Question

ou decide to invest in a portfolio consisting of 17 percent Stock X, 38 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 Return if State Occurs of Economy Stock X Stock Y Stock Z Normal .75 9.20% 2.60% 11.60% Boom .25 16.50% 24.50% 16.00%

Answer 1

5.00%

Step-by-step explanation:

The computation of the standard deviation is as follows;

Stock return for Normal state of the economy

= 0.17 × 9.20 + 0.38 × 2.60 + 0.45 × 11.60

= 1.564% + 0.988% + 5.22%

= 7.78%

Now

Stock return for Boom state of the economy

= 0.17 × 16.50 + 0.38 × 24.50 + 0.45 × 16

= 2.805% + 9.31% + 7.2%

= 19.32%

Now Weighted average return

= 0.75 × 7.78 + 0.25 × 19.32

= 5.835% + 4.83%

= 10.67%

Standard deviation = Normal probability × (Stock return for Normal state of the economy - Weighted average return)^number of years + Boom probability × (Stock return for Boom state of the economy - Weighted average return)^number of years)^percentage

= 0.75 × (7.78 - 10.67)^2 + 0.25 × (19.32 - 10.67)^2)^0.5

= 5.00%