Question

As a new analyst, you have calculated the following annual rates of return for the stocks of both Lauren Corporation and Kayleigh Industries.
Year Lauren’s Rate of Return Kayleigh’s Rate of Return
2007 5 5
2008 12 15
2009 −11 5
2010 10 7
2011 12 −10
Your manager suggests that because these companies produce similar products, you should continue your analysis by computing their covariance and coefficient of correlation. Calculate covariance and correlation for both companies and explain, would the combination of the common stock of Lauren and Kayleigh be good for diversification?

Answer 1

First we will calculate the mean return of both the stocks

Mean = Sum of observations / Number of observations

Mean Return of Lauren Corp = (5%+12%+(-11%)+10%+12%)/5 = 28% / 5 = 5.6%

Mean Return of Kayleigh's Industries = (5%+15%+5%+7%+(-10%))/5 = 22% / 5 = 4.4%

Covariance Formula =

Covariance(Lauren, Kayleigh's) = ((5%-5.6%)*(5%-4.4%)+(12%-5.6%)*(15%-4.4%)+(-11%-5.6%)*(5%-4.4%)+(10%-5.6%)*(7%-4.4%)+(12%-5.6%)*(-10%-4.4%))

Covariance (L,K) = -0.000464 or -0.0464%

Standard Deviation = (Summation of squared deviations)^1/2 / N

Standard Deviation of Lauren = ((5%-5.6%)² + (12%-5.6%)² + (-11%-5.6%)² + (10%-5.6%)² + (12%-5.6%)²)^1/2 / 5

Standard Deviation of Lauren = 8.686%

Standard Deviation of Kayleigh's = ((5%-4.4%)² + (15%-4.4%)² + (5%-4.4%)² + (7%-4.4%)² + (-10%-4.4%)²)^1/2 / 5

Standard Deviation of Kayleigh's = 8.089%

Correlation = Covariance (A,B) / (StdevA * StdevB)

Correlation (L,K) = -0.000464 / (8.686%*8.089%) = - 0.06603824 or - 6.603824%

Looking at the covariance and correlation of Lauren Corp and Kayleigh's Industries, there's very little diversification. Even though covariance and correlation are negative which is good, however, both the metrics are not big enough to have a significant impact on the portfolio's risk. Therefore, Combination of stock will not be good for diversification.