corner portfolio determine, question, because, problem

krause2

Would we always be told whether there's restrictions on leverage for a corner portfolio problem? i.e. is there any other way to determine whether we should use short-constrained methodology or not, other than being explicitly told?

I ask because it's not mentioned in the CFAI EOC question (rdg 26, p333, #9). Doesn't mention any constraint, but solves the problem as such

Zestt

I believe they will use the word "corner portfolio" in the question rather than saying there is a constraint on short-sale.

justin88

So if shorting is allowed - we use one corner portfolio and a riskfree-asset?

And if shorting is NOT allowed - we use 2 corner portfolio's?


Sorry it's pretty late and mental farts are unavoidable!

liangfeng

B_C Wrote:
-------------------------------------------------------
> If E(R) > tangency portfolio and no short sale
> allowed.
> => choose 2 corner portfolio
>
> If E(R) > tangency portfolio and short sale is
> allowed.
> => Combine rf asset with the tangency portfolio
> (highest sharpe portfolio)
>
> If E(R) < tangency portfolio, whether short sale
> allowed or not
> => Combine rf asset with the tangency portfolio
> (highest sharpe portfolio)


hmm.. I hadn't thought of that last scenario, where if borrowing rf is not necessary then always use highest sharpe. though I suppose that is the optimal thing to do..

I was always going about it as:
shorting allowed --> highest sharpe + rf
not allowed --> adjacent porfolios

former

B_C Wrote:
> If E(R) < tangency portfolio, whether short sale
> allowed or not
> => Combine rf asset with the tangency portfolio
> (highest sharpe portfolio)

I think in this case, short sale is not required. Am I wrong ?

Darien

yes, if If E(R) < tangency portfolio

You don't need to borrow, so whether short sale is allowed or not is irrelevant to you. You just need to invest in both risk free asset and tangency portfolio. Tangency portfolio has the highest sharpe ratio, adding risk free asset just help lower the overall portfolio risk without compromising on the sharpe.

mik82

Excellent B_C, Thanks!

Windjammer

green360 Wrote:
-------------------------------------------------------
> B_C Wrote:
> --------------------------------------------------
> -----
> > If E(R) > tangency portfolio and no short sale
> > allowed.
> > => choose 2 corner portfolio
> >
> > If E(R) > tangency portfolio and short sale is
> > allowed.
> > => Combine rf asset with the tangency portfolio
> > (highest sharpe portfolio)
> >
> > If E(R) < tangency portfolio, whether short
> sale
> > allowed or not
> > => Combine rf asset with the tangency portfolio
> > (highest sharpe portfolio)
>
>
> hmm.. I hadn't thought of that last scenario,
> where if borrowing rf is not necessary then always
> use highest sharpe. though I suppose that is the
> optimal thing to do..
>
> I was always going about it as:
> shorting allowed --> highest sharpe + rf
> not allowed --> adjacent porfolios

yep! this is the way I remembered.