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: -16% in recession, +8% in moderate growth, and +36% in a boom. Estimates for the market as a whole in the same economic states are -10% in recession, +10% 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.

Explanation / Answer

Beta =AB /B^2

   = 853.3333/552.6667

= 1.54

Average return for stock = [-16+8+36]/3= 9.33%

Average return for market = [-10+10+23]/3= 7.67%

Nature Stock(X) Market(Y) A=(X-average return) B=(Y-average return) AB B^2 Recession -16 -10 -16-9.33=-25.33 -10-7.67=-17.67 447.5811 312.2289 Moderate 8 10 8-9.33= -1.33 10-7.67= 2.33 -3.0989 5.4289 Boom 36 23 36-9.33=26.67 23-7.67= 15.33 408.8511 235.0089 853.3333 552.6667

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