A multivariate GARCH in mean approach to testing uncovered interest parity: evidence from Asia-Pacific foreign exchange markets

The existence of time-varying risk premia in deviations from uncovered interest parity (UIP) is investigated based on a conditional capital asset pricing model (CAPM) using data from four Asia-Pacific foreign exchange markets. A parsimonious multivariate generalized autoregressive conditional heteroskedasticity in mean (GARCH-M) parameterization is employed to model the conditional covariance matrix of excess returns. The empirical results indicate that when each currency is estimated separately with an univariate GARCH-M parameterization, no evidence of time-varying risk premia is found except Malaysian ringgit. However, when all currencies are estimated simultaneously with the multivariate GARCH-M parameterization, strong evidence of time-varying risk premia is detected. As a result, the evidence supports the idea that deviations from UIP are due to a risk premium and not to irrationality among market participants. In addition, the empirical evidence found in this study points out that simply modeling the conditional second moments is not sufficient enough to explain the dynamics of the risk premia. A time-varying price of risk is still needed in addition to the conditional volatility. Finally, significant asymmetric world market volatility shocks are found in Asia-Pacific foreign exchange markets.     

The Expectations Hypothesis of the Term Structure and Time-Varying Risk Premia: a Panel Data Approach

One implication of the expectations hypothesis is that the yield spread should forecast subsequent changes in the long yield. However, regression tests based on this specification strongly reject the expectations hypothesis. One explanation for this rejection is that these tests fail to allow for a time varying risk premium that is correlated with this yield spread, leading to a bias in the estimated regression coefficients. This paper uses panel data in order to testm the expectations hypothesis under the assumption that risk premia are time-varying but driven by a single factor. It is found that while the expectations hypothesis is still rejected, the bias in the estimated coefficient is verysubstantially reduced.     

Probabilistic forecasts of volatility and its risk premia

The object of this paper is to produce distributional forecasts of asset price volatility and its associated risk premia using a non-linear state space approach. Option and spot market information on the latent variance process is captured by using dual ‘model-free’ variance measures to define a bivariate observation equation in the state space model. The premium for variance diffusive risk is defined as linear in the latent variance (in the usual fashion) whilst the premium for variance jump risk is specified as a conditionally deterministic dynamic process, driven by a function of past measurements. The inferential approach adopted is Bayesian, implemented via a Markov chain Monte Carlo algorithm that caters for the multiple sources of non-linearity in the model and for the bivariate measure. The method is applied to spot and option price data on the S&P500 index from 1999 to 2008, with conclusions drawn about investors’ required compensation for variance risk during the recent financial turmoil. The accuracy of the probabilistic forecasts of the observable variance measures is demonstrated, and compared with that of forecasts yielded by alternative methods. To illustrate the benefits of the approach, it is used to produce forecasts of prices of derivatives on volatility itself. In addition, the posterior distribution is augmented by information on daily returns to produce value at risk predictions. Linking the variance risk premia to the risk aversion parameter in a representative agent model, probabilistic forecasts of (approximate) relative risk aversion are also produced.     

Off-balance sheet activities and bank default-risk premia: A comparison of risk measures

This paper examines the market discipline of off-balance sheet activities on the default-risk premia of subordinated bank debt. The standard approach for determining whether market prices of subordinated debt reflect the risk of default is to regress the yield spread against accounting measures of bank risk. This approach may be inadequate because yield spreads are neither linear nor monotonic functions of bank risk. Moreover, the standard approach fails to consider that banks are regulated. This paper compares this approach and one where risk is measured with a contingent claims pricing model. Observed yields on subordinated bank debt over equivalent maturity treasuries are used to compute implied asset variances. OBS banking activities appear to reduce both linear risk-premia and implied asset variances. These results suggest that bank regulators may be overly concerned with the risk exposure of off-balance sheet banking activities.     

