Question

Suppose a stock has an expected return of 12% and a standard deviation of 6%. What is the likelihood that this stock returns between 12% and 18%

Answer 1

Answer: 34.13%.

Explanation:

Given : Expected return : $\mu=12\%=0.12$

Standard deviation: $\sigma=6\%=0.06$

Let x be the stock returns.

Then, the probability that stock returns between 12% and 18%:

$P(0.12<x<0.18)=P(\dfrac{0.12-0.12}{0.06}<\dfrac{x-\mu}{\sigma}<\dfrac{0.18-0.12}{0.06})\\\\=P(0<Z<1)\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=P(Z<1)-P(Z<0)\\\\=0.8413-0.5\ \ \ \text{[By z-table]}\\\\=0.3413$

Hence, the likelihood that this stock returns between 12% and 18% is 34.13%.