Quantitative Methods - Quantitative Methods Section 2

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6. A portfolio of large-cap companies’ stocks generated a mean portfolio return of 20% when the risk free rate was 6% in the economy. The variance of portfolio returns was found to be 0.025. The Sharpe ratio of the portfolio is closest to:

  • Option : B
  • Explanation : Sharpe Ratio = (Portfolio return − Risk free rate) ‚ standard deviation of returns = (0.2 - 0.06) ÷ sqrt(0.025) = 0.89
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7. Diana Sorenson, an equity fund manager has the following information about a common stock portfolio:

Arithmetic mean return 12.9%
Geometric mean return 10.3%
Portfolio beta 1.6
Risk-free rate of return 3.50%
Variance of returns 212

  • Option : A
  • Explanation : The coefficient of variation is: (Standard deviation of return) / (Mean return) = √212 / 12.9 = 1.13
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8. An analyst gathered the following information on a common stock portfolio:

Arithmetic mean return 15.0%
Geometric mean return 13.2%
Portfolio beta 1.22
Risk-free rate of return5.0%
Variance of returns 520

  • Option : B
  • Explanation : The Sharpe Ratio is: (Return on portfolio – Risk free return)/ (Standard deviation of portfolio) = (15.0 – 5.0) / sqrt (520) = 0.44.
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9. The table below shows information about three portfolios:

Portfolio Mean return onportfolio (%)Standard deviation of the return on the portfolio (%)
A  1632
B  1115
98

  • Option : C
  • Explanation : The Sharpe ratio is defined as Sp = (Rp- RF)/ p SA = (16 – 3)/32 = 0.40625 SB = (11 – 3)/15 = 0.6 SC = (9 – 3)/8 = 0.75
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10. The table below provides data on annual mean returns and standard deviations

Asset Class 

Arithmetic mean return(%)Standard deviation of return (%)
Bond A  16.4%4.9%
Bond B12.6%3.5%
Bond C  14.8%4.2%

  • Option : B
  • Explanation : In order to find the bond with the lowest risk per unit of return, we need to determine the bond with the lowest coefficient of variation. CV¯ = s/¯X ¯¯ where s is the sample standard de¯ viation¯ and ¯X ¯¯ is the sample mean. Bond A: CV = 4.9 = 0.299 Bond B: CV = 3.5 = 0.277 Bond C: CV = 4.2 = 0.284 Bond B, whose standard deviation and CV are the lowest, is least risky.
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