Predicting recession probabilities with financial variables over multiple horizons

We forecast recession probabilities for the United States, Germany and Japan. The predictions are based on the widely-used probit approach, but the dynamics of regressors are endogenized using a VAR. The combined model is called a ‘ProbVAR’. At any point in time, the ProbVAR allows to generate conditional recession probabilities for any sequence of forecast horizons. At the same time, the ProbVAR is as easy to implement as traditional probit regressions. The slope of the yield curve turns out to be a successful predictor, but forecasts can be markedly improved by adding other financial variables such as the short-term interest rate, stock returns or corporate bond spreads. The forecasting performance is very good for the United States: for the out-of-sample exercise (1995 to 2009), the best ProbVAR specification correctly identifies the ex-post classification of recessions and non-recessions 95% of the time for the one-quarter forecast horizon and 87% of the time for the four-quarter horizon. Moreover, the ProbVAR turns out to significantly improve upon survey forecasts. Relative to the good performance reached for the United States, the ProbVAR forecasts are slightly worse for Germany, but considerably inferior for Japan. JEL Classification: C25, C32, E32, E37forecasting, probit, recessions, VAR

The Probability Density Function of Interest Rates Implied in the Price of Options

The paper contributes to the stochastic volatility literature by developing simulation schemes for the conditional distributions of the price of long term bonds and their variability based on non-standard distributional assumptions and volatility concepts; it illustrates the potential value of the information contained in the prices of options on long and short term lira interest rate futures for the conduct of monetary policy in Italy, at times when significant regime shifts have occured.stochastic models, statistical analysis, interest rates, financial market

Recovering the Probability Density Function of Asset Prices Using GARCH as Diffusion Approximations

This paper uses Garch models to estimate the objective and risk-neutral density functions of financial asset prices and, by comparing their shapes, recover detailed information on economic agents' attitudes toward risk. It differs from recent papers investigating analogous issues because it uses Nelson's (1990) result that Garch schemes are approximations of the kind of differential equations typically employed in finance to describe the evolution of asset prices. This feature of Garch schemes usually has been overshadowed by their well-known role as simple econometric tools providing reliable estimates of unobserved conditional variances. We show instead that the diffusion approximation property of Garch gives good results and can be extended to situations with i) non-standard distributions for the innovations of a conditional mean equation of asset price changes and ii) volatility concepts different from the variance. The objective PDF of the asset price is recovered from the estimation of a nonlinear Garch fitted to the historical path of the asset price. The risk-neutral PDF is extracted from crosssections of bond option prices, after introducing a volatility risk premium function. The direct comparison of the shapes of the two PDFS reveals the price attached by economic agents to the different states of nature. Applications are carried out with regard to the futures written on the Italian 10-year bond.option pricing, stochastic volatility, ARCH, volatility risk premium

Stock Values and Fundamentals; Link or Irrationality?

In this paper, econometric techniques are employed to analyze the continuous and remarkable growth which has characterized international stock markets since 1995. The Campbell and Shiller dividend discount model, a dynamic version of Gordon's formula commonly employed by financial analysts to rate individual firms, is the main tool of the paper. Given the information set available at any time, the future values of the real interest rate and the expected growth of dividends are evaluated and employed as explanatory variables for the current dividend yield. The results of the econometric analysis demonstrate that current dividend yields are not in line with the expected trend in the underlying variables, for all the countries considered. A decline in the real interest rate or an increase in the expected growth of dividends, or a combination of the two, could reconcile fundamentals and current dividend yields. The assessment of whether or not such divergences are rational cannot be made safely on the basis of expectations of the fundamentals derived from the econometric scheme. These, in fact, rest on the hypothesis of rational expectations for agents utilizing the full information set of past information; of course, information related to a larger set, including survey data, or the effects of shifts in economic regimes are excluded in this setup.asset pricing, dividend yield, dividend discount model

A Simple Approach to the Estimation of Continuous Time CEV Stochastic Volatility Models of the Short-Term Rate

Aim of this article is to judge the empirical performance of 'ARCH models as diffusion approximations' of models of the short-term rate with stochastic volatility. Our estimation strategy is based both on moment conditions needed to guarantee the convergence of the discrete time models and on the quasi indirect inference principle. Unlike previous literature in which standard ARCH models approximate only specific diffusion models (those in which the variance of volatility is proportional to the square of volatility), our estimation strategy relies on ARCH models that approximate any CEV-diffusion model for volatility. A MonteCarlo study reveals that the filtering performances of these models are remarkably good, even in the presence of important misspecification. Finally, based on a natural substitute of a global specification test for just-identified problems designed within indirect inference methods, we provide strong empirical evidence that approximating diffusions with our models gives rise to a disaggregation bias that is not significant.stochastic volatility, CEV-ARCH, indirect inference, yield curve

Assessing the compensation for volatility risk implicit in interest rate derivatives

Volatilities implied from interest rate swaptions are used to assess the size and the sign of the compensation for volatility risk, for dollar, euro and pound rates at a daily frequency, between October 1998 and August 2006. The measurement of the volatility risk premium rests on a simple model according to which variance forecasts are generated under the objective probability measure. Results show that especially between September 2001 and mid-2003 dollar implieds were embodying a large - negative - compensation for volatility risk, a component which was smaller in absolute terms - but not relative to the level of the respective implied volatilities - for the other two currencies. While the negative compensation for volatility risk is in line with previous studies focusing on other asset classes, we also document that it exhibits a term structure, more evident for dollar and euro rates than for pound rates. The volatility risk premium is strongly changing through time but much less than implied volatilities. Estimates of risk aversion based on the physical skewness and kurtosis of interest rate changes suggest that (minus) the volatility risk premium can almost directly be read as risk aversion, as its proportionality with such risk aversion measure is about 0.8. Also, compensation for volatility risk is positively related to expected volatility, although the relation is not completely linear. Daily compensation for volatility risk is influenced, as expected, by the level of the short term rate and its volatility as well as by a small but robust number of macroeconomic surprises. The latter induce more sizeable changes on compensation for volatility risk of dollar rates than of euro or pound rates. JEL Classification: G120, G130, G140economic surprises, risk aversion, Volatility risk premium

