Two questions:
Does efficient frontier incorporate within its assumptions diversification effects at the security level?
Is correlation really that useful of a proxy for computing diversification? Generally historical correlations between markets (EU, US, EM) is high. Does that mean that you should concentrate your portfolio mainly in the one with the highest return/risk or should you still diversify before hand to avoid the “Oh Shit” Greece bailout scenario?
Efficient Frontier is just a mapping between risk and return for a defined set of investments (either securities, assets, etc). If you define investments as securities, it would include diversiification effects at the security levels.
Efficient Frontier is constructed based on assumptions. If you decide to use historical correlations you would get an EF that is very different from one you would get if you use shrunk correlations, etc. Think of an EF as a calculator that uses your assumptions about expected returns, volatility and correlations to define a mapping between risk and return along with optimal allocations for each level of risk.
In addition to what maratikus said, another way to interpret the efficient frontier is to realise that every point on it is the output of the mean-variance optimisation programme. Every point on the frontier is a minimum variance portfolio and each such portfolio is just a collection of weights associated with the investment universe, which could be asset classes or individual securities of an asset class depending on how the boundaries are defined.
The standard Markowitz approach involves either minimising portfolio risk subject to a given expected return or maximising portfolio returns subject to a given level of risk. Evidently risk can be defined in a number of ways. You could look at standard deviation,downside deviation and other candidates. Estimating such risk measures are subject to error and one could use statistical methods to obtain a better estimate (perhaps shrinkage)
Mathematically, the markowitz procedure is basically set in stone. What changes are the inputs : expected returns and variance-covariances across assets.Do you use historical returns as an estimate of expected returns or do you try to obtain an estimate via a factor model (CAPM,APT,Fama/French,Macrofundamentals,Principal component analysis)? Depending on your choice, the risk estimate will vary aswell.
Not sure if i understand your second question,but the point of diversification is to find assets that are less than perfectly correlated with one another. One issue here is how to measure dependency. If asset returns are normally distributed, pearson correlation is useful as an indicator or linear dependency. Under non-normality, you would look to other measures beyond pearson’s coefficient.