A bank was reviewing the 2017 performance of traders working at its trade desk.

Question

A bank was reviewing the 2017 performance of traders working at its trade desk. It standardized the returns for all traders by computing the annual return for each trader per $100,000 invested. The resulting histogram had a Normal shape with mean = $13,721 and standard deviation = $5,898.

(a) What return did a trader need to obtain in order to be classified among the top 25% of traders at this bank? (Rounding to the nearest integer is sufficient, although you may enter more decimals if you prefer.)  

(b) The top 1%?  

(c) Compute the IQR of these annual returns:  

Explanation / Answer

a) z score corresponding to top 25% of the area = 0.67

Hence,

Return that top 25% traders get = 13721 + 0.67*5898 = $ 17673

b) z score corresponding to top 1% of the area = 2.33

Hence,

Return that top 25% traders get = 13721 + 2.33*5898 = $ 27463

c) z score for bottom 25% area = -0.67

Hence,

Q1 = 13721 - 0.67*5898 = $ 9769

From part c), Q3 = $ 27463

Hence,

IQR = Q3 - Q1 = $ 27463 - $ 9769 = $ 17694

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