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 =
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>