Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility

Realized measures employing intra-day sources of data have proven effective for dynamic volatility and tail-risk estimation and forecasting. Expected shortfall (ES) is a tail risk measure, now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to implicitly model ES, has been extended to allow the intra-day range, not just the daily return, as an input. This model class is here further extended to incorporate information on realized measures of volatility, including realized variance and realized range (RR), as well as scaled and smoothed versions of these. An asymmetric Gaussian density error formulation allows a likelihood that leads to direct estimation and one-step-ahead forecasts of quantiles and expectiles, and subsequently of ES. A Bayesian adaptive Markov chain Monte Carlo method is developed and employed for estimation and forecasting. In an empirical study forecasting daily tail risk measures in six financial market return series, over a seven-year period, models employing the RR generate the most accurate tail risk forecasts, compared to models employing other realized measures as well as to a range of well-known competitors.     

Term structure dynamics with macro-factors using high frequency data

This paper empirically studies the role of macro-factors in explaining and predicting daily bond yields. In general, macro-finance models use low-frequency data to match with macroeconomic variables available only at low frequencies. To deal with this, we construct and estimate a tractable no-arbitrage affine model with both conventional latent factors and macro-factors by imposing cross-equation restrictions on the daily yields of bonds with different maturities, credit risks, and inflation indexation. The estimation results using both the US and the UK data show that the estimated macro-factors significantly predict actual inflation and the output gap. In addition, our daily macro-term structure model forecasts better than no-arbitrage models with only latent factors as well as other statistical models.     

Do macro variables, asset markets, or surveys forecast inflation better?

Surveys do! We examine the forecasting power of four alternative methods of forecasting U.S. inflation out-of-sample: time-series ARIMA models; regressions using real activity measures motivated from the Phillips curve; term structure models that include linear, non-linear, and arbitrage-free specifications; and survey-based measures. We also investigate several methods of combining forecasts. Our results show that surveys outperform the other forecasting methods and that the term structure specifications perform relatively poorly. We find little evidence that combining forecasts produces superior forecasts to survey information alone. When combining forecasts, the data consistently places the highest weights on survey information.     

Forecasting the term structure of Chinese Treasury yields

This paper is the first to study the forecasting of the term structure of Chinese Treasury yields. We extend the Nelson–Siegel class of models to estimate and forecast the term structure of Chinese Treasury yields. Our empirical analysis shows that the models fit the data very well, and that more flexible specifications dramatically improve in-sample fitting performance. In particular, the model which enhances slope fitting is the best in capturing the Chinese yield curve dynamics. We also demonstrate that time-varying factors of the models may be interpreted as the level, slope and curvature of the yield curve. Furthermore, we use five dynamic processes for the time-varying factors to forecast the term structure at both short and long horizons. Our forecasts are much more accurate than the random walk, the Cochrane–Piazzesi regression and the AR(1) benchmark models at long horizons.     

Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Quantile forecasts are central to risk management decisions because of the widespread use of Value-at-Risk. A quantile forecast is the product of two factors: the model used to forecast volatility, and the method of computing quantiles from the volatility forecasts. In this paper we calculate and evaluate quantile forecasts of the daily exchange rate returns of five currencies. The forecasting models that have been used in recent analyses of the predictability of daily realized volatility permit a comparison of the predictive power of different measures of intraday variation and intraday returns in forecasting exchange rate variability. The methods of computing quantile forecasts include making distributional assumptions for future daily returns as well as using the empirical distribution of predicted standardized returns with both rolling and recursive samples. Our main findings are that the Heterogenous Autoregressive model provides more accurate volatility and quantile forecasts for currencies which experience shifts in volatility, such as the Canadian dollar, and that the use of the empirical distribution to calculate quantiles can improve forecasts when there are shifts.     

Accounting for a Shift in Term Structure Behavior with No-Arbitrage and Macro-Finance Models

This paper examines a shift in the dynamics of the term structure of interest rates in the United States during the mid-1980s. We document this shift using standard interest rate regressions and using dynamic, affine, no-arbitrage models estimated for the pre- and post-shift subsamples. The term structure shift largely appears to be the result of changes in the pricing of risk associated with a "level" factor. Using a macro-finance model, we suggest a link between this shift in term structure behavior and changes in the dynamics and risk pricing of the Federal Reserve's inflation target as perceived by investors.     

