"Honey, I Shrunk the Portfolio Concentration Risk!"

The 2008 crisis was unique in terms of its speed, the jump in correlations and the fall in liquidity. Multiple asset-class returns have been headed in the same direction: down!

The dramatic downturn in 2008 severely shook the confidence of investors in the ability of traditional risk management practices to mitigate their downside exposure. Traditional portfolio optimization with asset weights constraints might not generate truly risk-diversified portfolio. The resulting optimal portfolios tend to be overly concentrated in a very limited subset of the full assets or securities spectrum. For example, traditional 60/40 (i.e., S&P 500 and Lehman Aggregate) or so-called balanced portfolios do not offer investors true diversification because the 60% stock allocation (S&P 500) actually accounts for almost 95% of the portfolio risk. In a sense, 60/40 portfolios put almost all the “eggs” in one basket. When (not if) the stock market has a severe downturn (as witnessed recently), 60/40 portfolios would also suffer tremendous losses.

A direct relationship exists between loss contribution to a portfolio from its underlying components, and their risk contribution counterparts. The risk contribution of component i is the share of total risk of the portfolio which is attributable to this component.

I propose a simple way to measure the homogeneity of risk contributions, which is related to the efficiency of the portfolio risk diversification. The risk diversification efficiency measure guarantees that the risk contribution weights are not too widespread. It works with negative risk contributions which are typical with bonds in a traditional portfolio, due to the negative correlations with stocks or alternative assets. The lower the value of the risk diversification measure, the more efficient the risk diversification of the portfolio.