Narrow Results

We propose a new framework to measure the risk of a single asset and of a portfolio of financial assets which takes the agent's investment horizon into account. The methodology is based on the moderate and large deviations theory in its simplest form. We show how it can be used to select optimal portfolios given investors' planning horizons and preferences for fatter right or left tails. For practical purposes, we introduce a new parameter, the "dilation exponent" α to characterize asset returns' distributions beyond the information contained in the mean-variance framework. We estimate α for Swiss individual stocks and for MSCI country and sector stock market indices. Finally, we show how to use the dilation exponent in conjunction with Sharpe's ratio for portfolio allocation purposes.

Correlation graphs are introduced to delineate the levels observed in data and models for return and squared return correlations. A sample of 2048 representative pairs of equity assets is selected from a possible collection of $381,501$ pairs by quantization. Five copulas are estimated and simulated on these pairs of returns, the Gaussian, t-copula, Clayton, Gumbel and Frank. Additionally, the multivariate bilateral gamma (MBG) model that introduces dependence via common time changes is also fit and simulated. Results of fit statistics on returns, CoSkew and CoKurtosis pairs are reported. The general ordering of the models is MBG, t-copula, followed by the Gaussian, Frank, Gumbel and Clayton copulas.