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Let's say I am performing mean-variance optimization subject to some weight constraints.

I'd like to identify the set of corner portfolios so that I can interpolate the entire efficient frontier. A corner portfolio defines a segment on the minimum-variance frontier within which i) portfolios hold identical assets, and ii) the rate of change of asset weights in moving from one portfolio to another is constant. Incidentally, The Global Minimum Variance portfolio is a corner portfolio.

Any convex combination of two adjacent corner portfolios is also a portfolio on the efficient frontier. So these corner portfolios can drastically improve the performance of tracing out the frontier.

Are there tools in R to identify the corner portfolios, or a research paper on an efficient algorithm to identify the portfolios? Markowitz himself introduced the critical line algorithm, however, I recall Sharpe and others have some approaches as well. R or matrix calculus approaches are preferred but I'll take research citations as well.

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Correct me if I'm wrong, but efficient frontier is a linear combination of any two efficient portfolios. –  Alexey Kalmykov Dec 23 '12 at 8:46
    
No - an efficient portfolio is only a linear combination of any two corner portfolios. –  Quant Guy Dec 23 '12 at 20:31
    
Are you sure? Check the paper provided in the answer by Bryce, page 4, in the bottom: "The the set of efficient portfolios of risky assets can be computed as a convex combination of any two efficient portfolios." –  Alexey Kalmykov Dec 23 '12 at 20:34
    
*Also, see zivot links below. "The the set of efficient portfolios of risky assets can be computed as a convex combination of any two efficient portfolios." –  pat Dec 25 '12 at 7:41

1 Answer 1

This piece of research provides everything you need:

http://faculty.washington.edu/ezivot/econ424/portfoliofunctions.pdf

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Could you summarize the contents of that link? –  chrisaycock Dec 23 '12 at 2:26

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