Consider an economy with assets with return processes $A$, $B$, $C$, $D$. Consider a weighted index with return process $I=aA + bB + cC + dD$ where $a,b,c,d$ are coefficients, and $a+b+c+d = 1$.
Suppose I want to find $cov(I,A)$. Is this possible given that I know the covariance between all possible pairs of $A,B,C,D$?
Also, suppose I have some asset $E$. Suppose I know $cov(A,E),cov(B,E),cov(C,E),cov(D,E)$. How do I find $cov(I,E)$.