There are three economy situations and two stocks Information is as follows Economy Stock A Stock B Booming 0.3 10 20 Neutral 0.3 5 0 Recession 0.4 0 10 a What are the expected returns for both stock A and B respectively b What is the standard deviation risk for stock A c What is the portfolio return given that you have $10000 and allocate $4000 in stock A

a) A = 4.50% and B = 2.00%

b) SD for A = 4.15 %

c) Portfolio Return = 3.0%

Explanation:

a) Expected Returns for Both A and B respectively:

In order to calculate the expected returns, let's categorize the given data first.

Economy        Probability      Stock A       Stock B

Booming            0.30               10%               20%

Neutral               0.30                5%                 0%

Recession          0.40                 0%                -10% (not 10%)

So,

Expected Return for Stock A:

A =   Sum of (all Probability x Stock A)

A = (0.30 x 0.10) + (0.30 x 0.05) + (0.40 x 0.00)

A = 0.045

A = 4.50 %

Return for Stock B:

B = Sum of all Probability x Stock B

B = (0.30 x 0.20) + (0.30 x 0.00) + (0.40 x -0.10)

B = 0.002

B = 2.0%  

b) Standard Deviation /Risk for Stock A:

SD for A = Sum (Square Root (Probability*(Stock A Return - Expected Return of Stock A)²) )

SD for A =

SD for A = 0.0415

SD for A = 4.15%

c) Portfolio Return Given that:

                                        Value          Weight         Return

Stock A                          4000              0.4               4.50%

Stock B                          6000             0.6                 2.0%

                                      10000

Portfolio Return =  Sum of ( Weight x Return)

                          = (0.4 x 0.045) + (0.6 x 0.02)

                          = 0.03

Portfolio Return = 3%