Quantitative Methods MCQ - Quantitative Methods Section 2

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:

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

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

From the given information, the coefficient of variation is closest to:

The coefficient of variation is: (Standard deviation of return) / (Mean return) = √212 / 12.9 = 1.13

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 return	5.0%
Variance of returns	520

From the given information, the Sharpe Ratio is closest to:

The Sharpe Ratio is: (Return on portfolio – Risk free return)/ (Standard deviation of portfolio) = (15.0 – 5.0) / sqrt (520) = 0.44.

9 The table below shows information about three portfolios:

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

If the risk-free rate is 3%, which portfolio has the highest Sharpe ratio?

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

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 B	12.6%	3.5%
Bond C	14.8%	4.2%

Which of the above bonds is least risky using a relative measure?

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.