Question

Financial analysts have estimated the returns on shares of Drucker Corporation and the overall market portfolio under various economic conditions as follows. The return for Drucker in the following three economic states of nature are forecasted to be: -15% in recession, +9% in moderate growth, and +36% in a boom. Estimates for the market as a whole in the same economic states are -12% in recession, +7% in moderate growth, and +25% in boom. The analyst considers each state to be equally likely. Using these data, compute the beta of Drucker Corporation's stock.

Place your answer as a number with at least three decimal places.

Answer 1

To compute the beta of Drucker Corporation's stock, we need to calculate the expected return and the variance of Drucker's stock and the market portfolio. By using the given data, we can calculate the beta.

Step-by-step explanation:

To compute the beta of Drucker Corporation's stock, we need to calculate the expected return and the variance of Drucker's stock and the market portfolio. First, let's calculate the expected return:

• Expected return of Drucker Corporation = (-15% * 1/3) + (9% * 1/3) + (36% * 1/3) = 10%
• Expected return of the market portfolio = (-12% * 1/3) + (7% * 1/3) + (25% * 1/3) = 6.67%

Next, let's calculate the variance:

• Variance of Drucker Corporation = [(Return in recession - Expected return)^2 * 1/3] + [(Return in moderate growth - Expected return)^2 * 1/3] + [(Return in boom - Expected return)^2 * 1/3]
• Variance of the market portfolio = [(Return in recession - Expected return)^2 * 1/3] + [(Return in moderate growth - Expected return)^2 * 1/3] + [(Return in boom - Expected return)^2 * 1/3]

Finally, the beta of Drucker Corporation's stock can be calculated as:

• Beta = Variance of Drucker Corporation / Variance of the market portfolio

By using the given data, we can calculate the beta.