Modern Portfolio Theory Revisited

In the first place the behavior of (online) traders on markets is analyzed and modeled, and it is shown that the average investor behaves as a mean-variance optimizer in finance. Within this description, transaction costs play a key role in explaining observed investment patterns and in particular an important uncovered relation between average investment and portfolio value. As online investors take into account transaction costs in their investment strategy, they are also sensitive to high portfolio rebalancing costs. Solutions to avoid high portfolio turnovers are investigated: first in the one-dimensional case, where it is shown that estimators with minimal-dispersion improve both the accuracy and the variance of volatility and Value-at-Risk forecasts; second, in a multi-asset environment where the ideal covariance matrix must have good conditioning properties to maintain reasonable portfolio turnover. Theoretical results are derived using Random Matrix Theory, as for instance an equation for the Stieltjes transform of the eigenvalue density of i.i.d. correlation matrices with general time-decreasing weight profiles. Results found in the one-dimensional case are generalized leading to long-memory covariance matrices. Finally, a "curse of dimensionality" in portfolio allocation is tackled by generalizing the Spectral Coarse Graining, a method of reduction for complex networks, that is extended to the simplification of the mean-variance optimization problem.