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Measures of market risk and uncertainty

In financial markets, risk refers to the probability distribution of future returns. Uncertainty is a broader concept that encompasses ambiguity about the parameters of this probability distribution. There are various types of measures seeking to estimate risk and uncertainty: [1] realized and derivatives-implied distributions of returns across assets, [2] news-based measures of policy and political uncertainty, [3] survey-based indicators, [4] econometric measures, and [5] ambiguity indices. The benefits for macro trading are threefold. First, uncertainty measures provide a basis for comparing the market’s assessment of risk with private information and research. Second, changes in uncertainty indicators often predict near-term flows in and out of risky asset classes. Third, the level of public and market uncertainty is indicative of risk premia offered across asset classes.

Cascaldi-Garcia, Danilo, Cisil Sarisoy, Juan M. Londono, John Rogers, Deepa Datta, Thiago Ferreira, Olesya Grishchenko, Mohammad R. Jahan-Parvar, Francesca Loria, Sai Ma, Marius Rodriguez, and Ilknur Zer (2020). “What is Certain about Uncertainty?,” International Finance Discussion Papers 1294. Washington: Board of Governors of the Federal Reserve System.

The below are condensed annotated quotes of the comprehensive summary paper.
Cursive text and text in brackets have been added for clarity.
The post ties up with this site’s summary on endogenous market risk, particularly the section on exit risk.

Distinguishing risk and uncertainty

“Knightian uncertainty…disentangles risk from uncertainty…Roughly speaking, risk refers to the situation where there is a probability measure to guide a choice, while ambiguity [Knightian uncertainty] refers to the situation where the decision-maker is uncertain about this probability measure due to cognitive or informational constraints.”

“Alternatively, think about ambiguity as uncertainty about the ‘true’ probability distribution governing future paths of state variables. The decision-makers’ ambiguity attitude determines how and to what extent such uncertainty affects their choices. As a result, compared with a solely risk-averse agent, the ambiguity-averse agent effectively assigns more probability weight to ‘bad’ states that are associated with lower levels of the continuation values. Alternatively, one may characterize ambiguity averse agents as lacking the confidence to assign probabilities to all relevant events.”

“Ambiguity aversion has emerged as a powerful contender for rational expectations explanations of financial market behavior…Applications to risky financial assets include equity risk premium portfolio choice, term structure of interest rates, variance risk premium, and CDS spreads.”

On the difference between financial risk (the probability and scope of permanent losses) and volatility (the magnitude of price fluctuations) see SRSV post here.

The importance for trading strategies

“Transmission of risks is substantial, both across sectors and across countries…Uncertainty shocks are important to understand cross-sectional dynamics…[There is] evidence of strong correlations in stock market volatility across countries…All this suggests a sizeable global component to uncertainty.”

“Although most of the literature still speaks in broad-brush terms about ‘uncertainty’ or ‘risk’, carefully defining the nature of risk is quite important…Measures are, by construction, limited to characterize particular types of uncertainty at particular horizons. For instance, although the VIX is a widely used measure of financial uncertainty, it is designed to capture near-term risk assessments related to the U.S. stock market.”

Prolonged periods of low volatility have strong in- and out-of-sample predictive power for the incidence of banking crises and can be used as a reliable crisis indicator…Perceptions of risk, especially when it deviates from what economic agents expect, affect risk-taking behavior. ..Prolonged periods of low volatility (that is, if volatility stays low for at least 1 year) increases both banking sector leverage and aggregate credit, which they interpret as increased risk appetite and risk-taking…These notions [were formalized by] by Minsky (1977) in what the author refers to as the instability hypothesis, where economic agents that observe stable economic environments are induced to take on more risk, which ultimately leads to a higher probability of a crisis.”

Market-based measures

Realized volatility

“Realized volatility (RV)[is] defined as the scaled sum of squared daily returns [and] offers a nonparametric alternative to traditional parametric volatility measures [such as GARCH]. RV estimators are feasible in multivariate applications, flexible, and easy to implement. The properties of RV-style estimators are well documented in the [academic] literature, and they are routinely used for forecasting volatility…RV-style measures have proved successful in predicting future volatility.”

