Christopher Cole argues that volatility markets are about trading both known and unknown risks. These risks require different pricing and cause different “crashes”. Most portfolio managers either hold implicit short volatility or long volatility positions. After the great financial crisis, monetary policy has suppressed volatility, but steep volatility curves are indicating a “bull market in fear”.

“Volatility: The Market Price of Uncertainty”, Christopher R. Cole
CFA Institute Conference Proceedings Quarterly, 2014 Q1

The below are excerpts from the article. Cursive text and underscores have been added.

What is volatility trading about?

“Modern financial markets are an impossible object [an optical illusion, which is perceived differently depending on what part one looks at], and the volatility of an impossible object is the changing perception of risk. So, if bonds are viewed as safe havens today but tomorrow they are not, that is a source of great volatility. And if today the assumption is that bonds and stocks are uncorrelated with one another but tomorrow they are correlated, that is also a source of great volatility.”

“Everything you need to know about volatility trading is in this quote from Rumsfeld…:’There are known knowns; there are things we know that we know. There are known unknowns; that is to say there are things that we now know we don’t know. But there are also unknown unknowns—there are things we do not know we don’t know.’ Volatility trading is about putting a price on known unknowns and unknown unknowns…The unknown unknowns are the true shocks. They are the risk factors that come out of the blue, such as 9/11. They can arguably be priced, through convexity and tail risk…but they can never be predicted.”

“It is possible to…hedge unknown unknowns and sell known unknowns. When the market identifies a risk factor, it tends to be overpriced in volatility markets, which means that there is an opportunity to sell that risk to fund underpriced volatility positions elsewhere…. those areas in which risk is not priced into the markets.”

What products are traded in volatility markets?

“The volatility product spectrum [can be divided into three groups]:

  • In the first part of the volatility product spectrum, investors gain volatility exposure using listed calls and options and then measure that exposure through a Black–Scholes model. These instruments are path dependent because the volatility exposure must be delta hedged [i.e. in order to avoid exposure to market direction must hold and dynamically adjust an offsetting position in the underlying].
  • Financial engineering led to the creation of a liquid OTC variance swap market and to the creation or refinement of major volatility indices, such as the VIX. The VIX measures the implied volatility of the S&P 500 30 days in the future. Simply put, the VIX is the quoted rate of a constantly rebalanced, constant maturity, 30-day variance swap.
  • An arbitrage boundary exists between a forward variance swap on the S&P 500 and a VIX future. Based on this arbitrage relationship, institutions began to offer listed volatility exposure through VIX futures on the Chicago Board Options Exchange. The VIX futures lead to options that are priced from VIX futures, and then to the creation of popular VIX exchange-traded products, such as the VXX (iPath S&P 500 VIX Short-Term Futures ETN) and XIV (Velocity Shares Daily Inverse VIX Short-Term ETN), which are at the very end of the volatility derivatives spectrum (and most easily accessible to retail investors).”

Volatility curves and skew contain embedded expectations for future variance, probability of asset returns, and tail risk across different asset classes. Value can be found in volatility by quantitatively valuing these expectations through time and trading over- and underpriced known unknowns in a comparative value framework.”

How is volatility priced?

“When investors buy volatility, they are not buying realized volatility; they are buying the expectation of volatility across some time frame The price is based on both known unknowns and unknown unknowns.

  • So, how is the price of known unknowns quantified? One way is to compare the implied with the realized variance risk premium. Some other ways are to consider the skew or the term structure of volatility.
  • And how are unknown unknowns priced? This pricing is a lot more difficult, but the market actually tries to price them using the price of convexity. If the price of convexity is backed out—that is, roughly the price of tail risk, far out-of-the money skew, or the variance to volatility swap premium—the result is a theoretical price of unknown unknowns.”

“[Corresponding to this distinction] two types of market crashes can occur…

  • A known unknown crash is a traditional leverage-based crash. This crash occurs over a long period of time—days or even months. It tends to occur after a leveraging cycle with long periods of very high volatility. Many people think that volatility mean-reverts, but in a systemic known unknown type of crash, volatility can remain elevated for long periods of time, whereas the volatility of volatility actually reaches an equilibrium.
  • Examples of an unknown unknown crash would be Black Monday in 1987 and the 2010 Flash Crash. These are hyper-speed crashes with a lot of reflexivity [circular relationship between cause and effect] and tremendous volatility of volatility—that is, the changes in volatility itself are massive. These crashes tend to correct as quickly as they occur.”

Who is holding volatility positions?

“Nearly all active traders are hidden volatility traders.”

“Institutions are focused on countless asset buckets, such as fixed income, equity value, or macro, but ignore the fact that active manager returns largely fall into two simple categories: (1) short volatility bias or (2) long volatility bias. The first group comprises the majority of active managers who are secretly short some combination of volatility, correlation, and liquidity or are simply leveraging beta… A lot of active managers are simply short volatility traders in disguise, so it is not surprising that most underperform in a crisis…The second group contains true hedgers, the crisis alpha players, whose portfolios are uncorrelated with the markets.”

“In the universe of active managers it becomes very hard, even over long periods of time, to determine the true future loss of the hidden short volatility component in performance. “

How did volatility evolve after the great financial crisis?

“The idea of a bull market in fear is a new paradigm for pricing risk that emerged after the financial crisis…A volatility term structure reflects expectations for tail risk, the volatility of volatility, and other risk factors. Since 2009, investors have experienced a bull market in fear whereby the volatility term structure has steepened dramatically, driving up the cost to hedge. As Alfred Hitchcock said, ‘There is no terror in the bang, only in the anticipation of it.’…So, volatility might be low today, but the expectation of volatility tomorrow might be very high.”

“Four factors play a role in the bull market in fear.

  • The first is the emotional factor….people have a strong emotional memory of the last collapse and want to buy protection to avoid repeating that process again.
  • The second factor is monetary. The Fed’s quantitative easing and low interest rate policies have forced investors to take more risk and to chase yield. Investors do not feel comfortable doing so and want to be protected.
  • The third factor is macro risks, which are the true geopolitical risks…
  • The fourth factor is government regulation, including the Dodd– Frank Act and the Volcker Rule. New regulation has constrained the risk appetite of banks to supply volatility, but there is no one else available to take the place of banks, which has caused an increase in the term structure of volatility.”
“Today, the most effective model for determining the future volatility is, sadly, the Fed’s balance sheet. When the Fed expands its balance sheet, volatility drops. When the Fed stops expanding its balance sheet, volatility spikes.”

“Another indication of suppressed volatility is rising mean reversion of daily returns or negative autocorrelation. Mean reversion generally peaks before rising volatility… high mean reversion tends to occur before crises, as seen in the peak in 2000 before the recession in 2001–2002. The last peak in mean reversion was in 2008 before the most recent recession.”