Equity and bond market volatility can be decomposed into persistent and transitory components by means of statistical methods. The distinction is relevant for macro trading because plausibility and empirical research suggest that the persistent component is associated with macroeconomic fundamentals. This means that persistent volatility is an important signal itself and that its sustainability depends on macroeconomic trends and events. Meanwhile, the transitory component, if correctly identified, is more closely associated with market sentiment and can indicate mean-reverting price dynamics.

Chiu, Ching-Wai (Jeremy), Richard Harris, Evarist Stoja, and Michael Chin (2016), “Financial market volatility, macroeconomic fundamentals and investor sentiment”, Bank of England, Staff Working Paper No. 608

*The post ties in with SRSV’s lecture on monitoring macroeconomic trends, particularly section on best practices for using financial market data.
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*The below are excerpts from the paper. Emphasis and cursive text have been added for easier reading.*

### Volatility and macroeconomics in a nutshell

“It is by now well established that financial market volatility and macroeconomic fundamentals are inextricably linked.”

“Persistent volatility is closely associated with macroeconomic fundamentals. We first show that __traditional macroeconomic structural shocks cause significant responses in persistent volatility__ but not in transitory volatility…Adverse shocks to aggregate demand and supply cause an increase in the persistent component of both stock and bond market volatility…We then show that __shocks to persistent volatility lead to macroeconomic fluctuations, but transitory volatility shocks do not have this effect__…Adverse shocks to the persistent component of either stock or bond market volatility cause a deterioration in macroeconomic fundamentals…This provides support to the hypothesis that it is the persistent component of volatility that is linked to the market’s expectations of future cash flows and discount rates.”

“We find that __the transitory component of volatility is more closely associated with changes in investor sentiment__…With limits to arbitrage, sentiment-based decisions of uninformed investors lead to excess volatility. Changes in sentiment can trigger strong liquidity shocks with a significant impact on volatility. In the short run, a change in one set of prices may influence investor sentiment triggering changes in a seemingly unrelated set of prices…__Changes in investor sentiment explain asset price movement in the short-term better than fundamental factors__.”

### The two components of market volatility

“It is well documented that __financial market volatility is characterised by a two-factor process, with a slowly varying long run component and a strongly mean-reverting short run component__…We use the semi-parametric cyclical volatility model of Harris, Stoja and Yilmaz [*HSY*] to decompose financial market volatility into a long run persistent component and a short run transitory component.”

“The HSY framework offers a simple and flexible way to decompose volatility…The natural logarithm of the asset price…follows a continuous time diffusion given by…a Wiener process [*a continuous-time stochastic process with mean zero a variance that is proportional to the time elapsed*] multiplied with the instantaneous variance, which is [*changing overtime but*] strictly stationary and independent of the Wiener process…HSY assume that the…standard deviation [*of price changes over periods of time*] follows a two-factor dynamic structure, with a persistent long run component, and a transitory short run component.”

“HSY leave the precise dynamics of the long run component unspecified and…estimate it non-parametrically. Conditional on the trend, HSY assume that the transitory component [*the difference between total standard deviation and its long-term trend*] follows a stationary first order autoregressive process [*meaning that tomorrow’s transitory standard deviation depends on today’s and a random error term with zero mean and constant variance*].”

“We…estimate the persistent and transitory components of the realized standard deviation of *monthly* stock and bond returns…__we extract the persistent component from the daily standard deviation and aggregate this to yield the persistent component of the monthly realized standard deviation__…We…apply the one-sided low-pass filter of Hodrick and Prescott [

*that uses only past values*] to estimate the persistent component…For each iteration of the rolling window procedure, we save the estimated value of the persistent component for the most recent day…The rolling window daily persistent component is then aggregated to yield the persistent component of the standard deviation for each month.”

“The transitory component of the monthly standard deviation is then computed as [*the difference between the realized standard deviation of the month and the persistent component*].”

