Returns on Jointly Normal Stock

[Oxymoron]

Homework Statement

If the returns on two stock are jointly normal and let's say I know the means, variances (and therefore standard deviations), and correlation of each and both.

Then if I know the return of one of the stocks over some time period, then would it be possible to calculate the return on the other over the same time period?

Homework Equations

The bivariate normal density (maybe?)
Weights of assets given their prices at time t=0.
Return on a portfolio.

The Attempt at a Solution

I have 2 of stock 1 and 5 of stock 2. Their prices are $10.50 and $15 at time 0 respectively. Therefore their weights are 0.21875 and 0.78125 respectively. The return on stock 1 is 0.06. But how do I find the return on the second stock? I'm sure there is some property of the bivariate normal probability density that I need.

 

[Stephen Tashi]

You'll probably have to define the calculation for "return" on a stock if you want help from a wide audience.

Just taking "return" as a random variable, if you know the return for one stock, what you can get is the conditional probability distribution for the return on the other. Knowing one return doesn't remove all the uncertainty about the other one.

 

[Oxymoron]

Hi Stephen. Good idea with the conditional probability distribution. Turns out you can derive a formula for the conditional bivariate (because I am considering only 2 stocks) normal density by dividing the bivariate normal density by one of the marginals. Then you can extract the conditional expectation and conditional variance from the exponential just like you would with the univariate normal density. Works a treat! Thanks for the insight!