Low volatility

“To estimate ‘unusually’ low volatility, Danielsson et al. (2018) first calculate realized volatility as the standard deviation of 12 monthly real returns for 60 countries, spanning from 1800 to 2010. Volatility differs considerably across countries, and even throughout the history for a given country. Hence, a particular measurement of volatility could be seen as high or low, depending on the country or year. To obtain a threshold for each country indicating the usual/expected value of volatility, the authors use the long-run historical trend, calculated via the one-sided Hodrick and Prescott filter. Low volatility is then defined as the deviation of realized stock market volatility below its historical trend.”

Cross-Sectional Distribution of Stock Market Returns

“Measures of volatility can be computed by exploiting the distribution of stock returns across firms at each point in time (for example, all stocks in the S&P 500 index). For instance…the variance across individual stock returns at each point in time [serves] as a measure of cross-sectional uncertainty…Exogenous shocks to these measures are important sources of business cycle fluctuations…Higher-order moments of the cross-sectional distribution of stock returns can also provide useful information about the economic cycle…The skewness of the distribution of log returns across firms and [indicates] the balance between upside and downside risks…Cross-sectional stock return skewness (financial skewness) not only closely tracks the business cycle but predicts economic activity.”

Derivative-implied risk and uncertainty measures (in general)

“The prices of derivatives at different strikes contain commingled information about the probabilities assigned to each possible market outcome as well as investor preferences. Derivative-implied distributions allow us to calculate…moments, such as…implied volatility or skewness, as well as the cost of insurance against any potential outcome (for example, a price drop of a certain magnitude).”

The derivative-implied distribution used to generate these moments is often referred to as the risk-neutral distribution because, by construction, this is the probability measure that makes the expected return on a risky investment equal to the risk-free rate. It is not called a risk-neutral measure because we assume that agents are risk neutral, but rather because, under this measure, probabilities are calculated as though agents only cared about the mean return. Because investors are not risk neutral in most cases, derivative-implied distributions contain information about risk premiums.”

Comparing the estimated physical distribution with the derivative-implied distribution can provide some information about investors’ risk preferences, that is about investors’ outcome-specific preferences, such as their preference for having positive returns in one state of the economy (for example, a large drop in asset prices) versus another. For example, if the risk-neutral distribution systematically has wider tails than the physical distribution (that is, more probability assigned to extreme market outcomes), we can infer that either investors systematically overestimate the probability of tail events or that their estimations are correct but they particularly value positive returns in those tail events.”

Market-based measures of monetary policy uncertainty

“Several papers derive measures of uncertainty about the path of monetary policy from policy-sensitive interest rates derivatives. Swanson (2006) developed a measure of monetary policy uncertainty based on the width of the probability distribution of the federal funds rate one-year ahead, as implied by market prices on interest rate derivatives. [The figure below] shows the 90%-confidence interval of the market-implied distribution for the effective federal funds rate at the one-year horizon, computed from at-the-money eurodollar futures options and adjusted for the level difference in volatility between the federal funds rate and eurodollar rates.”

Option-implied volatilities for equity indexes

Option-implied volatility is formally defined as the risk-neutral expectation of the volatility of the equity index over the next 30 days…The U.S. option-implied volatility, the VIX, is perhaps the most popular derivative-implied risk measure…In particular, the VIX has been shown to be a useful predictor of future realized volatility…and is frequently used by researchers and market participants to gauge fear or uncertainty with respect to the U.S. equity market and even with respect to global equity markets. Although there has been extensive research on the usefulness of the VIX as a tool to monitor equity and other financial asset markets, its informational content is often misunderstood.”

