Respuesta :
Answer:
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%
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;
[tex]0.15*10.9 + 0.51 * 4.3 + 0.34 *13.3\\= 8.35[/tex]
The boom economy would give returns on the stock as follows;
[tex]0.15 * 18.2 + 0.51 * 26.2 + 0.34 * 17.7\\=2.11[/tex]
Therefore, the weighted average return would be computed as:
[tex]0.78 * 8.35 + 0.22 * 22.11\\=11.38[/tex]
Hence, the standard deviation would be:
[tex]0.78 * (8.35 - 11.38)^{2} + 0.22 * [(22.11 - 11.38)^{2} ]^{0.5} \\= 5.70[/tex]
Learn more about standard deviation here:
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