Question

Roenfeld Corp believes the following probability distribution exists for its stock. What is the coefficient of variation on the company's stock? Do not round your intermediate calculations. Probability Stock's of State Expected the Economy Occurring Return 0.14 Boom Normal Recession 0.50 0.36 0.5775 0.4725 0.4463 5513

Answer 1

Correct answer is 0.52508059.

Answer is not given in the options.

First we will calculate the mean. The formula for mean is:

Mean = p1 * r1 + p2 * r2 + p3 * r3

where, p1,p2 and p3 are the probabilities and r1,r2 and r3 are the returns.

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

Mean = (0.14 * 25%) + (0.5 * 15%) + (0.36 * 5%)

Mean = 3.5 + 7.5 + 1.8

Mean = 12.8%

Next we will calculate the standard deviation. Steps for calculating standard deviation are:

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

Boom : 25 - 12.8 = 12.2

Normal: 15 - 12.8 = 2.2

Recession 5 - 12.8 = -7.8

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

Boom: (12.2)² = 148.84

Normal: (2.2)² = 4.84

Recession : (-7.8)² = 60.84

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

Boom: 148.84 * 0.14 = 20.8376

Normal growth: 4.84 * 0.5 = 2.42

Recession: 60.84 * 0.36 = 21.9024

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

Variance = 20.8376 + 2.42 + 21.9024 = 45.16

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

Standard deviation = (45.16)^1/2 = 6.72011904656

In the final step, we will calculate the coefficient of variation as per below:

Coefficient of variation = Standard / Mean * 100

Coefficient of variation = 6.72011904656 / 12.8

Coefficient of variation = 0.5250