Over the past 50 years, the financial markets have been rocked by major shocks, which have led to the introduction of financial instruments that could cope with uncertainty in general and extreme events in particular. To manage the uncertainty surrounding the financial markets, there was a need for reliable uncertainty indicators. The traditional measure of uncertainty―stock volatility―has been challenged by advanced statistical methodologies (GARCH) and derivatives-based forward-looking forecasts (VIX). In a new paper, we discuss the history of volatility and uncertainty measures, their informativeness, and the information derived from volatility derivatives.

Volatility measures (simple historical volatility, ARCH/GARCH, and the VIX) assume that probabilities of outcomes are known. However, in reality, the probabilities of future states of the economy and of the financial market are unknown. In nearly any decision in life, we face ambiguity―the uncertainty about likelihoods. Nevertheless, this dimension of uncertainty is often ignored. Even when encountering a “black swan” event, we tend to classify it as a “fat-tail” event. Ignoring the fact that the probabilities are unknown may lead to sub-optimal decisions, especially when this aspect of uncertainty is significant. Rare events, such as the 2008 financial crisis and the current Covid-19 pandemic, seem to create ambiguity of a magnitude that cannot be ignored. Recent academic research proposes theory-based measures of the historical ambiguity, as well as of the forward-looking ambiguity (AMBIX).

Both measures, the VIX and the AMBIX, have a theoretical underpinning and complement each other. While the VIX is considered a measure of ** risk** (volatility of outcomes), the AMBIX is a measure of

**(volatility of probabilities). More specifically, ambiguity is the uncertainty about the probabilities that make up the risk measure. Introducing ambiguity alongside risk portrays a clearer picture of the (expected) uncertainty in the financial markets.**

*ambiguity*During the past 20 years, an unprecedented period of extreme Volatility and Volatility of Volatility accompanied two major market crashes: the 2008 financial crisis and the Covid-19 crisis. During this period, the VIX reached levels below 10 percent and above 80 percent, while the long-run average volatility was about 20 percent. The Volatility of Volatility reached levels above 200 percent, compared with an average of about 120 [ercent. During the same period, ambiguity ranged between 5 percent and 60 percent.

Even though the two market crashes―the 2008 financial crisis and the Covid-19 crisis―were accompanied by extremely high levels of the VIX (80 percent and above), there are several differences between the two. While in the 2008 crisis, the high values of the VIX preceded the financial market bottom (March 9, 2009) by about four months, in the Covid-19 pandemic crisis, the high level of the VIX and the financial market crash happened almost simultaneously. Moreover, in 2020, the speed of the decline in the financial market was unprecedented. From its peak on February 19, 2020, the S&P500 declined by 33 percent by March 23, a decline faster than in the 1929 and 1987 crises. For a frame of reference, both in 1929 and in 1987, it took about two months for the market to decline from its peaks by the same magnitude (33-35 percent).

The degree of ambiguity is associated with the severity of rare events and seems to have a predictive power, as can be observed in the figure below (the red line).

For example, ambiguity was very high just before the 2008 financial crisis, while the VIX (the blue line) was at historically low levels. Another example is the period before February 5, 2018, when the February VIX futures contract more than doubled, causing the collapse of two short volatility funds, ETNs. Earlier, in December 2017, the ambiguity was at a high level while the VIX was at its lower levels.

The distinction between risk and ambiguity is not new; it was introduced a century ago by Frank Knight (1921). “Knightian uncertainty,” now known as ** ambiguity**, is the “unknown unknown” in popular terms. In particular,

**is the condition in which outcomes are a priori unknown, but the odds of all possible outcomes are perfectly known. Ambiguity is the condition in which the possible outcomes are a priori unknown, and the odds of these possible outcomes are either unknown or not uniquely assigned. To illustrate the distinction between risk and ambiguity, consider a bet whose payoff is determined by a flip of a balanced coin, for which the investor knows the odds of heads (50 percent) and tails (50 percent). As the outcome is unknown, there is risk in betting, but there is no ambiguity, as the probabilities are known. However, if the coin is not balanced, the probabilities of heads and tails are no longer certain. As the probabilities are now unknown (ambiguous), the investor faces not only risk but also ambiguity.**

*risk*Ambiguity is an essential measure during the current Covid-19 crisis. As we have seen in the 2008 financial crisis, ambiguity has a predictive power, which is not the case for the VIX. In the months leading to the current COVID-19 crisis, before the market strongly reacted to the pandemic and before the VIX started climbing sharply, the VIX was low, but ambiguity was high. When the fear from the Covid-19 pandemic was relieved, ambiguity started declining before the VIX began declining. The VIX futures term structure, which extends to the end of the year, is currently upward sloping and above the long-run average, telling us that financial market participants believe that the elevated risk levels are going to last for the foreseeable future. In contrast, ambiguity tells us that the probabilities about the state of the economy are not as uncertain as they were last year at the same time.

Investors who use the VIX as a measure of risk in their decision-making process could significantly benefit from tracking also the ambiguity measure, AMBIX.

*This post comes to us from professors Menachem Brenner (emeritus) at the Stern School of Business, New York University, and Yehuda Izhakian at the Zicklin School of Business, Baruch College. It is based on their recent article, “Risk and Ambiguity in Turbulent Times,” forthcoming in the Quarterly Journal of Finance and available here.*