19.5. TECHNICAL NOTES 741
Technical Note 19.5 The best-replication reading of the i-CAPM
The claim can be shown as follows. In the first line, we write the return on a general portfolio with
weightsxwandxsfor the world market and the foreign T-bill, and in the second line we group
terms inxwandxs:
E( ̃rj’s replication) = xwE( ̃rw) +xs(r∗+ ̃s) + (1−xw−xs)r (19.52)
= r+xwE( ̃rw−r) +xs(r∗+ E( ̃s)−r). (19.53)For best replication, we have to setxw=βj,w;sandxs=γj,s;w. Thus,
E( ̃rj’s replication−r) =βj,w;sE( ̃rw−r) +γj,s;w(r∗+ E( ̃s)−r). (19.54)