How do i calculate the covariance between 2 risky assets?

Question

There are two assets: A and B. If I have the correlation between the two, the standard deviation of A, and the standard deviation of B then can I calculate the covariance between A and B. Is the covariance equivalent to the correlation*standard deviation A* standard deviation B?

Answer 1

You are right. Anyways, if you still need help then, read on



Thanks God, there is a formula for everything.



Covariance between two assets= (standard deviation 1*2) * co-relation b/w the two assets

or just multiply each other and you would get the co-variance



e.g

sd1= .1544

sd2=.0892

co-relation b/w 2 assets=0.56

co-variance=0.007712589

Answer 2

The answer to this question is long, involved, and interesting. First off, the correlation between the indices is useless for any portfolio theory. You want the correlation of their returns. Second off, you have put your finger on an important problem. Good for you. But I'll bet you don;t yet realize the depth of the problem. If you just ignore the missing data and calculate pairwise covariances from available data you: a) Underestimate the covariance between markets because for example if France is closed on Bastille day, but Europe jumps 2% and then is flat on the day after Bastille day, you will ignore Bastille day for France and then say that France behaved much differently than Europe on the day after Bastille day. The result of that in your portfolio analysis is to overweight France because they take Bastille day off. That's dumb. b) (technical problem) When you calculate the covariance matrix by just pairwise elimination of missing data, you are not guaranteed to have a positive definite matrix, i.e., it's not a covariance matrix anymore. You may now think that's a techno-geek problem, but try entering that into your portfolio software and you will egt an error message that says (or means) "your matrix is not invertible". That sucks and it will stop you dead in your tracks. Here is what I believe (with my Stats Ph.D. and lots of time to think about this problem with serious hedge fund money riding on the answer). Steps: 1) Create a "mock" dataset in which there is a return on every day for every market in which at least one market is open. To create this mock data set, if a market is closed on a day like Bastille Day in France, pretend that both Bastille Day and the day after Bastille day are missing data but the combined return on those two days is the retrun on the day after Bastille day. Divide evenly among the missing data. So in my example above, if the day after Bastille day has a 2% return then I say that the return on each day is Sqrt(1.02) - 1 or like 0.995%. 2) Calculate covariance matrix on mock data. Call this matrix C. 3) Go back to original data set and create a new data set. The way to do this is to go to each of your missing data points (including the day after Bastille day that you wiped out) and impute new data using your constraints and your covariance matrix. There's a little math problem here because if you were just estimating one value using a covariance matrix the best estimator is the OLS regression estimate using the covariance matrix. That isn't exactly true here because you have the constraint. Since I can't give you the exact formula in this space, a decent approximation is to calculate the OLS estimate for each missing point and then standardize so that they meet the constraint (that's real close to optimal but it actually slightly overstates the covariance). 4) Calculate covariance matrix on newly imputed data. 5) Now you have a new covariance matrix so use it to impute different data. Rinse and repeat above steps until convergence. If you don't feel like checking convergence, just do it 10 times which ought to be plenty for most situations. Good luck! Edit: there's a tiny little problem with bias in the steps I wrote above so if there is serious money on the line, you have to do something very slightly different. The gist is that the imputed data is too exact so you need to do a little shrinkage. There's an optimal way to do that.

Answer 3

Have you tried using the COVAR() function in Excel?