Question

Historical nominal returns for Company A have been 8% and -20%. The nominal returns for the market index over the same periods were -15% and 28%. Calculate the beta for Company A.

Please include equations used, no excel. Thanks

Answer 1

Probability	Return % (Ra)	Market return % (Rm)	Deviation R(a)	Deviation Rm	D R(a) * D Rm	(Deviation of Rm)2
0.5	8	-15	14	-21.5	-301	462.25
0.5	-20	28	-14	21.5	-301	462.25
					-602	924.5

Average R(a) = 8*0.5-20*0.5

= -6%

Average Rm = -15*0.5+28*0.5

= 6.5%

Covariance = Σ(Deviation of Rm*Deviation of Ra)*Probability

= -301*0.5-301*0.5

= -301

Variance = Σ(Deviation of Rm)2 * Probability

= 462.25*0.5+462.25*0.5

= 462.25

β = -301/462.25

= -0.65

Therefore Beta Coefficient (β) is -0.65