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.

Answer 1

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

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%