Corner Portfolios

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Galli

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Can someone help me understand what a corner portfolio is?
Is a corner portfolio a segment along the EF where two portfolios hold the same assets but the weight of said assets vary between the two? Why is this important?
 
A corner portfolio is either the GMV portfolio (for sake of completeness), or a portfolio at which, as you move up-and-to-the-right along the efficient frontier, the weight on (at least) one asset goes from positive to zero or from zero to positive.
Suppose that you have three securities: A, B, and C.
  • The GMV portfolio is 60% A, 40% B; that’s a corner portfolio
  • As you move up the efficient frontier, the amount of A increases and the amount of B decreases.
  • You hit the spot on the efficient frontier which is 100% A: the weight of B has gone from positive to zero, so that’s a corner portfolio. (As we’ll see, it’s also the point where the weight of C goes from zero to positive, confirming that it’s a corner portfolio.)
  • As you move up the efficient frontier, the amount of A decreases and the amount of C increases.
  • When you hit the end of the efficient frontier, which is 100% C, the weight of A has gone from positive to zero, so that’s the third (and last) corner portfolio.
 
I see, thanks S2000. So a corner portfolio can only exist when 1 asset is at 100% and another is at 0%? The objective is to find the ‘optimal’ corner portfolios, and calculate a weight between them to find where the sharpe ratio is maximized?
If that’s true, why do we have to find the corner portfolios in order to solve the highest sharp ratio? Is it because the optimal allocation is not on the EF therefore was never solved originally?
 
Galli wrote:I see, thanks S2000. So a corner portfolio can only exist when 1 asset is at 100% and another is at 0%? The objective is to find the ‘optimal’ corner portfolios, and calculate a weight between them to find where the sharpe ratio is maximized?
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No.
You have to have (at least) one asset at 0%, but the rest can be anything. If you had a portfolio with 30% A, 70% B and 0% C, and when you move up it changes to 29%, 69%, and 2%, then the original portfolio’s a corner portfolio.
The obective is to find all corner portfolios on the efficient frontier, then interpolate for the rest of the efficient frontier.
Galli wrote:If that’s true, why do we have to find the corner portfolios in order to solve the highest sharp ratio? Is it because the optimal allocation is not on the EF therefore was never solved originally?
Click to expand...
You don’t. It’s just a nice part of the theory.
If I were looking for the portfolio with the highest Sharpe ratio (and I’ve done this many times), I’d simply put all of the formulae and constraints into Excel and tell Solver to calculate the weights that give the highese Sharpe ratio; I wouldn’t bother with corner portfolios.
 
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