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 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.2%.

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) P(At least 20% return)

= P(X > 20)

= P(z > (20 - 14.4)/4.2)

= P(z > 1.33)

= 0.0912

b) P(Less than or equal to 10% return)

= P(X < 10)

= P(z < (10 - 14.4)/4.2)

= P(z < -1.05)

= 0.1474

c) z score corresponding to top 10% area = 1.28

Hence,

Return = 14.4% + 1.28*4.2% = 19.78%

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