Volatility tends to drop when market risk is building up and leverage is rising, luring investors into complacency. Indeed, the lower volatility justifies investors taking on more leverage; if volatility has dropped by a third, why not take one and a half times the leverage? This pro-cyclical dynamic arising from lower volatility in times of increasing risk-taking is the volatility paradox. The main take-away from the volatility paradox is that we shouldn’t use shorter-term, contemporary risk measures when they are very low.

But there isn’t really a paradox, and we shouldn’t ignore the low volatility. Unusually low volatility has value, it is just that if it is being viewed as a typical volatility measure it is being looked at in the wrong way. We can rely on short term volatility as a risk indicator, not as an exogenous measure of risk, but rather as endogenous manifestation of the dynamics of the market because low volatility may be telling you that everyone is levered to the hilt and is willing to snap up any asset that moves, that everyone is casting aside negative information with hardly a second thought.

When viewed as endogenously determined by the behavior of the market, the relationship between risk of crisis and unusually low levels of volatility is simple: If people are levered and are at the ready to snap up positions, if they are ready to arbitrage out price differences and make markets oblivious to risk at razor thin margins, then it won’t take much of a price move to find the other side of a trade. If people don’t care about negative information, then the information flows will hardly move prices. The result is low volatility, and this in turn leads to more leverage and then another round of the dynamics that feed the low volatility. The result will be a descending level of volatility that is telling you that the market had been lulled into complacency, or worse, is in full-speed-ahead risk taking fervor, and hence is vulnerable.

Of course even if it is more the latter, it still will be the case that a low volatility derived from recent history will likely reflect low volatility in the near future, because if people are levered and ready to buy anything, if they are at a level of exuberance that leads them to discount anything negative in the market, the odds are high that that the same behavior will persist for the next while. But then suddenly it won’t. There is the chance that the floor will fall out and a crisis will be unleashed, and more than anything else, that is what we need to know for risk management.

We can see this when we think look at things from the other direction: what happens to volatility when the crisis finally hits. At that point no one wants to take on any risk, delevering has led to a reduction in liquidity, and so prices have to move a lot to entice buyers. The market is skittish, and so any news or rumors find everyone scurrying for cover. So for both liquidity and information reasons, prices move a lot more and thus volatility rises to the point that it is again not a useful measure for risk, but for the opposite reasons..

**The diversification paradox**

Related to the volatility paradox is what we can term the diversification paradox, which I discussed in a post some time back. As with volatility, correlations are low pre-crisis. So as is the case with low volatility, the low correlation and resulting apparent potential for diversification will lull investors into taking more risk. And because of the dynamics that create the low correlation, this in turn will feed into further reductions in correlation, thus adding to pro-cyclicality.

At least this is what will happen if we take the correlations as exogenous – that is if we say “they correlations are what they are, so let’s throw them into our variance-covariance matrix and then let the optimizer rip”. But as with volatility, if we look at the correlations as being endogenous to the dynamics of the market, they give us warning signs. Low correlation tells us that everyone is evaluating the most subtle differences between assets – for example, are the transportation costs for the Ford’s supply chain dropping relative to those of GM’s – and is also searching out opportunities in hinterland, esoteric markets. One asset is being finely differentiated from the other, correlations are therefore low, and investors take more leverage and more exposure because of the apparent potential for risk reduction through diversification.

Of course we all know that when the crisis hits the correlations suddenly rise and the benefits of diversification go out the window. Thus, as I wrote in my earlier post, diversification works all the time, except when it really matters.

When the crisis finally hits, correlations shoot up from the same endogenous dynamics. Suddenly, the only thing that matters is risk, not the subtleties of earnings and the opportunities in Malaysian onyx mines. It is like high energy physics, where matter become an undifferentiated white-hot plasma; assets that are risky are all viewed the same way, all of the risky assets meld together. So correlations rise.

**The Paradoxes and Risk Management**

There are two points from this discussion of the volatility paradox and the related diversification paradox.

The first and well-known point is that if investors take these measures as exogenous – that is, if the data are treated as a given in the computation of the statistics and the statistics are then applied based on their statistical interpretation – then they will lead to pro-cyclical behavior. Higher leverage and risk taking in general will be apparently justified by the lower volatility of the market and by the greater ability to diversify as indicated by the lower correlations.

The second is that just because the volatility is not a good indicator of the risks lurking in the market doesn’t mean it is not useful. If we recognize that volatility and correlation are endogenous measure that are a manifestation of market dynamics rather than exogenous statistics of market risk to be thrown into our risk management engines, if we dig deeper into the dynamics that are generating them as endogenous parts of the market dynamic, we will find that they actually are telling us far more about the markets.

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