# Quantitative Methods - Quantitative Methods Section 2

>>>>>>>>Quantitative Methods Section 2

• Option : B
• Explanation : Sharpe Ratio = (Portfolio return − Risk free rate) ‚ standard deviation of returns = (0.2 - 0.06) ÷ sqrt(0.025) = 0.89

 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

 Arithmetic mean return 15.0% Geometric mean return 13.2% Portfolio beta 1.22 Risk-free rate of return 5.0% 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.

 Portfolio Mean return onportfolio (%) Standard deviation of the return on the portfolio (%) A 16 32 B 11 15 C 9 8

• 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

 Asset Class Arithmetic mean return(%) Standard deviation of return (%) Bond A 16.4% 4.9% Bond B 12.6% 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.