Question

The expected return of a stock is 10 percent and the standard deviation of its returns is 20 percent. What is the probability of loss if the probability distribution of returns is normal.

Select one:

a. 20.00 percent

b. 10.00 percent

c. 30.85 percent

d. 15.86 percent

Answer 1

X - possible returns on the given stock

Expected Return of the stock = μ = 10% = 0.1

Standard Deviation of the stock = 20% = 0.2

We need to calculate the probability of loss which means that return or X < 0. It is given that the probability distribution of returns is normal. So we can convert it into Standard Normal Distribution.

We have to calculate;

P(X<0)

or,

We know that -

Therefore, we need to calculate the probability

Using Standard Normal Chart we get P(Z < -0.5) = 0.308538

We can also use the Excel Function to get the value of Standard Normal [=NORM.S.DIST(-0.5, TRUE)]

Hence the probability of loss if the probability distribution of return is Normal is 30.85 percent.

Answer -> 30.85 percent