Question

Sandra recentlt invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenerios. She believs that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. Assume the probabilities of the healthy, soft, and recessionary states are 0.4, 0.3, and 0.3, respectively. Calculate the coefficient of variation for investment.

Answer 1

To calculate the coefficient of variation, one must first find the expected return by multiplying each possible return by its probability and summing those products, then compute the variance, and from that, the standard deviation. The coefficient of variation is the standard deviation divided by the expected return.

Step-by-step explanation:

The student is asking how to calculate the coefficient of variation for an investment based on different economic scenarios with associated probabilities. To calculate the expected return, we multiply each return by its probability and sum them up. To find the standard deviation (a measure of risk), we calculate the variance by taking the squared differences between each scenario's returns and the expected return, multiplying by their probabilities, and summing these values - then taking the square root of the sum. The coefficient of variation is the standard deviation divided by the expected return.

The expected return for Sandra's real estate investment would be calculated as:

(0.4 * 0.30) + (0.3 * 0.10) + (0.3 * -0.25) = 0.12 + 0.03 - 0.075 = 0.075 or 7.5%

The variance would be calculated as:

(0.4 * (0.30 - 0.075)²) + (0.3 * (0.10 - 0.075)²) + (0.3 * (-0.25 - 0.075)²) = Value

The standard deviation would be the square root of this variance. Finally, the coefficient of variation is obtained by dividing the standard deviation by the 7.5% expected return.