The role of no-arbitrage on forecasting: Lessons from a parametric term structure model

Parametric term structure models have been successfully applied to numerous problems in fixed income markets, including pricing, hedging, managing risk, as well as to the study of monetary policy implications. In turn, dynamic term structure models, equipped with stronger economic structure, have been mainly adopted to price derivatives and explain empirical stylized facts. In this paper, we combine flavors of those two classes of models to test whether no-arbitrage affects forecasting. We construct cross-sectional (allowing arbitrages) and arbitrage-free versions of a parametric polynomial model to analyze how well they predict out-of-sample interest rates. Based on US Treasury yield data, we find that no-arbitrage restrictions significantly improve forecasts. Arbitrage-free versions achieve overall smaller biases and root mean square errors for most maturities and forecasting horizons. Furthermore, a decomposition of forecasts into forward-rates and holding return premia indicates that the superior performance of no-arbitrage versions is due to a better identification of bond risk premium.     

TIME-VARYING TERM PREMIA AND THE BEHAVIOR OF FORWARD INTEREST RATE PREDICTION ERRORS

In this paper I examine the time-varying expected term premium argument for the failure of the expectations hypothesis of the term structure of U.S. interest rates. Using an unobserved components model to estimate expected term premia from March 1951 to January 1991, I find considerable variation in estimated premia and significant persistence in their volatility over time.     

Macroeconomic Sources of Risk in the Term Structure

We develop a new way of modeling time variation in term premia, based on the stochastic discount factor model of asset pricing. The joint distribution of excess U.S. bond returns of different maturity and the observable fundamental macroeconomic factors is modeled using multivariate GARCH with conditional covariances in the mean to capture the term premia. By testing the assumption of no arbitrage we derive a specification test of our model. We estimate the contribution made to the term premia at different maturities through real and nominal sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the reported failures of the rational expectations hypothesis can be attributed to an omitted time-varying term premium.     

Time-variation in term premia: International survey-based evidence

Using a large, previously unexplored data set of survey-based interest rate forecasts that covers a broad range of countries, this paper re-examines the expectations hypothesis of the term structure of interest rates. We find that survey-based interest rate forecasts outperform not only a random walk forecast, but also outperform forecasts from forward rates. When using these superior survey-based forecasts in a modified expectations hypothesis test, the expectations hypothesis is rejected for fewer countries, at lower significance levels, and has greater explanatory power than when using a traditional forward rates-based test. We furthermore document strong time-variation in the term premia, which is an important reason why the traditional expectations hypothesis test is rejected so frequently. This time-variation seems to arise from the changing attitudes towards risk among market participants and as a compensation for the change in liquidity in the term structure. Finally, we find that generalizing findings from earlier U.S. studies to other countries may lead to bias in the true economic relationships in these countries.     

Real Rates, Expected Inflation, and Inflation Risk Premia

This paper studies the term structure of real rates, expected inflation, and inflation risk premia. The analysis is based on new estimates of the real term structure derived from the prices of index-linked and nominal debt in the U.K. I find strong evidence to reject both the Fisher Hypothesis and versions of the Expectations Hypothesis for real rates. The estimates also imply the presence of time-varying inflation risk premia throughout the term structure.     

The high-frequency impact of news on long-term yields and forward rates: Is it real?

Macroeconomic news announcements move yields and forward rates on nominal and index-linked bonds and inflation compensation. This paper estimates the reactions using high-frequency data on nominal and index-linked bond yields, allowing the effects of news announcements on real rates and inflation compensation to be parsed far more precisely than is possible using daily data. Long-term nominal yields and forward rates are very sensitive to macroeconomic news announcements. Inflation compensation is sensitive to announcements about price indices and monetary policy. However, for news announcements about real economic activity, such as nonfarm payrolls, the vast majority of the sensitivity is concentrated in real rates. Accordingly, most of the sizeable impact of news about real economic activity on the nominal term structure of interest rates represents changes in expected future real short-term interest rates and/or real risk premia rather than changes in expected future inflation and/or inflation risk premia. Such sensitivity of real rates to macroeconomics news is hard to rationalize within the framework of existing macroeconomic models.     

Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

In this paper, we study inflation risk and the term structure of inflation risk premia in the United States' nominal interest rates through the Treasury Inflation Protection Securities (TIPS) with a multi-factor, modified quadratic term structure model with correlated real and inflation rates. We derive closed form solutions to the real and nominal term structures of interest rates that drastically facilitate the estimation of model parameters and improve the accuracy of the valuation of nominal rates and TIPS prices. In addition, we contribute to the literature by estimating the term structure of inflation risk premia implied from the TIPS market. The empirical evidence using data from the period of January 1998 through October 2007 indicates that the expected inflation rate, contrary to data derived from the consumer price indices, is very stable and the inflation risk premia exhibit a positive term structure.     

