### The Volatility Paradox

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.

*The Securities and Exchange Commission disclaims responsibility for any private publication or statement of any SEC employee or Commissioner. This post expresses the author's views and does not necessarily reflect those of the Commission, the Commissioners, or other members of the staff. Similarly, this post expresses the author's views and does not necessarily reflect those of the Department of Treasury or its staff.*