Decoupling Volatility and Correlation: the Russo Ratio

A few weeks ago, a client asked a deceptively simple question: “You guys tell us how much risk our portfolio has, but can you tell me how much of that risk comes from volatilities and how much comes from correlations?” I sat there a bit dumfounded and finally said “well, that’s a pretty obvious thing to ask. I wonder why I’ve never heard that question before.” In 20 years of professional risk management, that really was the first time I heard that question. Risk attribution is a common thing to analyze, but it’s usually answered in terms of how much risk each part of the portfolio carries: e.g., what fraction of the risk is from stocks, from bonds, etc. or from my technology investments, from my energy sector investoments, and so on. But the basic formulas for calculating portfolio risk take three inputs: the investment amounts into different securities, the volatilities of those securities and the correlations between those investments. It makes a lot of sense to ask how much comes from each part, and I’m quite embarrassed that I never thought about asking it myself. So off we went to solve the problem…