Posted: April 10th, 2021

Consider the following scenario analysis for stocks a and b and for

Question:Risk and Return

1.Consider the following scenario analysis for Stocks A and B and for the market portfolio (M)

   

Rate of Return

 

State of Economy

Probability of State

Stock A %

Stock B %

Market %

 

 

 

 

 

 

 

Boom

0.1

30

45

    33

 

Good

0.6

12

10

    15

 

Average

0.2

1

-15

-5

 

Bust

0.1

-20

-30

-9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a)      Calculate the expected rate of return on each stock and the market?                        (15)

Stock A:

 

Expected Rate =  = 30*0.1+12*0.6+1*0.2-20*0.1

= 8.4%

 

Stock B:

 

Expected Rate =  = 45*0.1+10*0.6-15*0.2-30*0.1

= 4.5%

 

Market:

 

Expected Rate =  = 33*0.1+15*0.6-5*0.2-9*0.1

= 10.4%

 

 

b)      Find the standard deviation of returns for each asset?           (15)

Stock A:

 

Standard deviation  =

 

 

 

= 208.2

 

Stock B:

 

Standard deviation  =

 

 

 

= 393

 

 

Market:

 

Standard deviation  =

 

 

 

= 246.6

 

 

2. The risk free rate is 3% and the betas of the stocks are:

Stock               Beta

A                     1.20

B                     0.70

Are the stocks fairly priced?

Find required returns:

A:

 

B:

 

 

Find alphas:

A: Alpha =

B: Alpha =

 

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