# Corner Portfolios

(With reference to a practice exam question) Referencing: Vol 1 Exam 1 Morning Question 10 A For corner portfolios does one always choose two adjacent (next to each other) portfolios if there are constraints on negative weights? For example practice exam volume 1, exam 1 morning session, question 10 A. In this question portfolio 3 and 4 bracket the return objective, but portfolio 2 has a higher sharpe ratio than portfolio 3. If the question had not asked for adjacent corner portfolios and instead asked for the two corner portfolios (without the word adjacent), would it have been correct to select corner portfolios 2 and 4, based on corner portfolio 2’s superior sharpe ratio to portfolio 3 and the fact that the return objective was still bracketed? Doing so would not have exceeded the maximum standard deviation stated.

my understanding is that they are always next to each other b/c your target/required return lies between them - i have never seen it otherwise

calculate the combined sharpe for both combination. I think you’ll find that 3/4 is superior.

It depends on whether you can invest in risk-free asset and whether the higherst shape ratio portolio’s return above required return.

1.Short Constraints ( i.e. no shorting ) use bracketing portfolios 2.No constraints( i.e borrowing / lending allowed ) use the highest sharpe portfolio as first and risk-free as second portfolio

goodman , if highest sharpe portfolio has return below the required return ( and no constraints , obviously ) , then by leveraging/borrowing i.e. keeping the weight of the risk free negative , you can reach the required return . So the actual return of the highest sharpe is irrelevant. The formula will calculate the weights of highest sharpe and risk free correctly whether the return of highest sharpe is below or above the required

Constraints = corner port Uncobstrained = tangency port