Why Does Stock Market Volatility Change Over Time?

Source: Schwert, G. W. (1989). Journal of Finance 44(5), 1115–1153 (NBER Working Paper No. 2798, 1988). DOI: 10.1111/j.1540-6261.1989.tb02647.x

TL;DR

Schwert builds a long monthly series of aggregate stock-market volatility back to the 19th century and asks what economic forces drive its large swings over time. Volatility is markedly higher in recessions and during banking/financial crises (above all the 1929–1940 Depression), and it co-moves with bond-return, interest-rate, and macroeconomic volatility and with financial leverage — but each of these explains only a small part of the variation. The amplitude of volatility movements is hard to reconcile with simple stock-valuation models, leaving most of the time-variation a puzzle.

What it models

Time-varying conditional volatility of U.S. stock (and bond) returns, and its relation to the conditional volatility of macroeconomic fundamentals (inflation, monetary base growth, industrial production, business failures, bank activity), to corporate profitability, to financial leverage, and to stock trading activity. Monthly data span 2/1857–12/1986 (T≈1,560 for the longest series); a higher-frequency volatility estimate from daily/weekly returns runs 1/1926–12/1986.

Specification

Volatility is estimated, not assumed parametrically. Schwert's procedure (a generalization of the 12-month rolling standard deviation of Officer [1973], Fama [1976], Merton [1980]):

Fit a 12th-order autoregression for the return with monthly dummies to model the time-varying conditional mean: R_t = Σ α_j D_jt + Σ β_i R_{t−i} + ε_t.

Fit a 12th-order autoregression for the absolute residuals |ε_t| (with monthly dummies); the fitted value estimates the conditional standard deviation of R_t given information before month t.

Absolute errors are scaled by (π/2)^{1/2} ≈ 1.2533 to make them unbiased estimates of the standard deviation under normality (correction suggested by Dan Nelson). Using absolute (standard-deviation) rather than squared (variance) specifications follows Davidian–Carroll (1987) for robustness. The approach is close in spirit to Engle's (1982) ARCH.

Estimation

Same allowing-the-mean-to-vary autoregressive scheme is applied to the absolute innovations of each macro series to produce comparable conditional volatility estimates, which are then related to stock volatility via regressions and annual cross-correlations. The sum of the AR coefficients measures volatility persistence (near unity ⇒ near-nonstationarity / integrated conditional heteroskedasticity), and Box–Pierce Q(24) and F-tests for seasonality assess fit.

What it captures

Volatility clustering / persistence: predicted volatility is highly autocorrelated and persistent.

Countercyclicality: stock volatility rises in recessions and especially during financial crises; it was unusually high across many series during 1929–1940.

Co-movement: stock-return volatility is correlated with bond-return and interest-rate volatility and, more weakly, with macroeconomic (inflation, IP, business-failure) volatility.

Leverage effect: volatility increases with financial leverage as Black/Christie predict, but changing leverage explains only a small portion of the rise in volatility (e.g. in the Depression) and cannot account for most of it.

Use & extensions

Established the countercyclical-volatility stylized fact and a workhorse method for constructing realized/conditional monthly volatility from short-horizon returns; precursor to the high-frequency realized-volatility literature (Andersen–Bollerslev–Diebold–Labys) and to research linking volatility to the business cycle and uncertainty shocks.

Limitations

Pre-dates intraday data; the "realized" volatility proxy is built from monthly aggregates of daily/weekly returns and from absolute-residual autoregressions.

Relations are correlational, not causally identified.

The central result is largely negative: observable fundamentals, leverage, and trading activity together leave most of the variation in aggregate volatility unexplained.

Key references

Schwert, G. W. (1989) — Why Does Stock Market Volatility Change Over Time? — Journal of Finance

Officer, R. R. (1973) — The Variability of the Market Factor of the New York Stock Exchange — Journal of Business

Engle, R. F. (1982) — Autoregressive Conditional Heteroskedasticity — Econometrica

Christie, A. A. (1982) — The Stochastic Behavior of Common Stock Variances (leverage effect) — Journal of Financial Economics

Provenance: verified/generated from the paper's full text.