Answer:
14.86%
Explanation:
For computing the standard deviation, first we have to determine the expected return and then variance which is shown below:
= (Expected return of the boom × probability of boom) + (expected return of the normal growth × probability of normal growth) + (expected return of the recession × probability of recession)
= (0.30 × 0.40) + (0.11 × 0.40) + (-0.10 × 0.20)
= 0.12 + 0.044 - 0.02
= 0.144
Now the variance would equal to the
= Probability × (Return - Expected Return) ^2
For boom:
= 0.40 × (0.30 - 0.144) ^2
= 0.0097344
For normal growth:
= 0.40 × (0.11 - 0.144) ^2
= 0.0004624
For recession:
= 0.20 × (-0.10 - 0.144) ^2
= 0.0119072
So, the total variance would be
= 0.0097344 + 0.0004624 + 0.0119072
= 0.022104
Now as we know that
Standard deviation is
[tex]\sqrt{variance} \\\\ = \sqrt{0.022104}[/tex]
= 14.86%
