Corner portfolio - constraint against borrinwg, but not lending?

I understand that if you are not allowed to borrow, then you may not be able to use the tangency portfolio to calculate your allocation assuming your desired return is above the tangency portfolio’s return.

But what if your return goal is below the desired return and there’s no constraint against LENDING? Only against borrowing. In which case, should we still be using corner portfolios or should we do risk free asset + tangency portfolio?


You can lend, but not borrow. But only if it’s a constraint.

In other words, you can maximize your sharpe ratio for a given level of return by using a mix of the corner (tangent) portfolio with a risk free asset.

I need to get back to that topic, I don’t remember if the market portfolio is a corner portflio, guess it depends.

Lending means buying the risk-free asset.

EDIT: In my notes I have that the market portfolio is always a corner protfolio, and I thought that it would be the portfolio with the highest sharpe ratio, but after checking it seems it is the tangency portfolio which has the highest Sharpe.

The market portfolio is not necessarily a corner portfolio.

we will use tangency portfolio when

required return < exptd return on tangency portfolio. investsome in risk free and remain in tangency port.

The tangency portfolio is the market portflio, the CML. But it’s not always a corner as S2K said.

Ok, so I checked the CFAI text and it’s actually the GMV portfolio that is always a corner portfolio.

According to GoStudy, in their section about corner portfolios they say “note that the tangency portfolio is the portfolio with the highest Sharpe ratio. It’s the portfolio closest to the market portfolio and the exam will often ask you to ID it.” Which would imply to me that the tangency portfolio is always corner portfolio.

Now I am more confused about this now than I thought.

When I did a search on this site, I found a quote from s2000 “On the exam, you should assume that the corner portfolio with the highest Sharpe ratio is the market portfolio.”

Combining these statements, it sounds like the market portfolio is a corner portfolio, and that it’s approximating the tangency portfolio as the portfolio with the highest sharpe.

The market portfolio actually is most likely not a corner portfolio.

It is the tangent of the risk-free asset line and the EF, and therefore has the highest slope, and the highest sharpe ratio.

However, the corner portfolio closest to the market portfolio, will have the highest sharpe ratio out of all the others, I think this is what S2K was trying to say earlier.

And yes, the GMV is always a corner portfolio, so will the last attainable portfolio up the EF be as well, which should be stock heavy, if not 100% stock allocation.

The quote you got from GoStudy is plain wrong, or you simply pulled it out of context, if it’s latter, then I’ve explained what they wanted to put across.

The quote from GoStudy (daharmattan1 on this forum) is from

I did not pull it out of context. I think what he wanted to get across is exactly what he said, essentially if the exam asks you to ID the tangency portfolio in the list of corner portfolios, it’s the one with the highest sharpe ratio.

He is wrong, the MP is not the one closest to the tangency, it is the tangent portflio. I do not also like the synonym of tangency and highest sharpe ratio. ID’ing the CP with the highest sharpe ratio is not a tanget, but the closest to the tangent. This is how the question should come to you in the exam.

If you can borrow: use the single portoflio with the highest Sharpe ratio, this is the Market Portfolio.

If you can’t borrow: use two corner portfolios to hit your return requirement.

To be a market portfolio, doesn’t it need to be corner portfolio?

I mean it might not be in the given list. But it is out there somewhere.

No, it just needs to have the highest sharpe ratio. Which is highly unlikely to be a CP due to a missing asset class. Unless that risky asset was something awful.