Financial analysts have estimated the returns on shares of Drucker Corporation a

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: -18% in recession, +9% in moderate growth, and +35% in a boom. Estimates for the market as a whole in the same economic states are -12% in recession, +10% in moderate growth, and +21% in boom. The analyst considers each state to be equally likely. Using these data, compute the beta of Drucker Corporation's stock.

Explanation / Answer

Drucker Corporation Market Probability Return Prob X Return Return -Mean Return Return Prob X Return Return -Mean Return (Return -Mean Return) Squere Drucker (Return -Mean Return )X Market (Return -Mean Return) 0.33 -18.00 -5.94 -26.93 -12.00 -3.96 -18.48 341.51 497.67 0.33 9.00 2.97 0.07 10.00 3.30 3.52 12.39 0.25 0.34 35.00 11.90 26.07 21.00 7.14 14.52 210.83 378.54 1.00 8.93 6.48 564.73 876.45 Mean of Drucker = 8.93 Mean of Market = 6.48 Variance of Market = 564.73 Cov of Market and Drucker = 876.45 Therefore Beta = Cov of Market and Drucker/Variance of Market = 876.45/564.73 = 1.55

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