Does Risk Come Mostly From Volatility, or From Correlations?

By Damian Handzy, Investor Analytics

Originally published on Quant Forum 

When it comes to risk attribution, most people look at the contributions made by different asset classes, sectors or investment strategies. But very few look to assign attribution to volatility and correlation. 

When it comes to risk attribution, most people look at the contributions made by different asset classes, sectors or investment strategies. Some look at factors such as momentum or size. But very few look to assign attribution to two of the very inputs into most Value-at-Risk calculations: volatility and correlation.

Part of the reason is that the various approaches to calculating VaR don’t lend themselves to isolating these two parts very easily. But a closely related quantity – the square of the VaR number – can indeed be separated into two additive parts: one purely dependent on volatility and the other on correlations.

Investor Analytics’ white paper on this topic, “The Russo Ratio: Decoupling Volatility and Correlation” (which can be downloaded here), introduces three new analytics: CCR – the Correlation Contribution to Risk; VCR – the Volatility Contribution to Risk; and the Russo Ratio – CCR/VCR, which provides a compact way of understanding how much diversification benefit is inherent in the portfolio. The paper explains these measures and analyzes three different portfolios using these new measures to show the effects of low and high diversification.

The Volatility Contribution to Risk is always a positive number, since volatility always increases a portfolio’s risk. The Correlation Contribution to Risk can be either positive or negative, reflecting the potential lowering of risk through diversification. As a percent of total, it is therefore possible to have more than 100% coming from volatility, with a negative percent coming from correlation. For example, in the white paper we show periods of time in early 2005 when an asset-class diverse portfolio showed 110% risk from volatility with -10% risk from correlations. For a given portfolio, we show that the Russo Ratio of CCR/VCR is remarkably stable over time.

This Russo Ratio has a lower limit of -1, reflecting perfect hedging in which the correlations reduce the volatility risk perfectly. Values between -1 and zero represent partial hedging situations in which the correlations partially reduce the risk. Values near zero imply that the correlations don’t reduce or contribute to risk – that all the portfolio’s risk comes from volatility. While the Russo Ratio has no theoretical upper bound, values above 1 indicate that correlations contribute the bulk of a portfolio’s risk.

quant 7 15 14 

We received a number of interesting comments about the paper. While almost everyone had never seen such a decoupling of volatility and correlation, one correspondent indicated that he had implemented something very similar about 10 years ago while managing risk for a prominent hedge fund.

Several managers shared the view that CCR, VCR and the Russo Ratio are most useful when viewed over time to gain both familiarity with the values and to quickly identify outliers. In addition, one correspondent indicated that this is a new way of looking at risk information that can have an advantage in certain situations.