*N.B.: This statistical method is evidently misleading if sudden fundamental shocks affect both markets and fundamentals at the same time. Correctly identifying a transitory component hence requires judgment if a commensurate fundamental shock has occurred or not.*

“Our volatility estimation sample comprises monthly data for the period January 1990 to June 2015. We use the cyclical volatility model described in the previous section to estimate the persistent and transitory components of the standard deviation of aggregate stock and bond returns for the U.S.”

### Empirical findings

“In order to explore the relationship between volatility and the wider economy, we employ the structural vector autoregression methodology…We…__estimate a structural vector autoregression (SVAR) model for the components of financial market volatility, real activity (measured by output growth and inflation), monetary policy (as reflected in the short term interest rate) and investor sentiment__. We impose standard a priori sign restrictions that are defined according to well established micro-based macroeconomic principles in order to identify the structural shocks. We measure the impact of adverse shocks to aggregate demand, aggregate supply and investor sentiment on both stock and bond market volatility and the impact of adverse shocks to stock and bond market volatility on macroeconomic fundamentals and investor sentiment.”

*On structural VARs for trading strategies view post here.*

“We adopt the Bayesian sign restriction framework to identify structural shocks…

__adverse aggregate demand shocks__drive down output growth, the inflation rate and short-term interest rate contemporaneously;__adverse aggregate supply shocks__drive down output growth, but drive up the inflation rate and short-term interest rate contemporaneously;__adverse monetary policy shocks__drive up the short-term interest rate but lead to lower output growth and inflation rate contemporaneously.__adverse investor sentiment shocks__are assumed to be associated with no contemporaneous change in real activity, but its subsequent impact is unrestricted…__adverse financial market volatility shocks__are assumed to be associated with no contemporaneous change in either investor sentiment or real activity, but its subsequent impact is unrestricted.”

“The model is estimated for the U.S. using monthly data over the period July 2001 to June 2015. We show that adverse __shocks to aggregate demand and aggregate supply cause an increase in both stock and bond market volatility__ and that __adverse shocks to either stock or bond market volatility cause a deterioration in macroeconomic fundamentals__. Moreover, we show that it is the persistent component, not the transitory component, that is more closely related to macroeconomic fundamentals.”

“The impulse responses that are implied by the estimated SVAR coefficients…using stock market volatility [*are as follows*]:

__An adverse aggregate demand shock__, represented by a reduction of 35 basis points in output growth, a fall of 10 basis points in inflation and a slight decrease in the interest rate…__has a statistically significant, positive impact on stock market volatility__, with a similar magnitude for both total volatility and persistent volatility.__An adverse aggregate supply shock__, represented by an initial reduction in output growth by 43 basis points and an increase in inflation of 20 basis points as well as a short-lived rise in the interest rate…__yields a statistically significant increase in both total volatility and persistent volatility__, and a reduction in investor sentiment.__An adverse monetary policy shock__yields a small and marginally significant reduction in output growth and inflation, although in both cases, the impact is short lived. Both investor sentiment and volatility increase, but__in neither case is the impact statistically significant.____Increasing volatility – whether total volatility or persistent volatility – leads to a significant drop in output growth, inflation and sentiment__. The key difference is that shocks to persistent volatility lead to deeper economic contractions, which can be explained by its protracted rise in magnitude after the shock.- Transitory volatility shocks…apart from a very short-lived fall in prices and real activity…do not in general cause a significant macroeconomic response.”

“The results using bond market volatility are very similar to those using stock market volatility. In particular, there is a significant increase in volatility following an adverse shock to aggregate demand, aggregate supply and monetary policy… Following an adverse sentiment shock, volatility rises, but not significantly so.”

“As a further robustness check, we conducted the same SVAR analysis for the U.K. and Germany. We also conducted the SVAR analysis without the U.S. Crash Confidence Index, which allows us to extend the sample back to January 1990… For all the robustness tests, the results are qualitatively similar and the conclusions unchanged.”