Answer:
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%