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Alex787 [66]
3 years ago
8

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
Business
1 answer:
Bumek [7]3 years ago
6 0

Answer:

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

<u><em>A = 4.50 % </em></u>

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

<u>B = 2.0%</u>  

<em>b) Standard Deviation /Risk for Stock A:</em>

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

SD for A = \sqrt{0.30*(0.10-0.045)^2 + 0.30*(0.05-0.045)^2+0.40*(0.00-0.045)^2}

SD for A = 0.0415

<u><em>SD for A = 4.15%</em></u>

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

<em><u>Portfolio Return = 3%</u></em>

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