  The problem of estimation error in portfolio optimization is discussed, in
the limit where the portfolio size N and the sample size T go to infinity such
that their ratio is fixed. The estimation error strongly depends on the ratio
N/T and diverges for a critical value of this parameter. This divergence is the
manifestation of an algorithmic phase transition, it is accompanied by a number
of critical phenomena, and displays universality. As the structure of a large
number of multidimensional regression and modelling problems is very similar to
portfolio optimization, the scope of the above observations extends far beyond
finance, and covers a large number of problems in operations research, machine
learning, bioinformatics, medical science, economics, and technology.
