Quantitative Methods - 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 |
From the given information, the coefficient of variation is closest to:
- Option : A
- Explanation : 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:
- 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.
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?
- 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
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?
- 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.
