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: -18% in recession, 10% in moderate growth, and 30% in a boom. estimates for the market as a whole in the same economic states are -9% in recession, 8% in moderate growth, and 23% in boom. the analyst considers each state to be equally likely. using these data, compute the beta of drucker corporation's stock.

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09-12-2022
Business

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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: -18% in recession, 10% in moderate growth, and 30% in a boom. estimates for the market as a whole in the same economic states are -9% in recession, 8% in moderate growth, and 23% in boom. the analyst considers each state to be equally likely. using these data, compute the beta of drucker corporation's stock.

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-12-17T22:54:40-05:00

The beta of Drucker Corporation's stock Beta is 0.14.

The beta of Drucker Corporation's stock can be calculated using the following formula:

Beta = (Covariance of Drucker Corporation's returns and the market's returns) / (Variance of the market's returns)

Using the data provided, we can calculate the beta of Drucker Corporation's stock by first calculating the covariance and variance of the market's returns, and then calculating the covariance of Drucker Corporation's returns and the market's returns.

Covariance of the market's returns = ( (-9% - 0%) + (8% - 0%) + (23% - 0%) ) / 3 = 8%

Variance of the market's returns = ( (-9% - 0%)^2 + (8% - 0%)^2 + (23% - 0%)^2 ) / 3 = 99%

Covariance of Drucker Corporation's returns and the market's returns = ( (-18% - 0%) + (10% - 0%) + (30% - 0%) ) / 3 = 14%

Therefore, Beta = 14% / 99% = 0.14

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