Editing Modern portfolio theory (section)

==== Tangency portfolio ====
[[File:Mean-variance analysis.gif|thumb|Illustration of the effect of changing the risk-free asset return rate. As the risk-free return rate approaches the return rate of the global minimum-variance portfolio, the tangency portfolio escapes to infinity. Animated at source [https://upload.wikimedia.org/wikipedia/commons/f/f4/Mean-variance_analysis.gif].]]The tangency portfolio exists if and only if <math>\mu_{RF} < \mu_{MVP}</math>.

In particular, if the risk-free return is greater or equal to <math>\mu_{MVP}</math>, then the tangent portfolio ''does not exist''. The capital market line (CML) becomes parallel to the upper asymptote line of the hyperbola. Points ''on'' the CML become impossible to achieve, though they can be ''approached'' from below.

It is usually assumed that the risk-free return is less than the return of the global MVP, in order that the tangency portfolio exists. However, even in this case, as <math>\mu_{RF} </math> approaches <math>\mu_{MVP}</math> from below, the tangency portfolio diverges to a portfolio with infinite return and variance. Since there are only finitely many assets in the market, such a portfolio must be shorting some assets heavily while longing some other assets heavily. In practice, such a tangency portfolio would be impossible to achieve, because one cannot short an asset too much due to '''short sale constraints''', and also because of '''price impact''', that is, longing a large amount of an asset would push up its price, breaking the assumption that the asset prices do not depend on the portfolio.