Question

Problem 4: The Value of Best Candy stock is sensitive to the price of sugar. We can describe the fortunes of Best Candy stock using the following scenario analysis Abnormal Year Normal Year for Sugar Bullish Stock Market Bearish Stock Market 50% 15% Sugar Crisis 20% Probability Rate of Return 30% 10% I 5% On the other hand, the distribution of SugarKane stock return is as follows: Abnormal Year Normal Year for Sugar Bullish Stock Market Bearish Stock Market 50% 190 Sugar Crisis 20% 25% Probability Rate of Return 30% 5% a. What are the expected return and standard deviation of Sugarkane? What would be Sugarkane's correlation coefficient with Best? Suppose Humanex, a non-profit organization, splits its investment evenly between Best Candy stock and SugarKane What's the expected return of Humanex' portfolio? And what's the standard deviation? What are your conclusions from comparing the portfolio standard deviation to the individual standard deviations of Best and SugarKane? a. b.

Answer 1

a) expected return=4%

standard deviation=10.82%

correlation=covariance(sugarcane,best)/(std of sugarcane*std of best)

=-0.065

a)portfolio return=( wt of sugarcane*expected return of sugarcane)+( wt of sugarcane*expected return of sugarcane)

=(50%*4%)+(50%*7.5%)

=5.75%

std of portfolio=((wt of A^2*std of A^2)+(wt of B^2*std of B^2)+(2*wt of a*wt of B*corr(A,B)* std A*std B))^0.5

=((0.5*10.82%)^2)+((0.5*11.98%)^2)+(2*0.5*0.5*-0.065*10.82%*11.98%))^0.5

=7.8%

b) we can conclude that since the correlation coefficient is negative the standard deviation of portfolio is lesser than individual standard deviation