I understand the answer. But to get the answer, don’t we need to go through question b first? I.e. find out the weights? It is my understanding that we look at the annual expected return and the sharpe ratio. One could argue that you may have corner porfolios of 3 and 5 rather than 3 and 4. Since 5 has a sharpe ratio than 4. I understand that if we choose 5 though corner porfolio 3 would be overweighted. So back to my question, could we have answered problem ‘a’ without calculating the weights in problem ‘b’? Thanks in advance.

I actually get a ratio of 57 to 43 for 3 and 5 compared to 25 and 74 for 3 and 4.

yes you could’ve. think of corner portfolios in the context of the effeicent frontier. shifting from one to the other represents changes in the mix of each asset class, yielding higher expected returns and risks and you move up and to the right. in this context, you corner portfolios aren’t like differnet stocks or soemthing, they’re varying degrees of the same asset classes which encompass a specific effecient frontier. combining two, non adjacent portfolios as you’re looking to do would could create a sub-optimal combination of assets not represented on the effecient frontier. the key in selecting corner portfolios is that they bracket the required return.

the Sharpe ratio is only relevant when they’re borrowing involved, which there’s specifically not in this question. the portfolio with the highest sharpe ratio is the tangency portfolio for a given frontier, which if allowed to borrow you’d at the risk free rate (short it) and invest in the portfolio with the highest sharpe ratio to meet the required return.

ah I see. Thanks!