The following table shows the volatility of a series of funds that belong to the same peer group, ranked in ascending order:
A is correct. First, find the position of the first quintile with the following formula:
Ly = (n + 1) × (y / 100),
Where
y is the percentage point at which we are dividing the distribution. In our case we have y = 20, which corresponds to the 20th percentile (first quintile);
n is the number of observations (funds) in the peer group. In our case we have n = 13;
L20 corresponds to the location of the 20th percentile (first quintile).
L20 = (13 + 1) × (20/100) = 2.80.
Therefore, the location of the first quintile is between the volatility of Fund 2 and Fund 3 (because they are ranked in ascending order). Then, use linear interpolation to find the approximate value of the first quintile:
P20 ≈ X2 + (2.80 – 2) × (X3– X2 ),
where
X2 is the volatility of Fund 2
X3 is the volatility of Fund 3
P20 is the approximate value of the first quintile
P20 ≈ 10.12% + (2.80 – 2) × (10.84% –10.12%) = 10.70%