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, +11% in moderate growth, and +36% in a boom. Estimates for the market as a whole in the same economic states are -8% in recession, +8% 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.

Answer 1

Return on Drucker (x)	Return on Market (y)	xy	y^2
(16.00)	(8.00)	128.00	64.00
11.00	8.00	88.00	64.00
36.00	21.00	756.00	441.00

Mean return on stock (xm) = (-16+11+36)/3

= 31/3

= 10.33

Mean return on market (ym) = (-8+8+21)/3

= 21/3

= 7.00

Beta = ($\sum$xy-(n*xm*ym)) / ($\sum$y^2-(n*ym*ym))

= (972-(3*10.33*7)) / (569-(3*7*7))

= (972- 216.93 ) / (569- 147 )

= 755.07 / 422

= 1.78926540284

= 1.79