Skewness Risk and Bond Prices

This paper uses extreme value theory to study the implications of skewness risk for nominal loan contracts in a production economy. Productivity and inflation innovations are drawn from generalized extreme value distributions. The model is solved using a third‐order perturbation and estimated by the simulated method of moments. Results show that the data reject the hypothesis that innovations are drawn from normal distributions and favor instead the alternative that they are drawn from asymmetric distributions. Estimates indicate that skewness risk accounts for 12% of the risk premia and reduces bond yields by approximately 55 basis points. For a bond that pays 1 dollar at maturity, the adjustment factor associated with skewness risk ranges from 0.15 cents for a 3‐month bond to 2.05 cents for a 5‐year bond. Copyright © 2016 John Wiley & Sons, Ltd.     

Disaster risk and preference shifts in a New Keynesian model

In RBC models, disaster risk shocks reproduce countercyclical risk premia but generate an increase in consumption along the recession and asset price fall, through their effects on agents’ preferences (Gourio, 2012). This paper offers a solution to this puzzle by developing a New Keynesian model with such a small but time-varying probability of “disaster”. We show that price stickiness, combined with an EIS smaller than unity, restores procyclical consumption and wages, while preserving countercyclical risk premia, in response to disaster risk shocks. The mechanism then provides a rationale for discount factor first- and second-moment (“uncertainty”) shocks.     

Substitution,risk aversion,taste shocks and equity premia

This paper gauges the relative contribution of risk aversion, inter-temporal substitution and taste shocks on postwar monthly US equity premia. The time-varying consumption, market, and taste risks involved in the Euler equations are recovered from a common factor GARCH process and the MLE are obtained by applying the Kalman filter. Empirically, (1) the market risk is the only source of risk that does not statistically affect the equity premia, and thus, the hypothesis that the coefficient of relative risk aversion corresponds to the reciprocal of the elasticity of inter-temporal substitution is not rejected; (2) the estimates are reasonable, so that the equity premium puzzle is circumvented; and (3) taste risks are quantitatively important in capturing excess returns movements. © 1998 John Wiley & Sons, Ltd.     

Tests of risk premia in linear factor models

We show that statistical inference on the risk premia in linear factor models that is based on the Fama–MacBeth (FM) and generalized least squares (GLS) two-pass risk premia estimators is misleading when the β$\beta$’s are small and/or the number of assets is large. We propose novel statistics, that are based on the maximum likelihood estimator of Gibbons [Gibbons, M., 1982. Multivariate tests of financial models: A new approach. Journal of Financial Economics 10, 3–27], which remain trustworthy in these cases. The inadequacy of the FM and GLS two-pass t$t$/Wald statistics is highlighted in a power and size comparison using quarterly portfolio returns from Lettau and Ludvigson [Lettau, M., Ludvigson, S., 2001. Resurrecting the (C)CAPM: A cross-sectional test when risk premia are time-varying. Journal of Political Economy 109, 1238–1287]. The power and size comparison shows that the FM and GLS two-pass t$t$/Wald statistics can be severely size distorted. The 95% confidence sets for the risk premia in the above-cited work that result from the novel statistics differ substantially from those that result from the FM and GLS two-pass t$t$-statistics. They show support for the human capital asset pricing model although the 95% confidence set for the risk premia on labor income growth is unbounded. The 95% confidence sets show no support for the (scaled) consumption asset pricing model, since the 95% confidence set of the risk premia on the scaled consumption growth consists of the whole real line, but do not reject it either.     

Modeling the conditional distribution of financial returns with asymmetric tails

This paper proposes a conditional density model that allows for differing left/right tail indices and time-varying volatility based on the dynamic conditional score (DCS) approach. The asymptotic properties of the maximum likelihood estimates are presented under verifiable conditions together with simulations showing effective estimation with practical sample sizes. It is shown that tail asymmetry is prevalent in global equity index returns and can be mistaken for skewness through the center of the distribution. The importance of tail asymmetry for asset allocation and risk premia is demonstrated in-sample. Application to portfolio construction out-of-sample is then considered, with a representative investor willing to pay economically and statistically significant management fees to use the new model instead of traditional skewed models to determine their asset allocation.     

