Chi-squared tests for evaluation and comparison of asset pricing models

This paper presents a general statistical framework for estimation, testing and comparison of asset pricing models using the unconstrained distance measure of Hansen and Jagannathan (1997). The limiting results cover both linear and nonlinear models that could be correctly specified or misspecified. We propose modified versions of the existing model selection tests and new pivotal specification and model comparison tests with improved finite-sample properties. In addition, we provide formal tests of multiple model comparison. The excellent size and power properties of the proposed tests are demonstrated using simulated data from linear and nonlinear asset pricing models.     

Term structure models and the zero bound: An empirical investigation of Japanese yields

When Japanese short-term bond yields were near their zero bound, yields on long-term bonds showed substantial fluctuation, and there was a strong positive relationship between the level of interest rates and yield volatilities/risk premiums. We explore whether several families of dynamic term structure models that enforce a zero lower bound on short rates imply conditional distributions of Japanese bond yields consistent with these patterns. Multi-factor “shadow-rate” and quadratic-Gaussian models, evaluated at their maximum likelihood estimates, capture many features of the data. Furthermore, model-implied risk premiums track realized excess returns during extended periods of near-zero short rates. In contrast, the conditional distributions implied by non-negative affine models do not match their sample counterparts, and standard Gaussian affine models generate implausibly large negative risk premiums.     

Econometric analysis of jump-driven stochastic volatility models

This paper introduces and studies the econometric properties of a general new class of models, which I refer to as jump-driven stochastic volatility models, in which the volatility is a moving average of past jumps. I focus attention on two particular semiparametric classes of jump-driven stochastic volatility models. In the first, the price has a continuous component with time-varying volatility and time-homogeneous jumps. The second jump-driven stochastic volatility model analyzed here has only jumps in the price, which have time-varying size. In the empirical application I model the memory of the stochastic variance with a CARMA(2,1) kernel and set the jumps in the variance to be proportional to the squared price jumps. The estimation, which is based on matching moments of certain realized power variation statistics calculated from high-frequency foreign exchange data, shows that the jump-driven stochastic volatility model containing continuous component in the price performs best. It outperforms a standard two-factor affine jump–diffusion model, but also the pure-jump jump-driven stochastic volatility model for the particular jump specification.     

Realized Laplace transforms for estimation of jump diffusive volatility models

We develop an efficient and analytically tractable method for estimation of parametric volatility models that is robust to price-level jumps. The method entails first integrating intra-day data into the Realized Laplace Transform of volatility, which is a model-free estimate of the daily integrated empirical Laplace transform of the unobservable volatility. The estimation is then done by matching moments of the integrated joint Laplace transform with those implied by the parametric volatility model. In the empirical application, the best fitting volatility model is a non-diffusive two-factor model where low activity jumps drive its persistent component and more active jumps drive the transient one.     

No-arbitrage macroeconomic determinants of the yield curve

No-arbitrage macro-finance models use variance decompositions to gauge the extent of association between the macro variables and yields. We show that results generated by this approach are sensitive to the order of variables in the recursive identification scheme. In a four-factor model, one may obtain 18 different sets of answers out of 24 possible. We propose an alternative measure that is based on levels of macro variables as opposed to shocks. We account for the correlation between the macro and latent factors via projection of the latter onto the former. As a result, the association between macro variables and yields can be computed uniquely via an R²$R^2$. Macro variables explain 80% of the variation in the short rate and 50% of the slope, and 54% to 68% of the term premia.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.     