Backtesting extreme value theory models of expected shortfall

We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts.     

Forecasting EUR–USD implied volatility: The case of intraday data

This study models and forecasts the evolution of intraday implied volatility on an underlying EUR–USD exchange rate for a number of maturities. To our knowledge we are the first to employ high frequency data in this context. This allows the construction of forecasting models that can attempt to exploit intraday seasonalities such as overnight effects. Results show that implied volatility is predictable at shorter horizons, within a given day and across the term structure. Moreover, at the conventional daily frequency, intraday seasonality effects can be used to augment the forecasting power of models. The type of inefficiency revealed suggests potentially profitable trading models.     

Forecasting the yield curve with linear factor models

In this work we compare the interest rate forecasting performance of a broad class of linear models. The models are estimated through a MCMC procedure with data from the US and Brazilian markets. We show that a simple parametric specification has the best predictive power, but it does not outperform the random walk. We also find that macroeconomic variables and no-arbitrage conditions have little effect to improve the out-of-sample fit, while a financial variable (Stock Index) increases the forecasting accuracy.     

Forecasting government bond yields with large Bayesian vector autoregressions

We propose a new approach to forecasting the term structure of interest rates, which allows to efficiently extract the information contained in a large panel of yields. In particular, we use a large Bayesian Vector Autoregression (BVAR) with an optimal amount of shrinkage towards univariate AR models. The optimal shrinkage is chosen by maximizing the Marginal Likelihood of the model. Focusing on the US, we provide an extensive study on the forecasting performance of the proposed model relative to most of the existing alternative specifications. While most of the existing evidence focuses on statistical measures of forecast accuracy, we also consider alternative measures based on trading schemes and portfolio allocation. We extensively check the robustness of our results, using different datasets and Monte Carlo simulations. We find that the proposed BVAR approach produces competitive forecasts, systematically more accurate than random walk forecasts, even though the gains are small.     

Properties of foreign exchange risk premiums

We study the properties of foreign exchange risk premiums that can explain the forward bias puzzle, defined as the tendency of high-interest rate currencies to appreciate rather than depreciate. These risk premiums arise endogenously from the no-arbitrage condition relating the term structure of interest rates and exchange rates. Estimating affine (multi-currency) term structure models reveals a noticeable tradeoff between matching depreciation rates and accuracy in pricing bonds. Risk premiums implied by our global affine model generate unbiased predictions for currency excess returns and are closely related to global risk aversion, the business cycle, and traditional exchange rate fundamentals.     

A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables

We describe the joint dynamics of bond yields and macroeconomic variables in a Vector Autoregression, where identifying restrictions are based on the absence of arbitrage. Using a term structure model with inflation and economic growth factors, together with latent variables, we investigate how macro variables affect bond prices and the dynamics of the yield curve. We find that the forecasting performance of a VAR improves when no-arbitrage restrictions are imposed and that models with macro factors forecast better than models with only unobservable factors. Variance decompositions show that macro factors explain up to 85% of the variation in bond yields. Macro factors primarily explain movements at the short end and middle of the yield curve while unobservable factors still account for most of the movement at the long end of the yield curve.     

Analyst Pessimism and Forecast Timing

In this study, we show that on average relatively pessimistic analysts tend to reveal their earnings forecasts later than other analysts. Further, we find this forecast timing effect explains a substantial proportion of the well‐known decrease in consensus analyst forecast optimism over the forecast period prior to earnings announcements, which helps explain why analysts’ longer term earnings forecasts are more optimistically biased than their shorter term forecasts. We extend the theory of analyst self‐selection regarding their coverage decisions to argue that analysts with a relatively pessimistic view–compared to other analysts–are more reluctant to issue their earnings forecasts, with the result that they tend to defer revealing their earnings forecasts until later in the forecasting period than other analysts.     

