How the corner portfolios are determined ? derived, question, little, ask

prashantsahni

I know it's a little bit strange to ask this question now.

But I just like to know how those corner portfolios in the text are determined (how to get those corner portfolios or how the corner portfolios are derived) ?

IAmNeil

Thanks for you all. I don't know why these are even not explained in the text. I now have a more clear picture about it, although not completely clear.

segalm

yes...well kind of...they are the portfolios available to the investor. In theory, you would include all available portfolios/assets in the analysis.

In reality though, this exercise is more philosophical than practical. Deterministic, one period optimization is very constraining. And if you use historical sample stats, your optimal portfolio can look very strange. So oftentimes to get a realistic optimal portfolio, if you're going to do mean variance optimization, you have to choose a limited sample of available assets, or a set of assets already aggregated into portfolios/asset classes.

torontoanalyst

Another question. Are the 6 asset classes on P.252 of CFAI Text Vol 3 selected by the investor ? Or ?

tikfed

the simplest way is to use solver, where u set the target cell at each level of return u need, and minimize the variance, changing the cells with weights

cfalevel2011

There is no equation to solve for these points. An iterative program, like the critical line algorithm, must be used. The authors probably just used solver in excel (see DFW's comment above). Any method can probably be used as this is a simple process, unlike in 1954 when Markowitz proposed this and computers were a rarity and extremely slow.

How I would do this using excel:

Find the top corner portfolio (UK equity 100% in this case). From there, you just work your way down the frontier, adding more of the next asset (real estate in this case), calculating the weights of the portfolio by minimizing the risk for every given level of return. When you get to 8.85% return, you see that ex-UK equity joined the efficient set so you define the second corner portfolio to be at 8.86% return, just before the new asset joined the efficient set. Then you just repeat this til you get to the bottom defining a new corner portfolio every time a new asset joins or leaves the efficient set.

There are fancier and faster ways to do this. Two of the neater ones: since the asset allocation tradeoff is linear between each corner portfolio, you can use this to your advantage in creating faster algorithms. Also, if you know what the next asset is to join or leave the portfolio, you can actually calculate the exact corner portfolio. This is rarely known though.



Edited 1 time(s). Last edit at Tuesday, June 21, 2011 at 02:30PM by MathMan.

HuskyGrad2010

OK, can anyone explain tangibly/clearly how the seven corner portfolios on P.253 of CFAI Text Vol 3 are created ?

Walex

the corner portfolios arise when you derive mean-variance efficient frontier with a constraint of no short sales.... so when you minimize variance at each level of return playing with weights (w=>0) the corner portfolios lie on the efficient frontier where one of the component assets changes it's weight from 0% to positive or vice versa

bleach

It's tough to explain the whole process, but you can use solver in excel to run mean variance optimization to solve for asset class weights and determine these points based on your inputs of expected returns and standard deviation for each asset class.

hw0799

They are available portfolios and are the most efficient with a given level of risk/return they offer the best other variable (same exp return, lowest STD dev).

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