QUIZ 3: Diversification The expected returns, standard deviations, and correlati
ID: 2819968 • Letter: Q
Question
QUIZ 3: Diversification The expected returns, standard deviations, and correlation for Chihuahua Corporation and Labrador, Ltd. are shown below. Expected Return Standard Deviation of Returns Chihuahua 14% 42% Labrador 9% 22% Correlation(Chihuahua, Labrador) = 0.40 You have $10,000 to invest, and are trying to decide how much money to invest in each of the two companies. Calculate the expected return and standard deviations for the following mixtures: a. $7,000 of Chihuahua stock, and $3,000 of Labrador stock b. $5,000 of Chihuahua stock, and $5,000 of Labrador stock c. $2,000 of Chihuahua stock, and $8,000 of Labrador stock
Explanation / Answer
a. expected return = w(a)*return (a) + w(b)*return(b)
stardard dev = square root((w(a) stdev(a))^2 + (w(b) stdev(b))^2 + 2*w(a)*w(b)*stdev(a)*stdev(b)*corel)
when w(a) is 0.70 and w(b) = 0.3
expected return = 0.7*14 + 0.3*9 = 12.50%
standard dev = square root((0.7*0.42)^2 + (0.3*0.22)^2 + 2*0.7*0.3*0.42*0.22*0.4) = 32.61%
when w(a) = w(b) = 0.50
expected return = 11.50%
standard dev = 27.33%
when w(a) = 0.20 w(b) = 0.80
expected return = 0.2*14 + 0.8*9 = 10.00%
standard dev = 22.33%