Model-based earnings forecasts vs. financial analysts' earnings forecasts

Existing accounting-based forecasting models of earnings either do not fully consider information that is contained in stock prices or use an ad hoc specification that is not based on rigorous valuation theory. In this paper, we develop an earnings forecasting model built on the theoretical linkages between future earnings and stock prices as well as a number of accounting fundamental variables. We find that our model-based forecasts of earnings are in general less biased and more accurate than both existing model-based forecasts and analysts' consensus forecasts, at both shorter and longer horizons. We also show that the accuracy of both model-based forecasts and financial analysts' forecasts depend on firm-specific characteristics such as firm size and industry membership.     

Volatility forecasting: Intra-day versus inter-day models

Volatility prediction is the key variable in forecasting the prices of options, value-at-risk and, in general, the risk that investors face. By estimating not only inter-day volatility models that capture the main characteristics of asset returns, but also intra-day models, we were able to investigate their forecasting performance for three European equity indices. A consistent relation is shown between the examined models and the specific purpose of volatility forecasts. Although researchers cannot apply one model for all forecasting purposes, evidence in favor of models that are based on inter-day datasets when their criteria based on daily frequency, such as value-at-risk and forecasts of option prices, are provided.     

Forecasting the Term Structure of South African Government Bond Yields

This article uses the parsimonious dynamic Nelson–Siegel model to fit the yields of South African government bonds. We find that the dynamic Nelson–Siegel model has good fitting abilities for all maturities. We further forecast the term structure by seven different dynamic Nelson–Siegel models with time series models. We find that the DNS–VAR–GARCH model is useful for forecasting the short-term rates, the DNS–VAR best predicts the medium-term rates, and the DNS–RW best predicts the long-term rates. In addition, the dynamic Nelson–Siegel models provide better forecasts of yield data than a random walk model, especially for the 12-month forecasting horizons.     

预测中国宏观经济变量:专家与模型的组合预测

本文使用组合预测方法,探究以“朗润预测”为代表的专家预测以及计量模型对于中国宏观经济变量的预测效果,并研究对不同预测进行组合预测是否有助于改进预测效果。本文发现,对我国CPI和GDP的增长率,专家预测效果总体上优于模型预测。从原因看,一方面,专家在预测时已经考虑了计量模型的预测信息;另一方面,在经济出现“拐点”的时期,专家通过对实际经济环境和政策的把握,得出更准确的经济预测。组合预测有助于提升预测精度,对专家预测进行组合得到的预测效果优于大多数的专家预测,“模型—专家”组合预测的效果也优于所有的模型和大部分专家预测。     

Macro-finance VARs and bond risk premia: A caveat

At the turn of the century, US and euro area long-term bond yields experienced a remarkable decline and remained at historically low levels despite rising short-term rates (the so called “conundrum”). Estimating macro-finance VARs and no-arbitrage term structure models, many researchers find that the decline in long-term rates was primarily driven by an unprecedented reduction in risk premia. I show that this result might be an artefact of the class of models employed to study the phenomenon.     

Consumer credit-risk models via machine-learning algorithms

We apply machine-learning techniques to construct nonlinear nonparametric forecasting models of consumer credit risk. By combining customer transactions and credit bureau data from January 2005 to April 2009 for a sample of a major commercial bank’s customers, we are able to construct out-of-sample forecasts that significantly improve the classification rates of credit-card-holder delinquencies and defaults, with linear regression R²’s of forecasted/realized delinquencies of 85%. Using conservative assumptions for the costs and benefits of cutting credit lines based on machine-learning forecasts, we estimate the cost savings to range from 6% to 25% of total losses. Moreover, the time-series patterns of estimated delinquency rates from this model over the course of the recent financial crisis suggest that aggregated consumer credit-risk analytics may have important applications in forecasting systemic risk.     

How arbitrage-free is the Nelson-Siegel model?

We test whether the Nelson and Siegel (1987) yield curve model is arbitrage-free. Theoretically, the Nelson-Siegel model does not ensure the absence of arbitrage opportunities, as shown by Bjork and Christensen (1999) and Filipovic (1999). Still, central banks and wealth managers rely heavily on it. Using zero-coupon yield curve data from the US market, we find that the no-arbitrage parameters are not statistically different from those obtained from the Nelson-Siegel model. We therefore conclude that the Nelson-Siegel yield curve model is compatible with the no-arbitrage constraints on the US market. To corroborate this result, we also show that the Nelson-Siegel model performs as well as its no-arbitrage counterpart in an out-of-sample forecasting experiment.