Quantitative Methods - Quantitative Methods Section 1
| Bonds: | 27% |
| Mortgage: | 18% |
| Gold: | 17% |
The returns on the above assets on 31 December, 2012, were 5.4%, 8.9%, - 2.5%, -7%, and 11% respectively. The mean return earned by the portfolio is closest to:
- Option : A
- Explanation : Mean portfolio return is the weighted average of each asset class' returns.
- Option : A
- Explanation : First, calculate the holding period returns at the end of year 1 and year 2. Geometric Mean = [(1 + 0.2)(1 + 0.1667)]0.5 − 1 = 18.32%
- Option : C
- Explanation : Unless all observations in a data set are equal, the harmonic mean is less than the geometric mean which is less than the arithmetic mean.
| Stock | Return (%) | Stock | Return (%) |
| Stock 1 | 10.50 | Stock 6 | 14.24 |
| Stock 2 | 11.25 | Stock 7 | 14.75 |
| Stock 3 | 12.05 | Stock 8 | 15.30 |
| Stock 4 | 12.65 | Stock 9 | 16.00 |
| Stock 5 | 13.55 | Stock 10 | 17.45 |
The value of the third quintile is closest to:
- Option : B
- Explanation : The position of the third quintile can be found through the following formula: Ly = (n + 1) ∗ ( y ); Where, y is the percentage point at which we are dividing the distribution. Here, y = 60, the 60th percentile (third quintile); n = 10 L60 = (10 + 1) ∗ ( 60 ) = 6.6; Therefore, the location of the third quintile is between the return of Stock 6 and Stock 7. Linear interpolation is used for finding the approximate value of the third quintile. In the above case, return on the 6th stock is 14.24% and on the 7th stock is 14.75%. L60 = 14.55% which is 14.24% (6 th value) plus 0.6 times the linear distance between 14.24% and 14.75%
