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 14.5%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.1%. 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

Normal average return = 14.5%

Standard deviation of mean return = 4.1%

(a) Here if x is the large cap domestic funds of any random fund

then,

Pr(x > 20%) = 1 - NORMALCDF(x < 20% ; 14.5% , 4.1%)

Z= (20 - 14.5)/4.1= 1.3415

so,

Pr(x > 20%) = 1 - Pr(Z < 1.3415) = 1 - 0.9101 = 0.0899

(b) Pr(x < 10%) = NORMALCDF (x < 10 % ; 14.5% ; 4.1%)

Z = (10 - 14.5)/4.1 = -1.0975

Pr(x < 10%) = NORMALCDF (x < 10 % ; 14.5% ; 4.1%) = Pr(Z < -1.0975) = 0.1362

(c) Here the question writing mathematically,

Pr(x > x0) = 0.10

Pr(x < x0) = 0.90

Z = 1.28155

(x0 - 14.5%)/4.1% = 1.28155

x0 = 14.5 + 4.1 * 1.28155 = 19.75%

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