“While analogous measures for longer horizons are also available, the 30-day measure is the most widely used because of the relatively high liquidity for the options around this horizon. This relatively short horizon implies that this index likely does not capture expected volatility beyond the 30-day horizon, and this short horizon could be one possible driver of the discrepancy between the…VIX…and…perceived policy uncertainty.”

Variance risk premium

“The variance risk premium is a measure of the compensation that investors demand for bearing volatility risk or, in other words, a measure of investors’ preference for volatility. Formally, the variance risk premium is defined as the difference between a risk-neutral measure of expected variance (for example, the squared value of VIX) and a physical measure of expected realized variance.”

“The variance risk premium is often used as a time-varying and state-dependent measure of risk aversion…Empirically, it has been shown that the variance risk premium is one of the most successful short-term (between one month and one-quarter ahead) predictors of returns across a broad range of U.S. and international financial assets.”

The variance risk premium compensates investors for taking volatility risk. An SRSV summary post on the practical measurement of the premium can be found here.

Skewness risk premium

“The difference between upside and downside variance risk premiums, also known as the signed-jump premium, is a measure of the skewness risk premium. This measure…shares many similarities with the Bollerslev and Todorov ‘fear index’ [and] is a better reflection of the direction of uncertainty and market participants’ concerns about tail risks…The U.S. downside and upside variance risk premiums [have been] good predictors of international stock returns.”

Find an SRSV post on the downside variance premium here.

Option-implied insurance costs

“Options on equity indexes, unlike those on individual stocks, are fairly liquid and available for a wide range of strikes and time horizons, which facilitates the computation of option-implied probability distributions…A semiparametric method [can be] used to calculate option-implied probability distributions for headline equity indexes…This semiparametric method usually yields smooth option-implied distributions that are easy to interpret [for example as the  cost of insurance against outsized price moves].”

Interest rate uncertainty measures

“An interest rate swaption is an option to enter into a swap contract at a future date with a predetermined swap rate and given maturity. Market quotes of the interest rate swaptions provide a rich source of information about market participants’ uncertainty regarding future interest rates…The most liquid swaptions are at-the-money (ATM) swaptions, which are the swaptions with a strike rate that is equal to the forward swap rate that corresponds to the maturity of the swap specified in the swaption.”

“One approach commonly used by market participants to measure the uncertainty surrounding future movements in forward yields is the basis-point volatility implied by option prices. Basis-point volatility, defined as the standard deviation of the changes in the forward yields, allows for a more direct comparison of market participants’ uncertainty about future yield movements across different interest rate environments.”

Currency derivatives-implied distributions

“Unlike the options written on equity markets…most exchange rate derivatives are written as a combination of put and call options with the same deltas (the sensitivity of the option price to changes in the price of the underlying asset). Therefore, we can still use these combination derivatives to derive the risk-neutral distribution of currencies.”

“The most common strategies are risk reversals and strangles.

  • Risk reversals provide information about the cost of insurance against the depreciation of a currency relative to the cost of insurance against the appreciation of such currency. Specifically, a long position in a risk reversal is equivalent to purchasing a call option and selling a put option on a single bilateral exchange rate. Thus, this strategy protects the investor against an unfavorable drop in the exchange rate (for example, a drop in the dollar with respect to another currency for an exporter located in the United States) but limits investor gains if there is a favorable increase in the exchange rate.
  • In a strangle, the investor buys out-of-the-money calls and puts that have the same maturities and deltas. With this strategy, the investor can profit when a currency appreciates or depreciates significantly. The prices of call and put options at different strikes can be extracted from the prices of the different FX strategies.”

“All the methods to calculate option-implied distributions for equities described previously can be used for currencies once the option…In addition, the strategies also give us direct readings of the cost of insurance against a currency depreciation.”

