Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I took some classes in portfolio theory, and learnt the Markowitz Mean-Variance Analysis. If only two risky assets, the efficient frontier would be a hyperbola passing through the two points; now if added another asset has some correlation with them two, the efficient frontier would be pushed to the left of these three risky assets, generally not passing through them; so, if we keep adding more assets, it seems intuitively that the efficient frontier would be pushed further to the left of the assets points; wouldn't the efficient frontier be like tangent to the y-axis(y axis is for return), causing the standard deviation to be almost zero? I also read Pennacchi's book: Theory of Asset Pricing. it derived the equation for the minimum variance set using linear algebra. And found the position for the global minimum standard deviation point. And it's positive. I understand the equation derivation, but didn't get through the problem as I just thought of. Any help? Much appreciated.

share|improve this question

In mean-variance analysis, you combine different assets to minimize variance and maximize expected return. The hyperbola is not a function of the number of assets, but of their mean and variance. If the efficient frontier where a tangent to the y-axis (which can't be) or nearly a tangent, that would mean you would have almost zero portfolio-variance, which won't be the case for risky assets, and clearly not so by adding further assets with variance >0.

share|improve this answer
Thanks, Arne. e.g, only two risky assets, if perfectly negatively correlated, their efficient frontier would be two pieces of lines, and it can go pass a point on the y-axis, so by adding further assets with variance >0, but very negatively correlated with the assets we have, would it be possible to push the efficient frontier further to the left? – StayFoolish Sep 23 '13 at 20:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.