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Institute
Volatility forecasting
(2005)
Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1.
What do academics have to offer market risk management practitioners in financial institutions? Current industry practice largely follows one of two extremely restrictive approaches: historical simulation or RiskMetrics. In contrast, we favor flexible methods based on recent developments in financial econometrics, which are likely to produce more accurate assessments of market risk. Clearly, the demands of real-world risk management in financial institutions - in particular, real-time risk tracking in very high-dimensional situations - impose strict limits on model complexity. Hence we stress parsimonious models that are easily estimated, and we discuss a variety of practical approaches for high-dimensional covariance matrix modeling, along with what we see as some of the pitfalls and problems in current practice. In so doing we hope to encourage further dialog between the academic and practitioner communities, hopefully stimulating the development of improved market risk management technologies that draw on the best of both worlds.
A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from high-frequency returns coupled with relatively simple reduced-form time series modeling procedures. Building on recent theoretical results from Barndorff-Nielsen and Shephard (2003c,d) for related bi-power variation measures involving the sum of high-frequency absolute returns, the present paper provides a practical framework for non-parametrically measuring the jump component in realized volatility measurements. Exploiting these ideas for a decade of high-frequency five-minute returns for the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find the jump component of the price process to be distinctly less persistent than the continuous sample path component. Explicitly including the jump measure as an additional explanatory variable in an easy-to-implement reduced form model for realized volatility results in highly significant jump coefficient estimates at the daily, weekly and quarterly forecast horizons. As such, our results hold promise for improved financial asset allocation, risk management, and derivatives pricing, by separate modeling, forecasting and pricing of the continuous and jump components of total return variability.
We characterize the response of U.S., German and British stock, bond and foreign exchange markets to real-time U.S. macroeconomic news. Our analysis is based on a unique data set of high-frequency futures returns for each of the markets. We find that news surprises produce conditional mean jumps; hence high-frequency stock, bond and exchange rate dynamics are linked to fundamentals. The details of the linkages are particularly intriguing as regards equity markets. We show that equity markets react differently to the same news depending on the state of the economy, with bad news having a positive impact during expansions and the traditionally-expected negative impact during recessions. We rationalize this by temporal variation in the competing "cash flow" and "discount rate" effects for equity valuation. This finding helps explain the time-varying correlation between stock and bond returns, and the relatively small equity market news effect when averaged across expansions and recessions. Lastly, relying on the pronounced heteroskedasticity in the high-frequency data, we document important contemporaneous linkages across all markets and countries over-and-above the direct news announcement effects. JEL Klassifikation: F3, F4, G1, C5
We selectively survey, unify and extend the literature on realized volatility of financial asset returns. Rather than focusing exclusively on characterizing the properties of realized volatility, we progress by examining economically interesting functions of realized volatility, namely realized betas for equity portfolios, relating them both to their underlying realized variance and covariance parts and to underlying macroeconomic fundamentals.
A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, vis-à-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently-popularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionally-integrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management. JEL Klassifikation: C1, G1
We extend the important idea of range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator that is motivated by financial economic considerations (the absence of arbitrage), in addition to statistical considerations. We show that, unlike other univariate and multivariate volatility estimators, the range-based estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading. Finally, we provide an empirical example illustrating the value of the high-frequency sample path information contained in the range-based estimates in a multivariate GARCH framework.
We explore the macro/finance interface in the context of equity markets. In particular, using half a century of Livingston expected business conditions data we characterize directly the impact of expected business conditions on expected excess stock returns. Expected business conditions consistently affect expected excess returns in a statistically and economically significant counter-cyclical fashion: depressed expected business conditions are associated with high expected excess returns. Moreover, inclusion of expected business conditions in otherwise standard predictive return regressions substantially reduces the explanatory power of the conventional financial predictors, including the dividend yield, default premium, and term premium, while simultaneously increasing R2. Expected business conditions retain predictive power even after controlling for an important and recently introduced non-financial predictor, the generalized consumption/wealth ratio, which accords with the view that expected business conditions play a role in asset pricing different from and complementary to that of the consumption/wealth ratio. We argue that time-varying expected business conditions likely capture time-varying risk, while time-varying consumption/wealth may capture time-varying risk aversion. Klassifikation: G12
We take a simple time-series approach to modeling and forecasting daily average temperature in U.S. cities, and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market. The answer is, perhaps surprisingly, yes. Time-series modeling reveals conditional mean dynamics, and crucially, strong conditional variance dynamics, in daily average temperature, and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises. As we argue, it also holds promise for producing the long-horizon predictive densities crucial for pricing weather derivatives, so that additional inquiry into time-series weather forecasting methods will likely prove useful in weather derivatives contexts.
We consider three sets of phenomena that feature prominently - and separately - in the financial economics literature: conditional mean dependence (or lack thereof) in asset returns, dependence (and hence forecastability) in asset return signs, and dependence (and hence forecastability) in asset return volatilities. We show that they are very much interrelated, and we explore the relationships in detail. Among other things, we show that: (a) Volatility dependence produces sign dependence, so long as expected returns are nonzero, so that one should expect sign dependence, given the overwhelming evidence of volatility dependence; (b) The standard finding of little or no conditional mean dependence is entirely consistent with a significant degree of sign dependence and volatility dependence; (c) Sign dependence is not likely to be found via analysis of sign autocorrelations, runs tests, or traditional market timing tests, because of the special nonlinear nature of sign dependence; (d) Sign dependence is not likely to be found in very high-frequency (e.g., daily) or very low-frequency (e.g., annual) returns; instead, it is more likely to be found at intermediate return horizons; (e) Sign dependence is very much present in actual U.S. equity returns, and its properties match closely our theoretical predictions; (f) The link between volatility forecastability and sign forecastability remains intact in conditionally non-Gaussian environments, as for example with time-varying conditional skewness and/or kurtosis.