Question

6. he average return for large-cap domestic stock funds over three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%

1. What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20%?
2. What is the probability an individual large-cap domestic stock fund had a three-year return of 20% of less?
3. How big does the return have to be to put a domestic stock fund in the top 10% for the three-year period?

Answer 1

Solution :

Given that ,

mean = = 14.4% = 0.144

standard deviation = = 4.4% = 0.044

20% = 0.2

P(x   0.2 ) = 1 - P(x   0.2 )

= 1 - P[(x - ) / ( 0.2 - 0.144 ) / 0.044 ]

= 1 -  P(z 1.27)   

  Using z table,

= 1 - 0.8980

= 0.1020

Probability = 0.1020

2.

20% = 0.2

P(x < 0.2 ) = P[(x - ) / < ( 0.2 - 0.144) / 0.044 ]

= P(z < 1.27)

Using z table,

= 0.8980

Probability = 0.8980

3.

The z - distribution of the 10% is,

P(Z > z) = 10%

= 1 - P(Z < z ) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.282 ) = 0.90

z = 1.282

Using z-score formula,

x = z * +

x = 1.282 * 0.044 + 0.144

x = 0.200

Answer : x = 0.200