Quant Statistical Concepts & Mkt Returns problem

CFA Level I Quant
#1

An investor is using a screening program to select stocks. The first criterion is to limit further analysis to the top quintile of companies with return on assets (ROA). Ranking a database of 1,200 firms from lowest to highest ROA produced an array, which is excerpted in the following table.

Rank ROA Rank ROA 958 9.00% 962 10.30% 959 9.20% 963 10.60% 960 9.90% 964 10.70% 961 10.10% 965 10.90%

The top quintile is defined by all firms with a return on assets:

Can someone help me out with this problem, I wasn’t able to follow the explanation given.

#2

Hi,

Here is what I think the anwser:

10.06%

The formula to locate top quintile (which divide distribution to fifths) is 1+N* (Y/100). So your N looks to be 1200. Y is 80 as it is top quintile that divides the distribution to fifths, here 1/5 = .20 and 1-.20 =.80 so lets plug those bad boyz into the formula to locate top quintile: 1200 + 1 * (80/100) =

960.80

So ROA sits between observations 960 and 961. Here we need to perform linear interpolation as 960.80 is not an whole number.

So lets take the ROA for 960 and 961

960 - 9.90%

961 - 10.10%

We need to take the difference between those two percantage ( 10.10% - 9.90%) and multiple it with .80 ( derived from 960.80 - 960) 0.20 * 0.8 = 0.0016

at last we need to add 0.0016 to the ROA on the 960 observation which is 9.9% + 0.0016 =

10.06%

Hope that helps.

#3

Thank you so much, your explanation couldn’t have been any better. You have been a huge help.