New tips from TIPS: Identifying inflation expectations and the risk premia of break-even inflation

This paper decomposes the break-even inflation rates derived from inflation-indexed bonds into inflation risk premia, liquidity risk premia, and inflation expectations. I estimate a common factor model with autoregressive conditionally heteroscedastic (ARCH) errors that extracts co-movements from twenty-two monthly and quarterly indicators to identify these three components. The results indicate that the sharp declines in the 10-year and 5-year break-even inflation rates in 2009 reflect a substantial increase in liquidity risk rather than a decrease in inflation expectations. Break-even inflation rates underestimate inflation expectations over nearly the entire sample due to the liquidity risk premia carried by the inflation indexed bond yields. Also, the model-implied inflation expectations show better forecast performance for the average annual inflation rates than raw break-even inflation rates, the Survey of Professional Forecasters, and the Surveys of Consumers inflation forecasts.     

Expectations Formation and Risk in Three Financial Markets: Surveying What the Surveys Say

This paper attempts to provide a logical overview of the literature which exploits survey data to examine issues of expectations formation and risk aversion in financial markets. Our survey suggests that: short term expectations are excessively volatile and exhibit bandwagon effects, while longer term expectations appear to be regressive and therefore stabilising; in bond and foreign exchange markets the standard result of forward rate biasedness is due in part to time-varying premia; recent research using disaggregate foreign exchange survey data demonstrates the importance of heterogeneous expectations.     

Cross-sectional tests of asset pricing models with full-rank mimicking portfolios

In the standard tests of asset pricing models, factor risk premia are estimated on a test asset span so that models are tested with degrees of freedom reduced by the number of factors. Risk premia of traded factors can be further restricted to be equal to their expected returns, but such restrictions cannot be imposed on models with nontraded factors, which may create a problem of testing without full restrictions or on unequal asset spans across models. We propose a full-rank mimicking portfolio approach by projecting nontraded factors onto a combined span of test assets and benchmark traded factors. Under the Hansen-Jagannathan distance framework, we demonstrate that full-rank mimicking portfolios can provide improved power and fair performance comparison against a benchmark model in both specification and model comparison tests.     

Time-varying beta in functional factor models: Evidence from China

In this paper, we introduce a functional method to investigate how betas change over time in factor models. Based on the China A-share data, we drop the constant beta assumption in the CAPM and multi-factor models to estimate the time-varying betas directly from the functional data regression. The empirical results show that exposures to all risk factors have certain time-varying patterns in the Chinese A-share stock market.     

Premia for correlated default risk

Using data on corporate default experience in the U.S. and market rates of CDX index and tranche swaps of various maturities, we estimate reduced-form models of correlated default timing in the CDX High Yield and Investment Grade portfolios under actual and risk-neutral probabilities. The striking contrast between the estimated processes followed by the actual and risk-neutral arrival intensities of defaults, and between the parameters governing the actual and risk-neutral dynamics of the risk-neutral intensities, indicates the presence of substantial default risk premia in CDX swap market rates. The effects of risk premia on swap rates covary strongly across maturities, and depend on general stock market volatility and several measures of credit spreads. Large moves in the effects of these premia on swap rates have natural interpretations in terms of economic and financial market developments during the sample period, April 2004 to October 2007. Our results suggest that a large portion of the movements in CDX swap market rates observed during the sample period may be caused by changing attitudes toward correlated default risk rather than changes in the economic factors affecting the actual risk of clustered defaults, which ultimately governs swap payoffs.     

Tests of asset pricing with time‐varying factor loads

This paper proposes an empirical asset pricing test based on the homogeneity of the factor risk premia across risky assets. Factor loadings are considered to be dynamic and estimated from data at higher frequencies. The factor risk premia are obtained as estimates from time series regressions applied to each risky asset. We propose Swamy‐type tests robust to the presence of generated regressors and dependence between the pricing errors to assess the homogeneity of the factor risk premia and the zero intercept hypothesis. An application to US industry portfolios shows overwhelming evidence rejecting the capital asset pricing model, and the three and five factor models developed by Fama and French (Journal of Financial Economics, 1993, 33, 3–56; Journal of Financial Economics, 2015, 116, 1–22). In particular, we reject the null hypotheses of a zero intercept, homogeneous factor risk premia across risky assets, and the joint test involving both hypotheses.     