Optimal statistical decisions about some alternative financial models

We study Neyman–Pearson testing and Bayesian decision making based on observations of the price dynamics (_Xt:t∈[0,T])$(X_t:t\in [0,T])$ of a financial asset, when the hypothesis is the classical geometric Brownian motion with a given constant growth rate and the alternative is a different random diffusion process with a given, possibly price-dependent, growth rate. Examples of asset price observations are introduced and used throughout the paper to demonstrate the applicability of the theory. By a rigorous mathematical approach, we obtain exact formulae and bounds for the most common statistical characteristics of testing and decision making, such as the power of test (type II error probability), the Bayes factor and its moments (power divergences), and the Bayes risk or Bayes error. These bounds can be much more easily evaluated than the exact formulae themselves and, consequently, they are useful for practical applications. An important theoretical conclusion of this paper is that for the class of alternatives considered   neither the risk nor the errors converge to zero faster than exponentially in the observation time T$T$. We illustrate in concrete decision situations that the actual rate of convergence is well approximated by the bounds given in the paper.     

Determinacy,indeterminacy and dynamic misspecification in linear rational expectations models

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments is combined with a likelihood-based test for the cross-equation restrictions that the model places on its reduced form solution under determinacy. The resulting test has no power against a particular class of indeterminate equilibria, hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy. On the other hand, this test (i) circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy, (ii) does not involve inequality parametric restrictions and hence the use of nonstandard inference, (iii) is consistent against the dynamic misspecification of the LRE model, and (iv) is computationally simple. Monte Carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model of the US economy.     

Identification and estimation of Gaussian affine term structure models

This paper develops new results for identification and estimation of Gaussian affine term structure models. We establish that three popular canonical representations are unidentified, and demonstrate how unidentified regions can complicate numerical optimization. A separate contribution of the paper is the proposal of minimum-chi-square estimation as an alternative to MLE. We show that, although it is asymptotically equivalent to MLE, it can be much easier to compute. In some cases, MCSE allows researchers to recognize with certainty whether a given estimate represents a global maximum of the likelihood function and makes feasible the computation of small-sample standard errors.     

Firms’ fundamentals,macroeconomic variables and quarterly stock prices in the US

This paper modeled the effects of firms’ fundamentals such as total assets and long-term debt and of macroeconomic variables such as unemployment and interest rates on quarterly stock prices of over 3000 US firms in the period 2000–07. The merged CRSP/Compustat database was augmented by macroeconomic variables and comprehensive dynamic models were estimated by maximum likelihood taking into account heterogeneity across firms. Likelihood ratio statistics were developed for sequentially testing hypotheses regarding the adequacy of macroeconomic variables in the models. The main findings were that the estimated coefficients of lagged stock prices in simple dynamic random effects models were in the interval 0.90–0.95. Second, comprehensive dynamic models for stock prices showed that the firms’ earnings per share, total assets, long-term debt, dividends per share, and unemployment and interest rates were significant predictors; there were significant interactions between firms’ long-term debt and interest rates. Finally, implications of the results for corporate policies are discussed.     

Contemporaneous threshold autoregressive models: Estimation,testing and forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta [1998. Modelling economic relationships with smooth transition regressions. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York, pp. 507–552.], in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finite-sample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen [1992. The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP. Journal of Applied Econometrics 7, S61–S82.] procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed.     

The signalling content of asset prices for inflation: Implications for quantitative easing

We investigate the information content of financial variables as signalling devices of two abnormal inflationary regimes: (1) low inflation or deflation, and (2) high inflation. Specifically, we determine the information content of equity and house prices, private credit volumes, and sovereign and corporate bond yields, for 11 advanced economies over the past three decades, using both signalling extraction and logit modelling. The outcomes show that high asset prices more often signal high inflation than low inflation/deflation. However, in some countries, high asset prices and low bond yields are a significant indicator of low inflation or deflation as well. The transmission time of financial developments to inflation can be quite long (up to 8 quarters). For monetary policy, these findings imply that stimulating asset prices through Quantitative Easing (QE) can effectively influence inflation, but that the effects are quite uncertain, both regarding timing and direction.     

