Need some clarity on the corner portfolio concept:
Reference Quote:
From 2014 books
Adjacent corner portfolios define a segment of the minimum-variance frontier within which 1) portfolios hold identical assets and 2) the rate of change of asset weights in moving from one portfolio to another is constant. As the minimum-variance frontier passes through a corner portfolio, an asset weight either changes from zero to positive or from positive to zero. The GMV portfolio, however, is included as a corner portfolio irrespective of its asset weights.
As per the quote from the book “As the minimum-variance frontier passes through a corner portfolio, an asset weight either changes from zero to positive or from positive to zero.” So a corner portfolio must have a ZERO weight on one asset. So, does a corner portfolio necessarily have a zero weight on one of the assets? The only constraint we are putting is non-negativity of weights. So a corner portfolio can have positive or zero weight in that sense. But in every example, and book, I find that corner portfolios always have one of the assets as a zero weight.
Further, if the point no.1 is correct, (there must be a zero weight on one of the assets) and I was trying to create an Efficient frontier using 2 assets, then there can possibly be only 2 corner portfolios with (100,0) and (0,100) weights.
Lastly, The GMV is included as a corner portfolio irrespective of its weights, so even if had lets say a 70/30 allocation, it would get included. So its not really a corner portfolio (in the true sense as the weights of one the asset is not necesarily zero), but in order to construct the Mean Variance frontier we include it in our analysis.
Except for the GMV portfolio, every corner portfolio will have an asset with a weight of zero. Furthermore, if you move the tiniest bit either way on the efficient frontier from a corner portfolio, one of the zero-weight (at the corner portfolio) assets will now have a positive weight. Therefore, it’s most likely that at a corner portfolio you will have (at least) two assets whose weights are zero: as you move up-and-to-the-right along the efficient frontier, one of those assets’ weights will be positive until you hit the corner portfolio, whereupon it will become (and stay) zero, and another of those assets’ weights will be zero until you hit the corner portfolio, whereupon it will become positive.
Yup.
There are two criteria to be a corner portfolio: either
At least one asset’s weight changes from zero to positive or from positive to zero as you move up-and-to-the-right along the efficient frontier through that portfolio, or
It’s the GMV portfolio.
The GMV portfolio probably doesn’t meet the first criterion, but it meets the second. So it’s a corner portfolio, by definition.
So, except the GMVP all CP have at least one asset weight of zero. Right?
Cause on p. 178 of the recent Kaplan Schweser Book 2, the Professor’s Note state something with changes in assets’ weights. If I move up the EF from the GMVP to the “next CP”, there could be the situtation that there is no change in one of the portfolios asset’s weights to zero or non-zero. But, this only applies for the “first CP after the GMVP”.
THe cause of my confusion is a question on the Schweser book - page 268 Book 2, Self Test, Asset Allocation Chapter, where they have provided a list of corner portfolios and none of the portfolios has a zero weight.
So am guessing there is a mistake / misprint in the book.
