Corner Portfolio Question

Hypothetical question…looking for someone who can provide the answer. (Paraguay I am looking at you!) So you have a required return of 9% and you have three corner portfolios: Portfolio 1: Return = 8%, Sharpe = 0.7 Portfolio 2: Return = 10%, Sharpe = 0.8 Portfolio 3: Return = 12% , Sharpe = 1.1 According to Schweser the answer would be to take the corner portfolios 1 & 2 to solve for the answer which would be a 50% weight in each. Now my answer is, why are you not taking portfolio 3 & 1 since portfolio 3 has a much better risk adjusted return? The weight being 75% from port 1 and 25% from port 3. Thanks in advance guys!

corner portfolios are min var portfolios in which an asset class weight changes from zero to positive along the min var frontier. i dont know the textbook answer to your question but I dont think you would choose two portfolios that are not adjacent to each other. you increase your return/risk objectives as you move along the frontier

exactly, you would be below that concave curve

I wish i could draw a diagram here… but what if Portfolio 2 wouldn’t exist? Technically portfolio 3 would be the adjacent portfolio. If you do a linear line than technically both portfolios are in the concave curve right?