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: -15% in recession, +9% in moderate growth, and +30% in a boom. Estimates for the market as a whole in the same economic states are -8% 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

Calculation of Beta (β):

State	Probability	Drucker Corporation	Market	Deviation of Drucker's return	Deviation of Market returns	Deviation of Drucker's return* Deviation of Market return	(Deviation of Market returns)2
Recession	1/3	-15	-8	-23	(16.33)	375.67	266.78
Moderate	1/3	9	10	1	1.67	1.67	2.78
Boom	1/3	30	23	22	14.67	322.67	215.11
		24	25			700	484.67

Average R_Drucker = -15*1/3+9*1/3+30*1/3

= 8%

Average Rm = -8*1/3+10*1/3+23*1/3

= 8.33%

Covariance = Σ(Deviation of R_market*Deviation of R_Drucker)*Probability

= 375.67*1/3+1.67*1/3+322.67*1/3

= 700/3

= 233.33

Variance = Σ(Deviation of Rm)² * Probability

= 266.78*1/3+2.78*1/3+215.11*1/3

= 484.67/3

= 161.56

β = Covariance with market return/Variance of market returns

233.33/161.56

= 1.44

Therefore Beta Coefficient (β) is 1.44