Japan’s impactful augmentation of quantitative easing sovereign-bond purchases

This article examines how and to what extent large-scale government bond purchases in the Bank of Japan’s monetary policy affected two components of long-term interest rates over the period 2009–2015. The article divides market yields on popular 5 and 10-year government bonds into future policy-rate expectations with uncertainty and a specific type of term premia required by investors for the bonds’ demand/supply imbalances, by using overnight index swap rates as a proxy for the former. The Bank of Japan augmented the purchases substantially by starting Quantitative and Qualitative Monetary Easing (QQME) in 2013. The QQME became impactful in the sense that it encouraged investors to improve the first component whilst reducing the second component. These appeared mainly as persisting announcement-effects – upward level shifts of the expectations and downward ones of the term premia. The reduction of term premia was much greater for the 10-year maturity than for 5-year one and strengthened after an additional expansion of the QQME in 2014. The QQME is estimated to have enhanced 5-year sovereign bond yields by 11.9 basis points (bps) a month on average whilst reducing 10-year ones by 8.3 bps. The impact on the 5-year yields turned to be negative after the QQME expansion.     

The maturity structure of term premia with time-varying expected returns

This paper analyzes the maturity structure of term premia using McCulloch’s US Treasury yield curve data from 1953–91, allowing expected returns to vary across time. One, 3, 6, and 12 month holding period returns on maturities up to 5 years are projected on 3 ex ante variables to compute time-varying expected returns, and simulations are employed to generate distributions of conditionally expected return premia. The likelihood of expected returns monotonically increasing in maturity (as implied by the liquidity preference hypothesis) is relatively high when the yield curve is steep and interest rates are high, and with longer holding periods, but low in other cases. The hypothesis that intermediate maturity bonds have the highest expected returns (a “hump-shaped” maturity-return pattern) around the onset of recessions does not receive much support.     

Non-Parametric Regression Models of Deviations from Othogonality in the Expectations Theory of the Term Structure

Regression tests of the expectations theory of the term structure typically reject the null hypothesis of orthogonality between implied forecast errors and the yield spreads. In the statistical literature on the term structure, these rejections are sometimes attributed to time-varying liquidity premia, and Engle et al . (1987) suggest that the ARCH-M model of time-variation in the liquidity premium may be sufficient to account for rejections of the expectations theory. We use non-parametric (kernel) regression to explore the regression test results on a number of data sets, and find some evidence of a persistent deviation from orthogonality for large absolute values of the spread. Incorporating ARCH-in-mean into models of the term premium indicates that this specification does explain significant time variation in liquidity premia, but the effect does not apepar to be sufficient to account for all of the deviations from orthogonality of forecast errors and spreads.     

The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts

The recent theoretical asset allocation literature has derived optimal dynamic investment strategies in various advanced models of asset returns. But how sensitive is investor welfare to deviations from the theoretically optimal strategy? Will unsophisticated investors do almost as well as sophisticated investors? This paper develops a general theoretical framework for answering such questions and applies it to three specific models of interest rate risk, stochastic stock volatility, and mean reversion and growth/value tilts of stock portfolios. Among other things, we find that growth/value tilts are highly valuable, but the hedging of time-varying stock risk premia is less important.     

General Bayesian time-varying parameter vector autoregressions for modeling government bond yields

US yield curve dynamics are subject to time-variation, but there is ambiguity about its precise form. This paper develops a vector autoregressive (VAR) model with time-varying parameters and stochastic volatility, which treats the nature of parameter dynamics as unknown. Coefficients can evolve according to a random walk, a Markov switching process, observed predictors, or depend on a mixture of these. To decide which form is supported by the data and to carry out model selection, we adopt Bayesian shrinkage priors. Our framework is applied to model the US yield curve. We show that the model forecasts well, and focus on selected in-sample features to analyze determinants of structural breaks in US yield curve dynamics.