# Corner Port - No Constraints

Just a quick question.

When SAA, and you have no constraints, do you always attack the Market Portfolio and then use Rf to adjust to get to your required return?

i.e.

Required 10

Port 1: 9

Port 2: 10.5

Port 3: 11 - this is the market port.

For constraint you do port 1 and 2, but for uncontraint you always go for the market?

Just thinking of a possible question they might ask.

with unconstraint you always go with the highest sharpe ratio ( normally the market portfolio )

Summer - thanks.

Just was thinking… If they ask something like Summerside has no constraints on weights, find the optimal portfolio given these on the EF.

Thanks

Yea be careful, not the highest return but the highest sharpe

Yup. Tangent Portfolio as they call it.

This was an easy question to get us back up and confident!

yes exactly, normally they dont say that < this is the market portfolio > so check the highest sharpe.

also, be aware, the highest sharpe ratio may have investment in a constrained asset class. they will say < this investor dont want to be invested in real estate > so if the highest sharpe has real estate, dont take it, go for the one within the investor demand, with the highest sharpe

Does this logic apply to the constrained one too? So by default I am picking say corner portfolios 3 and 4 but 4 has real estate and client doesn’t want that then what? Do I go 3 and 5 or 5 ? Don’t they have to be adjacent for accuracy and assumptions to hold?

adjacent portfolio is always better, but even with adjacent portfolio, their is other portfolio lying between them.

the corner portfolio method is a aproximation formula assuming that the EF is linear between 2 points, which is not the case ( their is diminishing benefit for taking more and more risk )

in the scneario you are giving, yes I would not touch the portfolio 4, and use 3 and 5. the approximation would be less accurate, but it would not include the constrained assets. I would be very suprise if they do this trick in the exam.

I agree with summer.

The theorem is based on linear interpolation so adjacent is not required. However, the further away the two portfolio’s are, the less ‘accurate’ you’r asset allocation is.

Given the title of this thread, I think we should be clear on one point:

Corner portfolios apply only to the constrained (no negative weights) efficient frontier; the unconstrained efficient frontier does not have corner portfolios.

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Adding to s2000 comment… if assumption is no constraint AGAINST LEVERAGE. We can use highest sharpe ratio portfolio and risk free security (could be negative weight) to achieve our target. Here assumption is no constraint against leverage as against no constraint against short sell. S2000 pls confirm ths?

I am fucking praying that this comes.

I’m not working today.

But, yes.

(Then use the client’s utility indifference curves to determine the optimal mix of the risky portfolio and the risk-free asset.)