In the aftermath of the financial crisis, institutions have been asked to reduce leverage in order to reduce risk. To address the effectiveness of this measure, we build a model of equity volatility that accounts for leverage. Our approach blends Merton’s insights on capital structure with traditional time-series models of volatility. We estimate that precautionary capital needs for the entire financial sector reached $2 trillion during the crisis. We also investigate the long-standing observation that equity volatility asymmetrically responds to positive and negative news. Volatility asymmetry is mostly explained by exposure to the aggregate market, not a mechanical leverage effect. Received March 27, 2015; editorial decision February 25, 2017 by Editor Andrew Karolyi.

The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x first achieves stationarity after differencing, but a linear combination a'x is already stationary, the time series x are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a becomes a matrix. Interpreting a'x,= 0 as a long run equilibrium, co-integration implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are nonstationary and have infinite variance. The paper presents a representation theorem based on Granger (1983), which connects the moving average, autoregressive, and error correction representations for co-integrated systems. A vector autoregression in differenced variables is incompatible with these representations. Estimation of these models is discussed and a simple but asymptotically efficient two-step estimator is proposed. Testing for co-integration combines the problems of unit root tests and tests with parameters unidentified under the null. Seven statistics are formulated and analyzed. The critical values of these statistics are calculated based on a Monte Carlo simulation. Using these critical values, the power properties of the tests are examined and one test procedure is recommended for application. In a series of examples it is found that consumption and income are co-integrated, wages and prices are not, short and long interest rates are, and nominal GNP is co-integrated with M2, but not M1, M3, or aggregate liquid assets.

We introduce SRISK to measure the systemic risk contribution of a financial firm. SRISK measures the capital shortfall of a firm conditional on a severe market decline, and is a function of its size, leverage and risk. We use the measure to study top financial institutions in the recent financial crisis. SRISK delivers useful rankings of systemic institutions at various stages of the crisis and identifies Fannie Mae, Freddie Mac, Morgan Stanley, Bear Stearns, and Lehman Brothers as top contributors as early as 2005-Q1. Moreover, aggregate SRISK provides early warning signals of distress in indicators of real activity.

The expectati on of the excess holding yield on a long bond is postulated to depend upon its conditional variance. Engle's ARCH model is extended to allow the conditional variance to be a determinant of the mean and is called ARCH-M. Estimation and infer ence procedures are proposed, and the model is applied to three interest rate data sets. In most cases the ARCH process and the time varying risk premium are highly significant. A collection of LM diagnostic tests reveals the robustness of the model to various specification changes such as alternative volatility or ARCH measures, regime changes, and interest rate formulations. The model explains and interprets the recent econometric failures of the expectations hypothesis of the term structure.

Twenty-five years of volatility research has left the macroeconomic environment playing a minor role. This paper proposes modeling equity volatilities as a combination of macro- economic effects and time series dynamics. High-frequency return volatility is specified to be the product of a slow-moving component, represented by an exponential spline, and a unit GARCH. This slow-moving component is the low-frequency volatility, which in this model coincides with the unconditional volatility. This component is estimated for nearly 50 countries over various sample periods of daily data. Low-frequency volatility is then modeled as a function of macroeconomic and financial variables in an unbalanced panel with a variety of dependence structures. It is found to vary over time and across countries. The low-frequency component of volatility is greater when the macroeconomic factors of GDP, inflation, and short-term interest rates are more volatile or when inflation is high and output growth is low. Volatility is higher not only for emerging markets and markets with small numbers of listed companies and market capitalization relative to GDP, but also for large economies. The model allows long horizon forecasts of volatility to depend on macroeconomic developments, and delivers estimates of the volatility to be anticipated in a newly opened market. The Author 2008. Published by Oxford University Press on behalf of the Society for Financial Studies. All rights reserved. For permissions, please e-mail: [email protected]., Oxford University Press.

We develop a market-based methodology to assess banks’ resilience to climate-related risks and study the climate-related risk exposure of large global banks. We introduce a new measure, CRISK, which is the expected capital shortfall of a bank in a climate stress scenario. To estimate CRISK, we construct climate risk factors and dynamically measure banks’ stock return sensitivity (that is, climate beta) to the climate risk factor. We validate the climate risk factor empirically and the climate beta estimates by using granular data on large US banks’ loan portfolios. The measure is useful in quantifying banks’ climate-related risk exposure through the market risk and the credit risk channels.

This paper proposes a new statistical model for the analysis of data which arrives at irregular intervals. The model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates. The conditional intensity is developed and compared with other self-exciting processes. The model is applied to the arrival times of financial transactions and therefore is a model of transaction volume, and also to the arrival of other events such as price changes. Models for the volatility of prices are estimated, and examined from a market microstructure point of view.

This paper bridges the gap between processes where shocks are permanent and those with transitory shocks by formulating a process in which the long-run impact of each innovation is time-varying and stochastic. In the stochastic permanent breaks (STOPBREAK) process, frequent transitory shocks are supplemented by occasional permanent shifts. Consistency and asymptotic normality of quasi-maximum-likelihood estimates is established, and locally best hypothesis tests of the null of a random walk are developed. The model is applied to relative prices of pairs of stocks and significant test statistics result.

A bstract-We discuss the problem of testing for constant versus time varying regression coefficients. Our alternative hypothesis allows the coefficients to follow a stationary AR(1) process with unknown autoregressive parameter. Standard testing procedures are inappropriate since this parameter is identified only under the alternative. We propose a test statistic which is a function of a sequence of Score statistics, and depends only on the regressors and the OLS residuals. The distribution of the test statistic is discussed, power and size are investigated using Monte Carlo methods, and an empirical example investigating stability in the gold and silver markets is presented.

We revisit the relation between stock market volatility and macroeconomic activity using a new class of component models that distinguish short-run from long-run movements. We formulate models with the long-term component driven by inflation and industrial production growth that are in terms of pseudo out-of-sample prediction for horizons of one quarter at par or outperform more traditional time series volatility models at longer horizons. Hence, imputing economic fundamentals into volatility models pays off in terms of long-horizon forecasting. We also find that macroeconomic fundamentals play a significant role even at short horizons.