The size of the equity premium

Among the many controversial variables in finance, risk premia stand out for their lack of observability. Measuring premia as the difference between realized returns on risky and risk-free assets has not led to unanimous conclusions about their size, which greatly depends on the length of the sample; in addition, investment allocations or inflation expectations are influenced by the ex-ante values of the risk premia and ex-post returns are, if any, rough approximations of these. Many papers have dealt with this issue, from the initial contribution of Mehra and Prescott (1985) to very recent advances within a bayesian framework of Pástor and Stambaugh (2001). This paper uses conditional variance models as approximations of static and intertemporal capital asset pricing models; the size of the equity premium is assessed for the US both at the market level and, through a conditional version of the three-factor model of Fama and French (1993), at a firm-level. The market premium has had large swings with short-lived peaks over the last 75 years, fluctuating around a mean value of 5 per cent on a yearly basis; this value rises to 6.5 percent when time-varying investment opportunities are allowed for. In periods of economic expansion the expected premium on the equity return is nearly half the value expected in recession, 20 percent less if the Great Depression period is excluded; the cross-sectional dispersion of the firm-level premia as a function of firm’s size is also influenced by the position of the economy within the business cycle.equity premium, garch

The role of financial variables in predicting economic activity

Previous research has shown that the US business cycle leads the European cycle by a few quarters, and can therefore help predicting euro area GDP. We investigate whether financial variables provide additional predictive power. We use a VAR model of the US and the euro area GDPs and extend it to take into account common global shocks and information provided by selected combinations of financial variables. In-sample analysis shows that shocks to financial variables influence real activity with a peak around 4 to 6 quarters after the shock. Out-of-sample Root-Mean- Squared Forecast Error (RMFE) shows that adding financial variables yields smaller errors in fore-casting US economic activity, especially at a five- quarter horizon, but the gain is overall tiny in economic terms. This link is even less prominent in the euro area, where financial indicators do not improve short and medium term GDP forecasts even when their timely availability, relative to a given GDP release, is exploited. The same conclusion is reached with a dataset of quarterly industrial production indices, although financial variables marginally improve fore- casts of monthly industrial production. We argue that the findings that financial variables have no predictive power for future activity in the euro area relate to the unconditional nature of the RMFE metric. When forecasting ability is assessed as if in real time (i.e. conditionally on the information available at the time when forecasts are made), we find that models using financial variables would have been preferred in many episodes, and in particular between 1999 and 2002. Results from the historical decomposition of a VAR model indeed suggest that in that period shocks were predominantly of financial nature. JEL Classification: F30, F42, F47conditional forecast, Financial Variables, international linkages, VAR

Stock market firm-level information and real economic activity

We provide evidence that changes in the equity price and volatility of individual firms (measures that approximate the definition of 'granular shock' given in Gabaix, 2010) are key to improve the predictability of aggregate business cycle fluctuations in a number of countries. Specifically, adding the return and the volatility of firm-level equity prices to aggregate financial information leads to a significant improvement in forecasting business cycle developments in four economic areas, at various horizons. Importantly, not only domestic firms but also foreign firms improve business cycle predictability for a given economic area. This is not immediately visible when one takes an unconditional standpoint (i.e. an average across the sample). However, conditioning on the business cycle position of the domestic economy, the relative importance of the two sets of firms - foreign and domestic - exhibits noticeable swings across time. Analogously, the sectoral classification of the firms that in a given month retain the highest predictive power for future IP changes also varies significantly over time as a function of the business cycle position of the domestic economy. Limited to the United States, predictive ability is found to be related to selected balance sheet items, suggesting that structural features differentiate the firms that can anticipate aggregate fluctuations from those that do not help to this aim. Beyond the purely forecasting application, this finding may enhance our understanding of the underlying origins of aggregate fluctuations. We also propose to use the cross sectional stock market information to macro-prudential aims through an economic Value at Risk. JEL Classification: C53, C58, F37, G15Business cycle forecasting, granular shock, international linkages

The Impact of News on the Exchange Rate of the Lira and Long-Term Interest Rates

This paper analyzes the impact of news on several Italian financial variables, paying particular attention to the effect on the conditional volatility of these variables. The analysis spans a period of great financial and political turbulence in Italy, including the rapid succession of three governments. News releases (articles on political and economic events collected daily from both the Italian and international economic press) are classified as unscheduled (mostly political) and scheduled (i.e. economic and monetary statistics whose announcement is expected by market participants). The analysis is divided into two phases: first, we estimate the impact of each single political and economic news item on asset price changes and their conditional variance; second, those items that are identified as significant in the first stage are then aggregated into six dummies according to their nature and origin and employed as exogenous variables in a trivariate Garch scheme. Results show that i) news affects both the first and the second moment of the daily changes in the analyzed variables; ii) there is a significant regime shift of the unconditional variance of the analyzed variables across the three different governments; iii) the conditional variances display a significant — albeit rather small — seasonal dayweek pattern; iv) contrary to the conventional view, the impact of news on the conditional variance is more pronounced for exchange rates than for Italian long-term interest rates.News; Asset pricing; Conditional volatility