portfolio has a beta of one,the weighted average of the alphas in equation(3)must be equal to zero.To understand the nature of the mistakes,we have to understand how the world beta of asset i,B,differs from the product of the world beta of the domestic market,B,and of the domestic beta of asset i,Bd.Using the multivariate normal distribution,we can write the return of asset i as: 5-r=&+B[-r]+e. (4) Similarly,the return of the domestic market portfolio can be written as: ra -r=B rw -r e. (5) Substituting equation(5)into equation(4),we have: 5-r=&+[B[w-r]+ea+e. (6) The world market beta of asset i is therefore: B=阳+ Cov(ed, (7) Var(r) Substituting(7)into(3),we get the result of Stehle(1977)that the pricing mistake from using the domestic CAPM when the global CAPM is appropriate is: 66 portfolio has a beta of one, the weighted average of the alphas in equation (3) must be equal to zero. To understand the nature of the mistakes, we have to understand how the world beta of asset i, w βi , differs from the product of the world beta of the domestic market, w βd , and of the domestic beta of asset i, d βi . Using the multivariate normal distribution, we can write the return of asset i as: [ ] d d i i id i r r rr −= + − + α β ε . (4) Similarly, the return of the domestic market portfolio can be written as: [ ] w w d dw d r r rr −= − + β ε . (5) Substituting equation (5) into equation (4), we have: [ ] dw w d i i i dw d i r r rr −= + − + + α β β  ε ε   . (6) The world market beta of asset i is therefore: d w dw i w i id w Cov( , r ) Var(r ) ε β ββ = + . (7) Substituting (7) into (3), we get the result of Stehle (1977) that the pricing mistake from using the domestic CAPM when the global CAPM is appropriate is: