Question

Consider the following data for two risk factors (1 and 2) and two securities (J and L):

λ0 = 0.06

bJ1 = 0.75

λ1 = 0.03

bJ2 = 1.30

λ2 = 0.04

bL1 = 1.60

b_L2 = 2.10

Compute the expected returns for both securities. Round your answers to two decimal places.

Expected return for security J:   %

Expected return for security L:   %

Suppose that Security J is currently priced at $21.00 while the price of Security L is $12.25. Further, it is expected that both securities will pay a dividend of $0.60 during the coming year. What is the expected price of each security one year from now? Do not round intermediate calculations. Round your answers to the nearest cent.

Expected price for security J: $

Expected price for security L: $

Answer 1

a) Computing the expected returns for Security J and L-:

Computing the expected returns for Security J

The equation for calculating the overall expected return is

E(RJ) = λ0+λ1bJ1+λ2bJ2

λ0 - the rate of return on a zero(Systematic risk asset)

λ1 - the risk premium related to the 1st common risk factor

λ2 - the risk premium related to the 2nd common risk factor

bJ1 - the price relationship between the risk premium and the asset that is, how responsive asset is to 1st factor

bJ2 - the price relationship between the risk premium and the asset that is, how responsive asset is to 2nd factor

Given

λ0 = 0.06

λ1 = 0.03

λ2 = 0.04

bJ1 = 0.75

bJ2 = 1.30

E(R3) = 0.06+0.03(0.75)+0.04(1.30)

= 0.06+0.0225+0.052

= 0.1345 or 13.45%

Computing the expected returns for Security L

The equation for calculating the overall expected return is

E(RL) = λ0+λ1bL1+λ2bL2

λ0 - the rate of return on a zero(Systematic risk asset)

λ1 - the risk premium related to the 1st common risk factor

λ2 - the risk premium related to the 2nd common risk factor

bL1 - the price relationship between the risk premium and the asset that is, how responsive asset is to 1st factor

bL2 - the price relationship between the risk premium and the asset that is, how responsive asset is to 2nd factor

Given:

λ0 =0.06

λ1 =0.03

λ2 =0.04

bL1 =1.60

bL2 =2.10

E(RL) = 0.06+0.03(1.60)+0.04(2.10)

=0.06+0.048+0.084

=0.192 or 19.2%

Therefore expected return on security J is 13.85% and security L is 19.2%.

b) Calculate the price of each security one year from now-:

security-J is currently priced at $21.00

Security-L is priced at $12.25

The dividends for both the securities are $0.60

To calculate the price, first we have to calculate the dividend yield and capital gains yield of each security

Dividend yeild = Dividend per share/Market price per share

Therefore;

Dividend yeild of Security J = 0.60/21

= 0.029 or 2.9%

Dividend yeild of Security L = 0.60/12.25

= 0.049 or 4.9%

So, the dividend yield for security J is 2.9% and security L is 4.9%.

Capital gains yeild = Total return - Dividend yeild

Therefore;

Capital gains yeild of Security J = 13.85 - 2.9

= 10.95% or 0.1095

Capital gains yeild of Security L = 19.2 - 4.9

= 14.3% or 0.143

So, the capital gains yeild of Security J is 10.95% and Security L is 14.3%.

Now we can find the expected price of securites.

Expected price = Current market price*(1+Capital gains yeild)

Expected price of security J = 21*(1+0.1095)

= 23.30

Expected price of security J = 12.25*(1+0.143)

= 14.00

So, the expected price of security J is $.23.30 and security L is $14.00.