You decide to invest in a portfolio consisting of 15 percent Stock X, 51 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 .78 10.90% 4.30% 13.30%
Boom .22 18.20% 26.20% 17.70%

5.70%
3.25%
8.31%
2.44%
7.13%

The standard deviation shows the dispersion seen in the set of values. Thus, the standard deviation for the portfolio would be 5.70%.  

The normal state of the economy would give the stock return as follows;

The boom economy would give returns on the stock as follows;

Therefore, the weighted average return would be computed as:

Hence, the standard deviation would be:

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5.70%

Explanation:

Stock return for Normal state of economy

= 0.15 × 10.9 + 0.51 × 4.3 + 0.34 × 13.3

= 8.35%

Stock return for Boom state of economy

= 0.15 × 18.2 + 0.51 × 26.2 + 0.34 × 17.7

= 22.11%

Weighted average return

= 0.78 × 8.35 + 0.22 × 22.11

= 11.38%

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

= 0.78 × (8.35 - 11.38)^2 + 0.22 × (22.11 - 11.38)^2)^0.5

= 5.70%

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