Disagreements with noisy signals and asset pricing

We consider a Lucas-type exchange economy with two trees and two investors to analyze the effects of heterogeneous beliefs and signal quality on stock market equilibrium. Our model has the following implications. There are spillover effects, in that the investors’ heterogeneous beliefs and signal quality related to one stock not only affect its own price and pricing moments, but also affect those of the other. Contrary to the conventional wisdom, we show that the volatility of one stock decreases with both its own and the other stock’s disagreements. Additionally, we reveal a negative correlation between the stocks, which decreases as the investors’ dispersions raise but increases as the discrepancy in signal quality reduces. We also show that heterogeneous beliefs and signal quality impact stock market beta mainly through scale and volatility effects, respectively. Furthermore, our findings suggest that both heterogeneous beliefs and signal quality have significant influences on the investors’ optimal portfolio plans.     

Automated Model Selection in Finance: General‐to‐Specific Modelling of the Mean and Volatility Specifications*

General‐to‐Specific (GETS) modelling has witnessed major advances thanks to the automation of multi‐path GETS specification search. However, the estimation complexity associated with financial models constitutes an obstacle to automated multi‐path GETS modelling in finance. Making use of a recent result we provide and study simple but general and flexible methods that automate financial multi‐path GETS modelling. Starting from a general model where the mean specification can contain autoregressive terms and explanatory variables, and where the exponential volatility specification can include log‐ARCH terms, asymmetry terms, volatility proxies and other explanatory variables, the algorithm we propose returns parsimonious mean and volatility specifications.     

Exact permutation tests for non-nested non-linear regression models

This paper proposes exact distribution-free permutation tests for the specification of a non-linear regression model against one or more possibly non-nested alternatives. The new tests may be validly applied to a wide class of models, including models with endogenous regressors and lag structures. These tests build on the well-known J test developed by Davidson and MacKinnon [1981. Several tests for model specification in the presence of alternative hypotheses. Econometrica 49, 781–793] and their exactness holds under broader assumptions than those underlying the conventional J test. The J-type test statistics are used with a randomization or Monte Carlo resampling technique which yields an exact and computationally inexpensive inference procedure. A simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions. The test procedure developed is illustrated by an application to inflation dynamics.     

Empirical implementation of nonparametric first-price auction models

Nonparametric estimators provide a flexible means of uncovering salient features of auction data. Although these estimators are popular in the literature, many key features necessary for proper implementation have yet to be uncovered. Here we provide several suggestions for nonparametric estimation of first-price auction models. Specifically, we show how to impose monotonicity of the equilibrium bidding strategy; a key property of structural auction models not guaranteed in standard nonparametric estimation. We further develop methods for automatic bandwidth selection. Finally, we discuss how to impose monotonicity in auctions with differing numbers of bidders, reserve prices, and auction-specific characteristics. Finite sample performance is examined using simulated data as well as experimental auction data.     

Forecasting the yield curve in a data-rich environment: A no-arbitrage factor-augmented VAR approach

This paper suggests a term structure model which parsimoniously exploits a broad macroeconomic information set. The model uses the short rate and the common components of a large number of macroeconomic variables as factors. Precisely, the dynamics of the short rate are modeled with a Factor-Augmented Vector Autoregression and the term structure is derived using parameter restrictions implied by no-arbitrage. The model has economic appeal and provides better out-of-sample yield forecasts at intermediate and long horizons than a number of previously suggested approaches. The forecast improvement is highly significant and particularly pronounced for short and medium-term maturities.     

The Cost Effectiveness of the UK's Sovereign Debt Portfolio*

This paper provides a recursive empirical analysis of the scope for cost minimization in public debt management when the debt manager faces a given short‐term interest rate dictated by monetary policy as well as risk and market impact constraints. It simulates the ‘real‐time’ interest costs of alternative portfolios for UK government debt between April 1985 and March 2000. These portfolios are constructed using forecasts of return spreads based on a recursive modelling procedure. While we find statistically significant evidence of predictability, the interest cost savings are quite small when portfolio shares are constrained to lie within historical bounds.