Question

1.   Acording to Investment Digest ("Diversificaion and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 16.5%, and the standard deviation of the annual return was 19%.

What is the probability that the stock returns are less than 18.5%?

___      .510

____     .490

_____    .468

______   .542

Answer 1

SOLUTION:

From given data,

According to Investment Digest ("Diversificaion and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 16.5%, and the standard deviation of the annual return was 19%.

We have,

Mean = = 16.5 %

Standard deviation = = 19%

Let us consider the X as a stock returns

Z = (X-) / = (X-16.5) / 19

What is the probability that the stock returns are less than 18.5%?

Where We haven to calculate P(X < 18.5)

P(X < 18.5) = P((X-) / < (18.5-16.5) / 19​​​​​​​)

P(X < 18.5) = P(Z < 2/19​​​​​​​)

P(X < 18.5) = P(Z < 0.105)

P(X < 18.5) = P(Z < 0.10)

P(X < 18.5) = 0 .542 (from z score table)

Answer : 4th option is correct.