Question

Prove or disprove: if two assets have positive betas, then the covariance of the two assets is positive.

Answer 1

Proof :  if two assets have positive betas, then the covariance of the two assets is positive.

Let the 2 assets be A and B

Beta of stock A = Covariance (A, market)/Variance(market)

Variance of market cannot be negative

Since Beta of stock A is positive, Covariance (A, market) is also positive.

Similarly Covariance (B , market) is also positive.

This implies that stock A and B moves in the direction in which the market moves.

Since, the movement of A and B would be in similar direction,  the covariance of the two assets is positive.