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 4%. Suppose also that there are three securities A, B, and C, characterized by the following data:

Security	βi	E(Ri)		σ(ei)
A	0.8	15	%	24	%
B	1.1	18		15
C	1.4	21		18

a. If σ_M = 20%, calculate the variance of returns of securities A, B, and C.

Security A=

Security B=

Security C=

b. 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.)

	Mean	Variance
Security A
Security B
Security C

Answer 1

a)

variance can be found by the following formula

variance = (beta * standard deviation of market)^2 + (standard deviation of error term)^2

for security A = (0.8*20)^2 + 24^2 = 832

Security B = (1.1*20)^2 + 15^2 = 709

Security C = (1.4*20)^2 + 18^2 = 1108

b)

if there are infinite number of assets with rerturn characteristics identical, then there will not be any unsystematic risk.only systematic risk will exist.and the mean return will equal to that of individual assets.

	Mean	Variance
Secutity A	15%	(0.8*20)^2 = 256
Security B	18%	(1.1*20)^2 = 484
Security C	21%	(1.4*20)^2 = 784