A lot of places mention one restriction of Efficient frontier is the assumption of normal distribution for the risk returns. However, where the assumption is applied in the process of mean variance analysis? It does not seem appear in the process of formulation of expected returns or covariance matrix neither in the process of tracing out the efficient front.

In general I don't think it has anything to do with Normal Distributed returns ( and someone can correct me on this) I think the problem is what the tangency portfolio attempts to optimize.It looks to find the best risk-reward payoff and weights more heavily assets with good sharpe ratio vs bad sharpe ratio with consideration to how these assets are correlated. One important assumption is that this risk only makes sense in symmetric return payoff.Ie it cares only about mean return and variance. If this distribution isn't symmetric or other factors like kurtosis or skewness are what investors care about, then the portfolio optimization theory won't be correct.

This is exactly what I think too. But look at the http://en.wikipedia.org/wiki/Modern_portfolio_theory on the criticism part. The first is "Asset returns are (jointly) normally distributed random variables". Do you know where this comes from?

You don't need to make distributional assumptions to calculate the efficient frontier. For CAPM to hold, however, you either need nomal distribution or the investors to care about only the first two moments of any distribution.

Thanks Gardener3! You mean everywhere people mentioning normal distribution assumption really refer to CAPM instead of efficient frontier. Correct?Even in the first developed CAPM, investors are assumed to make decision solely on mean and variance but an equivalent assumption is the normal distribution of the returns. Correct?

It's not only CAPM it's in general and you can find the link when you look at the problem as the optimization of the index of satisfaction(I'm following Meucci's, "Risk and Asset Allocation", 6.5.1). The only markets, for which the approximation of the investor's satisfaction in terms of the first 2 moments is exact, are the elliptical markets or if the investor's utility is quadratic.hth

Thanks iuliny. I will get the Meucci's book and read the relavent chapter for better understanding.

As a summary, there exist three situations where the assumptions for the efficient frontier hold:1. Investors have a quadratic utility over wealth. No distributional assumptions are needed on returns. 2. Investors have an exponential utility and returns are normally distributed. 3. Investors have a power utility and returns are lognormally distributed.