The average return for large-cap domestic stock funds over the three years 2009–

Question

The average return for large-cap domestic stock funds over the three years 2009–2011 was 14.2%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.9%.

a. What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)?

b. What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less (to 4 decimals)?

c. How big does the return have to be to put a domestic stock fund in the top 10% for the three-year period (to 2 decimals)?
%

Explanation / Answer

a) Mean = 14.2

SD = 4.9

z = (20 - 14.2)/4.9

z = 1.22

P = 0.1112

b) z = (10 - 14.2)/4.9

z = -0.857

P = 0.1949

c) z for top 10% = 1.28

(x - 14.2)/4.9 = 1.28

x = 20.47%

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