The expected return of 15% lies between corner portfolios 1 and 2 with expected returns of 12% and 16.50%. We solve for w in the following equation:
15 = w(12) + (1-w)(16.50)
w = 0.33
In other words, the efficient portfolio with an expected return of 15% has 33% weight of corner portfolio 1 and 67% weight of corner portfolio 2. With respect to the asset classes, the weights are then derived as follows:
Weight of asset class 1 = (0.33)(65%) + (0.67)(15%) = 31.50%
Weight of asset class 2 = (0.33)(0%) + (0.67)(20%) = 13.4%
Weight of asset class 3 = (0.33)(35%) + (0.67)(50%) = 45.05%
Asset class 3 has the highest weight and is the most significant.
Approximate standard deviation = (0.33)(10.50) + (0.67)(14) = 12.85%