Question

Assume that security returns are generated by the single-index model,

R_i = α_i + β_iR_M + e_i

where R_i is the excess return for security i and R_M is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data:

Security	βi	E(Ri)		σ(ei)
A	0.6	7	%	16	%
B	0.9	10		7
C	1.2	13		10

If σ_M = 10%, calculate the variance of returns of securities A, B, and C.

A:

B:

C:

Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)

A:

B:

C:

Answer 1

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Answer

Security	βi	E(Ri)	σ(ei)	variance	αi^2=βi^2[αM^2}+ αei^2
A	0.6	7%	16%
B	0.9	10	7%
C	1.2	13	10%
Calculating square
				Variance
Security	βi^2	σM2 =18%^2	σ(ei)^2	αi^2=βi^2[αM^2}+ αei^2
A	0.36	100	256	292
B	0.81	100	49	130
C	1.44	100	100	244
	Mean	Variance
Security A	7%	36
Security B	10	81
Security C	13	144