Question

If the economy booms, Meyer&Co. stock will have a return of 18.8 percent. If the economy goes into a recession, the stock will have a loss of 7.9 percent. The probability of a boom is 68 percent while the probability of a recession is 32 percent. What is the standard deviation of the returns on the stock?

Answer 1

First we will calculate the expected return as below:

The formula for expected return is:

Expected return = p1 * r1 + p2 * r2

where, p1,p2 are the probabilities of states of economy and r1,r2 are the expected returns.

Putting the given values in the above formula, we get,

Expected return = (0.68 * 18.8%) + (32% * -7.9%)

Expected return = 12.784 - 2.528

Expected return = 10.256

2. Steps for calculating standard deviation are:

First we will calculate the deviation of returns from the mean return as per below:

Boom : 18.8 - 10.256 = 8.544

Recession -7.9 - 10.256 = -18.156

In the next step, we will square the deviations computed above, as per below:

Boom: (8.544)2 = 72.999936

Recession : (-18.156)2 = 329.640336

In the next step, we will multiply the squared deviations computed above with their probabilities as per below:

Boom: 72.999936 * 0.68 = 49.63995648

Recession: 329.640336 * 0.32 = 105.4849075

In the next step we will add up the values calculated above to find the variance, as per below:

Variance = 49.63995648 + 105.4849075 = 155.124864

In the final step, we will square root the variance calculated above to find the standard deviation:

Standard deviation = (155.124864)1/2 = 12.4549