Question

What is the standard deviation of the returns on a stock given the following information? State of Economy Boom Normal Recession Probability of State of Economy .28 .67 .05 Rate of Return if State Occurs . 175 .128 .026 Multiple Choice 0 3.57 percent 3.28 percent

Answer 1

Option (b) is correct

First we will calculate the mean return as per below:

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 = (0.28 * .175) + (0.67* .128) + (0.05 * .026)

Mean = 0.049 + 0.08576 - 0.0013

Mean = 0.13606

2. Steps for calculating standard deviation are:

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

Boom : 0.175 - 0.13606 = 0.03894

Normal : 0.128 - 0.13606 = - 0.00806

Recession 0.026 - 0.13606 = -0.11006

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

Boom: (0.03894)² = 0.0015163236

Normal: (-0.00806)² = 0.0000649636

Recession : (-0.11006)² = 0.01223236

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

Boom: 0.0015163236 * 0.28 = 0.000424570608

Normal : 0.0000649636 * 0.67 = 0.00043525612

Recession: 0.01223236 * 0.05 = 0.000611618

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

Variance = 0.000424570608 + 0.000043525612 + 0.000611618 = 0.00107971422

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

Standard deviation = (0.00107971422)^1/2 = 0.0328 or 3.28%