Oil price option-implied distributions

“Options on oil futures contracts for West Texas Intermediate (WTI) crude oil are available on the New York Mercantile Exchange (NYMEX). As with other assets, the prices of options with different strikes and different horizons to maturity contain information about the probability assigned to each possible market outcome for crude oil prices as well as investor preferences. These option prices can be used to generate option-implied distributions, which, in turn, can be used to calculate option-implied moments, such as implied volatility or the cost of insurance against particular market outcomes. The bottom panel of [the figure below] depicts the implied volatility calculated from option-implied distributions as well as the Chicago Board Options Exchange (CBOE) oil VIX, which is an alternative summary measure of implied volatility for the WTI price of crude oil that is analogous to the S&P 500 VIX.”

News-based measures

Economic policy uncertainty index

One of the most widely used indicators of uncertainty is the economic policy uncertainty (EPU) index…For the United States, the EPU index is constructed from three components: The first quantifies policy-related uncertainty by searching the archives of 10 major U.S. newspapers for articles that contain terms related to EPU. The second component gauges uncertainty regarding the federal tax code, by counting the number of federal tax code provisions set to expire in future years. The third component measures disagreement among economic forecasters as an indicator of uncertainty. EPU indexes are constructed for almost 20 other countries or country aggregates, based on only…newspaper articles regarding policy uncertainty.
Updated economic policy uncertainty indices can be viewed here.

“There are two recent streams [of research] on news-based uncertainty that seem highly promising. The first stream links news-based and asset market indicators…relying on equity market volatility-related articles to construct a newspaper measure that closely tracks the VIX, allowing to parse the forces driving stock market volatility…The second stream incorporates machine learning techniques to summarize news coverage into aggregate uncertainty measures.”

Monetary policy uncertainty index

“To capture uncertainty related to central bank policies Husted, Rogers, and Sun (2020) apply the text-based methodology [of the economic policy uncertainty index]…by tracking the frequency of newspaper articles related to monetary policy uncertainty [MPU]. For the United States, the MPU index measures the perceived uncertainty surrounding the Federal Reserve Board’s policy decisions and their consequences.”
Updated monetary policy uncertainty indices can be viewed here.

Trade policy uncertainty index

“Caldara et al. (2019a) develop two measures of uncertainty related to trade policies (TPU). The first is based on searches of newspaper articles that discuss trade policy uncertainty. The second measure is constructed by aggregating firm-level TPU obtained from automated text searches of the quarterly earnings call transcripts of U.S.-listed corporations.”
The trade policy uncertainty index can be viewed here.

World uncertainty index

“Ahir, Bloom, and Furceri (2018) construct a panel of uncertainty measures for 143 developed and developing countries based on a word count of ‘uncertainty’ and its variants from Economist Intelligence Unit country reports. These reports cover specific topics related to political and economic developments and have a standardized structure across countries. More importantly, because these reports are all produced by the same source, the possibility of ideological bias between countries is mitigated. The World Uncertainty Index (WUI) is a GDP-weighted average of country-level uncertainty indexes, and is calculated using quarterly data spanning from 1996.”
The data for the world uncertainty index can be viewed here.

Geopolitical risk index

“Caldara and Iacoviello (2018) construct an index that measures geopolitical risk (GPR) based on a tally of newspaper stories that contain a fairly broad set of terms related to geopolitical tensions. The GPR index measures the risk associated with geopolitical events, such as wars, political tensions, and terrorist acts, that affect the normal course of domestic politics and international relations.”

“The GPR index is constructed by counting the occurrence of words related to geopolitical tensions in leading international newspapers. In particular, the GPR index reflects automated text searches in the electronic archives of 11 national and international newspapers for articles that contain several keywords, including ‘risk of war,’ ‘terrorist threats,’ and ‘geopolitical tensions.”
Data and charts for the geopolitical risk index index can be viewed here.

Survey-based measures

Economic surprise index

“Scotti (2016) uses macroeconomic news and survey forecasts to construct an ex post realized measure of uncertainty about the state of the economy. The macroeconomic uncertainty index…is calculated based on weighted averages of the square of economic data surprises, which are measured by examining deviations of recent economic data releases from consensus expectations from Bloomberg forecasts an hour before the data release. A dynamic factor model is employed to estimate monthly business condition indexes and compute the weights representing the contribution of the economic indicators to these business condition indexes. Those weights are then used to average the squared surprises to construct the uncertainty index.”

