Question

Use the following table: States of the Economy Boom Steady Recession 1 Probability of the State 0.3 0.5 0 .2 3-Month T-Bill 4% 4% 4% Large-Company Stock 10% 5% 0% Small-Company Stock 30% 20% 10% Estimate the difference between the standard deviations for large- and small-company stocks. Which is larger and by how much? Small company stocks by 3.50% O Small company stocks by 49.00% Large company stocks by 12.25% Small company stocks by 36.75%

Answer 1

first we have to calculate expected return of each stocks

expected return = $\sum probability *return$

Expected Expected return of return of large company Small company large stock small stock prob. company company 0.3 10 30 0.5 20 2.5 10 0.2 10 2 5.5 21

from the above table Expected return of large company(l') = 5.5%

small company(s') = 21%

now we have to calculate standard deviation for each stock:

Standard deviation = $\sqrt{\sum p*(x-x')^2}$

where p = probability

x = return with respect to probability

x' = expected return

Expected Expected return of return of large company Small company large small p*(l-l')^2 p*(5-s')^2 prob. stock stock company company 0.3 10 30 6.075 24.3 0.5 20 2.5 10 0.125 0.5 0.2 10 6.05 24.2 Total 5.5 21 12.25 49

standard deviation of large company = (12.25)^1/2 = 3.5%

standard deviation of small company = (49)^1/2 = 7%

difference = 7 - 3.5 = 3.5%

so standard deviation of small company stocks larger by 3.5%