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 14.3%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.6%. Use Table 1 in Appendix B.

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

mean is 14.3 and SD is 4.6

a) P(x>20)=P(z>(20-14.3)/4.6)=P(z>1.24) =1-P(z<1.24), from normal distrbution table it is 1-0.8925=0.1075

b) P(x<10)=P(z<(10-14.3)/4.6)=P(z<-0.93) or 1-P(z<0.93)=1-0.8238=0.1762

c) P(x>c)=0.1 or 1-P(x<c)=0.1 or P(x<c)=0.9

from normal distribution table, z for 0.9 probability is 1.29

thus (c-14.3)/4.6=1.29 thus c is 1.29*4.6+14.3=20.234

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