I am studying the Arbitrage Pricing Theory using Pairs Trading: Quantitative Methods and Analysis.In page 44 the author gives an example on how to calculate the covariance between two stocks. I will tell how the author do it first.
There are two stocks using two factor model, for stock A, the two factor model is (0.5, 0.75) and the factor covariance matrix is [ 0.625 0.0225,0.0225, 0.1024]. And for stock B, the two factor model is (0.75, 0.5). Then the author says we can calculate the covariance between stocks as [0.5, 0.75][0.625 0.0225,0.0225, 0.1024][0.75,0.5].
What I do not understand is that in calculating the covariance between stocks, the mid-term is the factor covariance matrix for stock A, we do not know the factor covariance matrix for stock B, so is it right to calculate the covariance between the stocks as the author says?