Asset allocation -- corner portfolios

[Kiakaha]

Hi all - I’m confused on the examples in the CFA book on corner portfolios. The first one (p241) calculates the strategic asset allocation as the weighted average of the two adjacent corner portfolios. So far, so good. But in the next example (p245) they just pick the first corner portfolio that meets his return requirements (even though it actually returns more). Any ideas why? I’m thinking they may have just skipped a step to save space because the second example then goes on to suggest allocating to the tangency portfolio and the risk free asset instead.
Anyone have any thoughts on this? Is there some subtle difference to the questions that I’m missing? Thanks!

 

[kyh]

G’Day Mate,
The general idea is to draw a tangent line that has the highest gradient, and to do that, we draw a line from RF to the tangency portfolio (without investigating combinations of corner portfolios, a simplification/ approximation would be that the tangency portfolio is the corner portfolio with the highest sharpe ratio)
I’m thinking for example 9:
Objective 8.5% annual return + “he does not want to borrow to purchase risky assets” (page 242)
To earn 8.5%, the most efficient way would be to choose the tangent portfolio, portfolio with highest sharpe ratio (portfolio 5) and combine it with some RF asset. However, since portfolio 5 has only return of 6.47%, he would need to borrow, which is against his decision. Hence we choose to use a combination of portfolio 3 and 4 to reach 8.5%. No need to discuss RF, since 100% in the combination portfolio achieves 8.5%
For example 10:
Objective 6.5%
Again, we choose the portfolio with highest sharpe ratio, corner portfolio 4. This time, however, the expected return is 7.24%. Hence he need to buy some RF asset to lower the return to 6.5%