Question

Consider the following information about two stocks and indicate which stock has the most systematic risk.

State	Probability	Stock A	Stock B
Recession	0.20	0.11	(0.25)
Norman	0.60	0.18	0.11
Boom	0.20	0.08	0.31

Market risk premium	6.50%
Risk-free rate	5.00%

???

Answer 1

Expected Return

Stock A = 14.60%

Stock B = 7.80%

As per CAPM,

Required Return = Risk Free rate + (Market Return - Risk Free Rate ) * Beta

= Risk Free rate + (Market Risk Premium ) * Beta

For Stock A:

14.60 % = 5% + 6.5% * Beta

or Beta = (14.60 % - 5%) / 6.5%

= 1.476923077

= 1.48

For Stock B:

7.80 % = 5% + 6.5% * Beta

or Beta = (7.8% - 5%) / 6.5%

= 0.43076923

= 0.43

Since the Beta of Stock A is 1.48 which is greater than the Beta of Stock B which is 0.43,stock A has the most systematic risk.

Hence the correct answer is stock A

Note :

Expected Return:

	Probability	Stock AReturn	Expected Return ( Probability * Expected Return)
Recession	0.20	0.11	0.02
Normal	0.60	0.18	0.11
Boom	0.20	0.08	0.02
	Expected Return		0.1460
	Expected Return   %		14.60

	Probability	Stock B Return	Expected Return   ( Probability * Expected Return
Recession	0.20	-0.25	-0.0500
Normal	0.60	0.11	0.0660
Boom	0.20	0.31	0.0620
		Expected Return	0.078
		Expected Return  %	7.80