher excess return per unit of risk.

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A higher Sharpe ratio indicates:

A) lower volatility of returns.

B) a lower risk per unit of return.

C) a higher excess return per unit of risk.

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

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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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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.

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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) 0.56.

B) 1.56.

C) 0.91.

bmaggie

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) 0.56.

B) 1.56.

C) 0.91.

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Sharpe ratio = (R_p – R_f) / σ_p, where (R_p – R_f) is the difference between the portfolio return and the risk free rate, and σ_p 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.

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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%.

bmaggie

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%.