Economic and financial risk factors, copula dependence and risk sensitivity of large multi-asset class portfolios

In this paper we propose a flexible tool to estimate the risk sensitivity of financial assets when exposed to any sort of risks, including extreme ones, from the financial markets and the real economy. This tool works with observations and a priori views. Our contribution is threefold. First, we combine copulas and factorial structures which allow us to capture the whole dependencies between the returns of a large number of assets of multiple classes. We build what we call a Cvine Risk Factors (CVRF) model, which can disentangle financial and explicitely economic like activity, inflation, emerging, etc, and more generally speaking real sphere related risks. Second, this model provides the way to extend the well known linear multibeta relationship in a non-linear version and to assess the exposures of any asset to several factorial risk directions in the cases where the risks are extreme. The exposure measures are relevant Cross Conditional Values at Risk (Cross-CVaR). Third, as an application of the methodology, we solve an optimization program to find portfolios that are the most diversified in capital while being immunized to extreme shocks to a given risk factorial direction. Varying the immunization constraint, we recover the portfolio strategies which are the most widely used today. For example, adopting the ERC (Equal Risk Contribution) rule insures optimal capital based diversification and immunization against inflation risk. Accordingly, we propose a unified view and a rationalization ex post of several current portfolio strategies that appear different at a first glance.