The average return for large tap domestic stock funds over the three years 2009

Question

The average return for large tap domestic stock funds over the three years 2009 2011 was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%. What Is the probability an individual large cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)? What is the probability an individual large-cap domestic stock (und had a three-year return of 10% or less (to 4 decimals)? How big does the return have to be to put a domestic stock fund in the top 10% (or the three-year period (to 2 decimals)?

Explanation / Answer

mean M = 14.4

standard deviation sd = 4.4

a) P(X>20) = 1 - P(Z at X=20) [P(Z) = P((X-M)/sd)]

P(X>20) = 1 - P(Z=(20-14.4)/4.4)

= 1 - P(1.27)

= 1 - 0.8980 (from standard normal distribution table)

= 0.1020

b) P(X<10) = P(Z = (10-14.4)/4.4)

= P(-1)

= 0.1587

c) Top 10% means probability of the value less than that stock value is 0.9

P(Z= (X-14.4)/4.4) = 0.9

so, (X-14.4)/4.4) = 1.28

X = 20.03%

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