Question

Problem 6.18 Following are the independent situations. Kate recently 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 scenarios. She believes 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. If the probabilities of the healthy, soft, and recessionary states are 0.3, 0.4 , and 0.3 , respectively, then calculate the coefficient of variation for the investment? (Round intermediate calculations and answer to 5 decimal places, e.g. 0.07680.) Coefficient of variation LINK TO TEXT LINK TO TEXT VIDEO CONCPS IN ACTION Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below calculate the coefficient of variation for the investment? (Round intermediate calculations and answer to 5 decimal places, e.g. 0.07680.) Probability Return Boom 0.4 25.00% 15.00% Good 0.1 10.00 Level Slump 02 5.00% Coefficient of variation LINK TO TET LINK TO TEXT ve cocs ACTON Ben would like to invest in gold and is aware that the returns on such an investment can be quite volatile. Use the following table of states, probabilities, and returns and calculate the coefficient of variation for the investment? (Round intermediate calculations and answer to 5 decimal places, e.g. 0.07680.) Probability 0.1 Return Boom Good 02 21% Ok 03 Level 02 Slump 02 Coefficient of variation

Answer 1

Answer to Part A:

Expected Return = 0.30 * 0.30 + 0.40 * 0.10 + 0.30 * (-0.25)
Expected Return = 0.0550

Variance = 0.30 * (0.30 - 0.055)^2 + 0.40 * (0.10 - 0.055)^2 + 0.30 * (-0.25 - 0.055)^2
Variance = 0.046725

Standard Deviation = (0.046725)^(1/2)
Standard Deviation = 0.21616

Coefficient of Variation = Standard Deviation / Expected Return
Coefficient of Variation = 0.21616 / 0.0550
Coefficient of Variation = 3.93018

Answer to Part B:

Expected Return = 0.40 * 0.25 + 0.10 * 0.15 + 0.30 * 0.10 + 0.20 * (-0.05)
Expected Return = 0.1350

Variance = 0.40 * (0.25 - 0.135)^2 + 0.10 * (0.15 - 0.135)^2 + 0.30 * (0.10 - 0.135)^2 + 0.20 * (-0.05 - 0.135)^2
Variance = 0.012525

Standard Deviation = (0.012525)^(1/2)
Standard Deviation = 0.111915

Coefficient of Variation = Standard Deviation / Expected Return
Coefficient of Variation = 0.111915 / 0.1350
Coefficient of Variation = 0.82900

Answer to Part C:

Expected Return = 0.10 * 0.36 + 0.20 * 0.21 + 0.30 * 0.08 + 0.20 * 0.03 + 0.20 * (-0.08)
Expected Return = 0.0920

Variance = 0.10 * (0.36 - 0.092)^2 + 0.20 * (0.21 - 0.092)^2 + 0.30 * (0.08 - 0.092)^2 + 0.20 * (0.03 - 0.092)^2 + 0.20 * (-0.08 - 0.092)^2
Variance = 0.016696

Standard Deviation = (0.016696)^(1/2)
Standard Deviation = 0.129213

Coefficient of Variation = Standard Deviation / Expected Return
Coefficient of Variation = 0.129213 / 0.0920
Coefficient of Variation = 1.40449