Question

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 3%. Suppose also that there are three securities A, B, and C, characterized by the following data:

Security	βi	E(Ri)		σ(ei)
A	0.5	13	%	26	%
B	0.9	17		12
C	1.3	21		21

a. If σ_M = 25%, calculate the variance of returns of securities A, B, and 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.)

b. How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100 stocks? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)

Answer 1

a) If = 25%

then the variance of Returns of securities will be:

Formula;

Variance ( ) =  

where;

= variance of market index return = 25%
=Beta variable of security ( A = 0.5 , B= 0.9 , C= 1.3)
= standard deviation of error term ( A= 26% , B= 12%, C=21%)

Now,

Variance of Returns of Security A= ( 25² * 0.5² )+ 26²

  = 832.25 or 832

Variance of Returns of Security B= ( 25² * 0.9² )+ 12²

  = 650.25 or 650

Variance of Returns of Security C= ( 25² * 1.3² )+ 21²

= 1497.25 or 1497

b) When there is an infinite number of assets with return characteristics identical to those of A, B, and C, respectively then a portfolio will have only systematic risk which will give Mean equal to the individual security's return.

= It will become 0 (it is unsystematic risk)

So, now,

The variance of Security will be=

Security A: ( 25² * 0.5² )

= 156.25 or 156

Secuirty B=  ( 25² * 0.9² )

= 506.25 or 506

Security C=  ( 25² * 1.3² )

= 1056.25 or 1056

Security	Mean	Variance
A	13%	156
B	17%	506
C	21%	1056

[ How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100 stocks? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)

[Note: Information is missing for the above question] ]