Question

An investment has a mean return of 10% and a standard deviation of returns equal to 5%. If the distribution of returns is approximately normal, the probability of obtaining a positive return is:

Select one:

A. 84.13%.

B. 97.72%.

C. 99.87%.

Answer 1

An investment has a mean return of 10% and standard deviation return equal to 5%.

The distribution of returns is approximately normal.

To find the probability of obtaining a positive return.

Let, X be the random variable denoting the return; then X follows a normal distribution with mean 10 and standard deviation of 5.

So, (X-10)/5 ~ standard normal distribution, ie. normal(0,1).

To find P(return is positive)

=P(X>0)

=P(X-10>-10)

=P((X-10)/5>-2)

=P(Z>-2)

Where, Z is the standard normal variate.

=1-phi(-2)

=phi(2)

Where, phi is the distribution function of the standard normal variate.

=0.9772 (from the standard normal table)

So, the corresponding percentage is 0.9772*100=97.72%.

So, the probability of obtaining a positive return is (B) 97.72%