# How to calculate two asset portfolio (problem finding the Population correlation coefficient)

I have two assets: A has an expected value of $12$ % and a standard deviation of $8$%. B has an expected value of $15$ % and a standard deviation of $12$ %.

Suppose that we invest $75$ % in A and $25$ % in B

Here is what the solution do to get the variance

$(.75 \cdot .08)^2 + (.25 \cdot .12)^2 \cdot2 \cdot .75 \cdot .25 \cdot .4 \cdot .08 \cdot .12 = 0.00594$

My question is : How do I get the $.4$ ?

From wikipedia and this site, I found that It is $\rho (a,b)$

And when I do $\rho (a,b)$ I get : $( (0.12-.1)(0.08-.1) ) / (0.08 * 0.12 )$

it gives me $\rho (a,b) =$ $-0.00040 \div 0.0096 = -0.04167$

Which is not $0.4$

You are rarely asked to find the variance of a weighted distribution without knowledge of the joint distribution of A and B. If only given two distributions without any indication of their correlation, it is not possible to calculate $p$. In particular, I dont know how you got the $Cov(A,B) = ((0.12−.1)(0.08−.1))$ part.