Lost in Diversification

As financial instruments grow in complexity more and more information is neglected by risk optimization practices. This brings down a curtain of opacity on the origination of risk, that has been one of the main culprits in the 2007-2008 global financial crisis. We discuss how the loss of transparency may be quantified in bits, using information theoretic concepts. We find that {\em i)} financial transformations imply large information losses, {\em ii)} portfolios are more information sensitive than individual stocks only if fundamental analysis is sufficiently informative on the co-movement of assets, that {\em iii)} securitisation, in the relevant range of parameters, yields assets that are less information sensitive than the original stocks and that {\em iv)} when diversification (or securitisation) is at its best (i.e. when assets are uncorrelated) information losses are maximal. We also address the issue of whether pricing schemes can be introduced to deal with information losses. This is relevant for the transmission of incentives to gather information on the risk origination side. Within a simple mean variance scheme, we find that market incentives are not generally sufficient to make information harvesting sustainable.