 # covariance and portfolio variance

I’m having trouble understanding the difference between the two. The way I’m thinking of them, which is obviously wrong, it seems like the covariance and variance of a 2 asset portfolio should be the same. Can somebody please try to clarify this for me. Thanks

http://en.wikipedia.org/wiki/Covariance Cov(X,X) = Var(X)

yes, variance is the dispersion around the mean, just as the calculation is. its the risk. OR you could say that it is the spread of how far the mean value could fall or rise( could be called the population parameter or sample statictis). THe covariance on the other hand is also a measure of risk but it is a measure of relative risk. It is meaningless unless compaired to another point estimate of some other data set. Like its calculation you are dividing the standard deviation by the mean return. In other words how much risk is there per unit of return. Remember that standard deviation is always in the same measure as the data set. SO if the data set is percent the SD is in % also. If the data is in \$ then the SD is dollars also.

Thanks btw, that helps. Stats has always been my weakest area of math. I can’t wait to get through it and move onto Econ!

one the exam you could see a question that gives the SD(standard deviation) the mean return, and the varience. It may ask which one has less risk. It could be tricky. It may not ask for the covarience, you have to remember and understand that the covarience is a relative risk measure. realitive means compaired to somethig else. some poeple may try to just look at the data to see which one has more risk by just looking at the SD. But this is wrong. You can not tell which one has more risk untill you compair how mch risk per unit of return is the the portfolio. exp: SD Stock 1 SD 9 Stock 2 SD 12 Mean Stock 1 25 Stock2 35 the answer is stock 1 has more varience thus more risk per unit of return. Just by looking at it, you may say that stock 2 is more risky because of the higher SD. THis is not correct. Note: If they give a problem with the same mean return then you dont have to calculate, you can just look at the SD because the means are the same. CO-VARANCE stock 1 9/25 = 36% CO-VARANCE stock2 12/ 35= 34%

Dude, you mixed Cov (covariance) and CV (coefficient of variation)! Covariance is something completly different. Now look up and see what maratikus wrote.

Pretty funny. Covariance is a measure of association between two random variables. That means it makes no sense to talk about the “covariance” of a portfolio. You can have the covariance between two stocks - a positive (negative) covariance means that if one goes up the other is likely to go up (down). A portfolio does have variance which is one measure of the risk of the portfolio as do each of its components. As I think btw pointed out, covariance has units so it depends on how you are measuring each random variable. This is pretty inconvenient for expressing association so we usually standardize it and get the correlation. The covariance is very useful for getting variabilities of sums and about the only question using covariance that you are likely to get is a question like Stock A Var = 10 Weight = 0.3 Stock B Var = 7 Weight = 0.7 Cov(A, B) = -2, find Variance portfolio. Answer = 0.3^2*Var(A) + 0.7^2*Var(B) + 2*0.3*0.7*Cov(A,B) = (whatever too lazy)