Inflation uncertainty measure

“Grishchenko, Mouabbi, and Renne (2019) use a range of inflation forecasts in the surveys of professional forecasters to construct an inflation uncertainty measure. To that end, they propose a term structure model with stochastic volatility estimated using information from various surveys of professional forecasters and define inflation uncertainty as the fitted second moment of the probability distribution of various inflation outcomes. Inflation uncertainty for different horizons is available in closed form thanks to the affine properties of the model.”
Survey consistent inflation expectations for the euro area and the U.S. can be viewed in a Shiny app here.

Econometric measures

Index of U.S. macroeconomic uncertainty

“Jurado et al. (2015) construct an index of macroeconomic uncertainty [for the U.S.] as an aggregate of the volatility of statistical forecasts for hundreds of economic series. This measure is an objective econometric-based uncertainty, rather than sentiment-based as reflected in news or in analysts’ forecasts…A monthly dataset comprising information from hundreds of macroeconomic indicators, [is used to] construct direct econometric estimates of uncertainty for each indicator. Formally…the h-period ahead uncertainty…[is defined] as the conditional volatility of the unforecastable component of the future value of the variable; that is, the difference between the future value of the variable and its expectation…The aggregate uncertainty at the macro level is the average of the uncertainty measures across all macro variables.”

Index of non-U.S. macroeconomic uncertainty

“Based on the JLN methodology, Londono et al. (2019) construct foreign real economic uncertainty indexes for the G-7 economies and Switzerland. They also calculate an aggregate non-U.S. measure as the GDP-weighted average across all countries but the United States.”

Quantile regression-based macroeconomic risk measure

“The value-at-risk (VaR) is defined…as a threshold such that the probability of a specific outcome not exceeding this threshold is equal to a desired level. This threshold is equivalent to the corresponding quantile of the desired level. The VaR has recently been used to construct measures of risk to U.S. macroeconomic aggregates drawing from quantile regressions. Unlike standard OLS regressions, quantile regressions look beyond the conditional mean and allow the study of the conditional quantiles of a given variable. Thus, this technique makes it possible to analyze how economic conditions influence not only the modal outlook but also the tail dynamics of economic time series. Using the VaR methodology, Adrian, Boyarchenko, and Giannone (2019) compute the downside risk to the annualized average growth rate of U.S. GDP over the next quarter/year by constructing a conditional distribution using quantile regressions… Caldara, Cascaldi-Garcia, Cuba-Borda, and Loria (2020) extend these results by employing new monthly measures of macroeconomic and financial factors, together with a monthly version of U.S. GDP growth that tracks fluctuations within the quarter in real-time.”

“Also using the quantile regression methodology, Lopez- Salido and Loria (2019) study the risks to the inflation outlook. They frame the effects of different risk factors on the annualized inflation rate of average core CPI over the next year within an augmented quantile Phillips curve model.”

Ambiguity index

“Brenner and Izhakian (2018) decompose the uncertainty premium into a risk premium (proportional to risk tolerance of the agent and the variance of returns) and an ambiguity premium (proportional to tolerance for ambiguity and perceptions of the magnitude of ambiguity). Ambiguity tolerance stems from the functional form of the agent’s preferences. The ambiguity index is a measure of the agent’s perception of ambiguity…The degree of ambiguity [is defined] as the expected product of the conditional expected value of the distribution of returns and the conditional variance of the distribution of returns.”

“To build this measure, the authors divide the daily range of intraday returns into 60 intervals (bins) between -6 and +6 percent. They sort intraday 5-minute returns into these bins and compute the probability of returns that occur outside the +/16 percent interval. Then, they compute the mean and variance for each of these 62 bins. The monthly realized ambiguity index is the scaled sum of the product of each bin’s mean and variance, conditioned on the bin’s computed mean and variance values.”


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