A portfolio with an expected return of 7.7% lies between corner portfolios A and B. One could construct such a portfolio with a 2/3 weight on portfolio A and 1/3 weight on portfolio B.
0.077 = wA(0.0644) + (1 - wA)(0.1022)
wA = 2/3 → wB = 1/3
(Note: This linear averaging technique assumes that there are no diversification benefits from combining portfolios A and B. That is, it assumes their correlation coefficient is one, which is probably not the actual case.) Multiplying these weights to the asset class proportions in portfolios A and B, the weight on U.S. large capitalization stocks is:
(2/3)(0.012) + (1/3)(0.104) = 0.043.
