# Combination of corner portoflio

Target return is given, i saw the example usually just choose the closest two adjacent corner portfolio which close to the target return and then weigh the corner portoflio.

However, why they don’t need to check if standard deviation meets the target as well?

Theory for cornor portfolio assumes restrictions on short selling. This causes minor bumps in the efficient frontier, which is other curvy and have highest sharp ratio (return over Rfr in comparison to risk assumed) for any portfolio falling on it.

In case of cornor portfolios, the same sharp ratio is not same and have some deviations due to inability to short sell.

When as an investor, you set your risk and return objective, you could either look at this from risk or return objective and accordingly select a portfolio. In general case when short-sell is allowed returns are propotionate to risk assumed, since all the portfolios on the efficient frontier neccesarily need to have highest sharp ratio. And therefore, you could go either way - with return objective or with risk

However, it is not the case with cornor portfolios. there are portfolios with different sharp ratios. You can then then either go by the risk objective or with return. Since return objective is generally quantifiable, at least compared to risk objective, it is seen from the return objective. if you have a number for risk objective in mind, I beleive you can do the weightages on that basis and run the calculation, although it would be relatively complex than doing it for returns; just a note, for cornor portfolios, it is assumed that the correlation is 1, which is fine in theory, but wouldn’t be the case in practice.

So if you then plan to go with return objective, you look for the cornor portofio that matches with your return objective and use required weights in case an exact match is not there. point to note these two cornor portfolio needs to one after another to be in line with the assumption of linear relationship. If you select any other cornor portfolio, you may end up taking more risk with lowered returns (simply imagine a straight line from one point to another, due to linear relationship)

You could also use Risk free securities to lower your risk / increase returns.

This is my understanding and may possibily not be absolutely correct. Others - please add. Thanks

Theory for cornor portfolio assumes restrictions on short selling. This causes minor bumps or deviations in the efficient frontier, which is other curvy and have highest sharp ratio (return over Rfr in comparison to risk assumed) for any portfolio falling on it.

In case of cornor portfolios, the same sharp ratio is not same and have some deviations due to inability to short sell.

When as an investor, you set your risk and return objective, you could either look at this from risk or return objective and accordingly select a portfolio. In general case when short-sell is allowed returns are propotionate to risk assumed, since all the portfolios on the efficient frontier neccesarily need to have highest sharp ratio. And therefore, you could go either way - with return objective or with risk

However, it is not the case with cornor portfolios. there are portfolios with different sharp ratios. You can then then either go by the risk objective or with return. Since return objective is generally quantifiable, at least compared to risk objective, it is seen from the return objective. if you have a number for risk objective in mind, I beleive you can do the weightages on that basis and run the calculation, although it would be relatively complex than doing it for returns; just a note, for cornor portfolios, it is assumed that the correlation is 1, which is fine in theory, but wouldn’t be the case in practice.

So if you then plan to go with return objective, you look for the cornor portofio that matches with your return objective and use required weights in case an exact match is not there. point to note these two cornor portfolio needs to one after another to be in line with the assumption of linear relationship. If you select any other cornor portfolio, you may end up taking more risk with lowered returns (simply imagine a straight line from one point to another, due to linear relationship)

You could also use Risk free securities to lower your risk / increase returns.

This is my understanding and may possibily not be absolutely correct. Others - please add. Thanks

Appreciated.