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 ambiguity (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.

Read the full LexBlog article.

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Menachem Brenner  is Professor Emeritus of Finance.