Question

You decide to invest in a portfolio consisting of 15 percent Stock X, 36 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio?

State of Economy Probability of State of Economy Return if State Occurs
Stock X Stock Y Stock Z
Normal 0.77   9.00% 2.40% 11.40%
Boom 0.23 16.30% 24.30% 15.80%

Answer 1

Ans 2.27

Stock Normal Boom Probability (0) 77.00% 23.00% Stock X (ii) 9.00% 16.30% Total Stock X Return (i)* (ii) 6.93% 3.75% 10.68% Stock Y (iii) 2.40% 24.30% Total Stock y Return (i)* (iii) 1.85% 5.59% 7.44% Stock Z (iv) 11.40% 15.80% Total Stock Z Return (i)* (iv) 8.78% 3.63% 12.41% Stock Probability (i) 15.00% 36.00% 49.00% > Return (ii) 10.68% 7.44% 12.41% Total Probability * Return (i)* (ii) 1.60% 2.68% 6.08% 10.36% N

Stock (P*Y) P* (Y-Average Return of Y)^2 Probability (P) 15% 36% 49% RETURN (Y) 10.68 7.44 12.41 TOTAL 1.60 2.68 6.08 10.36 0.02 3.07 2.06 5.14 Expected Return = (P*Y) 10.36% VARIANCE = p* (Y-Average Return of Y)^2 5.1441 Standard Deviation = Square root of (P * (Y-Average Return of Y)^2) Square root of 51.441 2.27