Quantitative Methods MCQ - Quantitative Methods Section 1

56 A portfolio manager is computing the weighted mean of a portfolio, whose asset allocation as of 31 December, 2012, is given below: Local Equities: 25% International Equities: 13%

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:

Mean portfolio return is the weighted average of each asset class' returns.

57 Judith Owen buys a share for $45 on January 1, 2011. The price of the share is $54 on January 1, 2012 and $63 on January 1, 2013. Assuming no dividends were paid, which of the following best represent the geometric mean annual return earned by Owen over the two year period?

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%

58 Judith Owen buys a share for $45 on January 1, 2011. The price of the share is $54 on January 1, 2012 and $63 on January 1, 2013. Assuming no dividends were paid, which of the following best represent the geometric mean annual return earned by Owen over the two year period?

59 If all the observations in a data set have different values, then which of the following relationships is most accurate?

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.

60 The following table shows the returns of various stocks of a portfolio, ranked in ascending order:

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:

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%