Answer:
Mean = 0.14
SD = 25.52%
Explanation:
To find the mean:
By using the holding period return;
[tex]E(r) = \sum \limits_s p(s) r(s)[/tex]
From the given information; we can compute the table as follows:
State of Probability Ending HPR ( including p(s) × r(s)
the market Price dividends)
p($) ($) r(s)
- Boom 0.35 140 44.5 0.156
- Normal 0.30 110 14.0 0.042
growth
- Recession 0.35 80 -16.5 -0.058
Total [tex]\mthbf{\sum = 0.14}[/tex]
The standard deviation is calculated by using the formula:
[tex]\sigma = \sqrt{\sum \limits_{s} p(s) [r(s) - E(r)]^2}[/tex]
State of p($) r(s) E(r) r(s) - E(r) [r(s) - E(r)]² p(s)*[r(s) - E(r)]²
the market
- Boom 0.35 44.5 14 30.5 930.25 325.59
- Normal 0.30 14.0 14 0 0 0
growth
- Recession 0.35 -16.5 14 -30.5 930.25 325.59
Total [tex]\mathbf{\sum = 651.18}[/tex]
[tex]\sigma = \sqrt{651.18} \\ \\ \mathbf{\sigma = 25.52\%}[/tex]
