# Covariance / correlation in portfolio

Kendra Jackson, CFA, is given the following information on two stocks, Rockaway and Bridgeport. Covariance between the two stocks = covRockaway, Bridgeport = 0.0325 Standard Deviation of Rockaway’s returns = sRockaway = 0.25 Standard Deviation of Bridgeport’s returns = sBridgeport = 0.13 Assuming that Jackson must construct a portfolio using only these two stocks, which of the following combinations will result in the minimum variance portfolio? A) 100% in Rockaway. B) 50% in Bridgeport, 50% in Rockaway. C) 80% in Bridgeport, 20% in Rockaway. D) 100% in Bridgeport.

d?

The answer is D because first you must compute the correlation coefficient. The corr coeff = 1, which means there are no benefits from diversification. Choose stock with smallest std

This is a good problem, taught me how to do variance of a portfolio, which i worked through the long way. if portfolio X = p*A + (1-p)*B where A and B are assets with weights p and (1-p) respectively, then the mean return is given by =p + (1-p) where and are mean returns of A and B. The messy part is calculating , and then using var(X)=-^2, working through the algebra, and ultimately getting (using the definition of covariance): var(X) = p^2*var(A) + (1-p)^2*var(B) + 2*p*(1-p)cov(A,B) The above seems like a good formula to know, knowing this hopefully I won’t have to rederive it at test time.

D since Bridgeport has lowest standard deviation…which means it has the lowest variance

rjs157 Wrote: ------------------------------------------------------- > D since Bridgeport has lowest standard > deviation…which means it has the lowest variance RJS157, you have to be careful in applying that logic in general because if there’s a negative covariance it could actually reduce total portfolio variance to mix the securities. I’m still thinking about whether a small positive covariance can decrease portfolio variance by mixing in small amounts of the larger-variance security, or whether the covariance needs to be specifically negative.

Stratus, I hear what your saying …it crossed my mind aswell but ultimitly if corr =1 we’re just let with a straight choose of which stock to buy…in this case looking for less var …var less on Bridgeport so D all the way.

in this problem, the only way a negative correlation could have come is if they had given covariance is a -ve number. Since covariance is positive, you would not need to calculate the correlation coefficient. selecting the lower stddev part of the portfolio @ 100% would give you the minimum variance overall.

yancey, They are Perfectly Positivel corelated, so there is no benefit from diversification So 100% stock in lowest STD will be the best pick… I’ll go with D too… - Dinesh S

D!

Whoa - If the stocks don’t have correlation 1 you can always reduce the portfolio variance by including it. In the case of two stocks, the stock with the lower std deviation always gets a higher weighting (if they’re independent their weights are proportional to the inverse of the variance). So I would just put down C and go on. Alas, that would be wrong because silly me did not immediately see that 0.13*0.25 = 0.0325 so here we have two stocks with correlation = 1. Yeah, right. Even A shares and B shares of the same company don’t have correlation = 1. This is about the worst kind of question I can imagine because it’s a deliberate trick that makes you think the concept of diversification doesn’t work with positive covariance and suggests that two stocks in presumably different companies can have correlation = 1. The answer is D but totally not for the reason given by rjs157. Stratus - Change the covariance to 0.025 and check out the answer. I get p’s = 1.4% and 98.6%

Why rjs157 shouldn`t be right? There is no reason to choose 2 stocks, because correlation is +1. So be happy with the one which has the lowest s.

Hannoversch Wrote: ------------------------------------------------------- > Why rjs157 shouldn`t be right? > There is no reason to choose 2 stocks, because > correlation is +1. > So be happy with the one which has the lowest s. Yes, and if rjs saw that his answer was correct because the correlation is 1 then his answer is correct. It’s such an obnoxious question because correlation = 1 for two different stocks is just silly.

you can automatically rule out A and B since Rockaway has a higer standard deviation than Bridgeport…then you’er left with either C and D. Since correlation is 1, then pick D and move on.

C’mon - how many of you saw that correlation = 1 when you read the question? A priori you should think that there is no way the correlation = 1…