Corner portfolio

If the highest Sharpe ratio efficient portfolio generates return higher than the required return, should i go for constructing portfolio using two adjacent corner portfolios??? or should i just go with the highest Sharpe ratio efficient portfolio???

When short selling is prohibited you go with 2 adjacent portfolios. When you are allowed you go with highest sharpe ratio.

if leverage is allowed - you would use the risk free with the highest sharpe ratio portfolio to get the required return.

otherwise you would use 2 corner portfolios that bracket the required return.

Well if the highest Sharpe portfolio is higher than required return you could just invest in the portfolio and risk free asset. I don’t think buying a risk free asset is consider leveraging.

Does it imply that whatever the situation is we have to build a portfolio for which expected return is JUST EQUAL to required return???

@s2000magician sir: Would you please write 2/3 lines. thanks for your time :slight_smile:

S2000- can you please also confirm/ weigh in on the following? A corner portfolio is basically a minimum variance portfolio where the weight of an asset class either goes from positive to zero, or zero to positive. The market portfolio is the corner portfolio (min variance portfolio) with the highest sharpe ratio. Therefore, if there is a “corner” portfolio listed where the weights do not change from either positive to zero (or vice-versa) and does not have the highest sharpe ratio, then we should ignore it in the analysis? IE- remove it from the table when calculating appropriate weights? I have seen this a few times in mocks, but the “non-corner” is not relevant to the required return so I’m not quite sure how to handle if the try and “trick” us during the exam. Side note- I do remember seeing a sample question where it was referenced that the analyst was aware that one portfolio listed was not a true corner and should be removed, but CFA will likely not be as generous in forewarning us of this instance.

My thoughts on above question: if market portfolio’s return is above the required return, then hold the market portflio and risk free in a manner which produces the required return, no need to accept additional risk if not needed…

I agree with Kys916 there is an example of this in the book.

You guys need to listen to cpk123: he knows whereof he speaks.

In practice, you would use optimization to find the (efficient) portfolio with the highest Sharpe ratio; that’s the market portfolio. (I used to teach a class in asset allocation in which we built an efficient frontier in Excel and did just this.)

On the exam, you should assume that the corner portfolio with the highest Sharpe ratio is the market portfolio.

I’m not the ultimate authority on all that is CFA. There are lots of other posters here (e.g., cpk123, or ro424 and Galli at Level II) who really know their stuff. Listen to them.

Relevant, but off topic due to too much unnecessary detail:

I did a my disseration on BL, so I can answer your question somewhat. Technically you can calculate without excel the efficient frontier of each portfolio. You use calculus in respect to a desire level return and solve to minimize variance (standard deviation^2, so power rule)… However if there are more tha two assets in the portfolio you need to use matrix multiplication, which I don’t think most ppl taking the CFA is able to do. The minimum variance portfolio is not the with the highest Sharpe, but lowest variance on the frontier. I think it’s just term confusion here, each corner portfolio will have the highest sharpe for that level of return, but there is only ONE minimum variance portfolio. We assume the highest Sharpe is the market portfolio due to supply and demand (CAL and BL uses this logic). If there are assets with a higher sharpe than market, ppl will buy it pushing price up (cost base of the asset is higher) and return down.

When CFA tells it to solve using the corner portfolio, it is a quick and dirty way that ignores correlations. This will over estimate the actually VaR.

There is an easy way to see if a portfolio is a corner portfolio or not due to limitation of knowledge and time on exam. If there is a portfolio with a lower return and a higher standard deviation than it’s neighbour ( P1: R= 6% Stdev = 11%, P2: R = 7% stdev= 16%, P3: 8% stdev= 12%). You know that P2 is not on the frontier usually do not kink (I have used actually data and gotten a zig zag line, but my frontiers allow leveraging and short selling of all asset classes), due to a whole lot of mathematicially and supply and demand factors.

from the CFA level 3 fourm: This example is uses the Risk free asset not adjcent portfolios, book 3 ss8 #19 example 10 on page 230.