Question

You are considering investing in a firm that has the following possible outcomes: economic boom: probability of 25%; return of 25% economic growth: probability of 60%; return of 15% economic decline: probability of 15%; return of -5% what is the standard deviation of returns on the investment?

A. 8.5%

B. 9.5%

C. 10.5%

D. 11.5%

Answer 1

To find the standard deviation, the expected return was first calculated using the given probabilities and returns. Then, the variance was calculated, and the standard deviation was found to be approximately 9.2055%, which closely aligns with answer choice B. 9.5%.

Step-by-step explanation:

To find the standard deviation of returns on the investment, we will first calculate the expected return (mean) and then use it to find the variance and standard deviation. The expected return ER is calculated as:

ER = (Probability1 * Return1) + (Probability2 * Return2) + (Probability3 * Return3)

Let's plug in the given probabilities and returns:

ER = (0.25 * 0.25) + (0.60 * 0.15) + (0.15 * -0.05)

ER = (0.0625) + (0.09) + (-0.0075) = 0.145 or 14.5%

Now, we calculate the variance VAR as:

VAR = (Probability1 * (Return1 - ER)^2) + (Probability2 * (Return2 - ER)^2) + (Probability3 * (Return3 - ER)^2)

VAR = (0.25 * (0.25 - 0.145)^2) + (0.60 * (0.15 - 0.145)^2) + (0.15 * (-0.05 - 0.145)^2)

VAR = (0.25 * 0.011025) + (0.60 * 0.000025) + (0.15 * 0.038025) = 0.00275625 + 0.000015 + 0.00570375 = 0.008475

The standard deviation SD is the square root of VAR:

SD = √0.008475 ≈ 0.092055 (or 9.2055%)

The closest answer choice to our calculated standard deviation is B. 9.5%.