The expectations hypothesis: New hope or illusory support?

Recent studies of the expectations hypothesis of the term structure (EHTS) find evidence in favor of the EHTS using post 1980s US data. This has been attributed to the relative macro stability of this period and greater market efficiency. Using a panel of forecasts for 3-month interest rates for ten countries we test separately for EHTS and rational expectations. Assuming rational expectations holds we find support for the EHTS is illusory due to an off-setting time-varying term premia and non-rational expectations. Previous forecast-based studies suggest biased expectations tend to reinforce the effect of a time varying term premium. This change can be understood in the context of Fama’s (2006) argument that markets tend to underestimate future spot rates during periods of long-run increases and overestimate during declines.     

Can interest rate factors explain exchange rate fluctuations?

The level, slope, and curvature of the yield curve reflect time variation in investors’ risk premia and are known predictors of excess bond returns and economic activity. In this paper, I develop a term structure model under complete markets and no arbitrage to relate these interest rate factors to exchange rate fluctuations. The Gaussian properties of the stochastic discount factors imply non-linearities in exchange rate risk premia that are shown to account for up to half of the in-sample variation in one-year currency returns for different country pairs during the 1980s–2015 period. I find that interest rate factors help explain exchange rate fluctuations in and out of sample, particularly at longer horizons, and yield profitable currency portfolios relative to standard carry trade strategies.     

The term structure of real interest rates: theory and evidence from UK index-linked bonds

This paper studies the behavior of the default-risk-free real term structure and term premia in two general equilibrium endowment economies with complete markets but without money. In the first economy there are no frictions as in Lucas (Econometrica 46 (1978) 1429) and in the second risk-sharing is limited by the risk of default as in Alvarez and Jermann (Econometrica 68 (2000) 775; Rev. Financial Studies 14 (2001) 1117). Both models are solved numerically, calibrated to UK aggregate and household data, and the predictions are compared to data on real interest rates constructed from the UK index-linked data. While both models produce time-varying risk or term premia, only the model with limited risk-sharing can generate enough variation in the term premia to account for the rejections of expectations hypothesis.     

Risk premia,asset price bubbles,and monetary policy

We develop a dynamic general equilibrium asset pricing model with heterogeneous beliefs to study the effects of monetary policy on prices, risk premia, asset price bubbles, and financial stability. We propose a new framework for monetary policy with respect to bubbles. Because bubble risk premia arise from an interaction between disagreements among investors and dynamic trading constraints, under a non-accommodative monetary policy, liquidity adjusted risk and bubble risk premia increase. What matters for policy is the trading constrained fraction/mass of agents that disagree about fundamentals (i.e. optimists/pessimists). Accommodative policy can lead to a larger fraction of trading constrained agents that disagree, larger bubbles, and increased systemic risk. An implication of our results is that accommodative monetary policy in response to the Covid-19 crisis does not increase systemic risk due to asset price bubbles, as long as the policy keeps inflation under control.     

What is the Intrinsic Value of the Dow?

We model the time-series relation between price and intrinsic value as a cointegrated system, so that price and value are long-term convergent. In this framework, we compare the performance of alternative estimates of intrinsic value for the Dow 30 stocks. During 1963–1996, traditional market multiples (e.g., B/P, E/P, and D/P ratios) have little predictive power. However, a V/P ratio, where V is based on a residual income valuation model, has statistically reliable predictive power. Further analysis shows time-varying interest rates and analyst forecasts are important to the success of V. Alternative forecast horizons and risk premia are less important.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

Rational Asset Prices

The mean, covariability, and predictability of the return of different classes of financial assets challenge the rational economic model for an explanation. The unconditional mean aggregate equity premium is almost seven percent per year and remains high after adjusting downwards the sample mean premium by introducing prior beliefs about the stationarity of the price–dividend ratio and the (non)forecastability of the long–term dividend growth and price–dividend ratio. Recognition that idiosyncratic income shocks are uninsurable and concentrated in recessions contributes toward an explanation. Also borrowing constraints over the investors' life cycle that shift the stock market risk to the saving middle–aged consumers contribute toward an explanation.     

The October 1979 Change in the U.S. Monetary Regime: Its Impact on the Forecastability of Canadian Interest Rates

Subsequent to the October 1979 shift in monetary policy in the United States, interest rates in North America not only reached unprecedented levels but also exhibited unprecedented volatility. Using Canadian data, the authors show that anticipated quarterly changes in long-term rates associated with the rational-expectations model have remained small during this post-shift period. The authors examine three sets of recorded forecasts of long-term interest rates in Canada and note their failure to improve upon the no-change prediction. The “perverse” relationship between the slope of the yield curve and the subsequent movement in long-term rates exists in the Canadian data but is of only modest value in a forecasting context. The excess returns on long-term bonds implicit in the recorded forecasts of the level of interest rates vary sharply, yet there is little evidence that forecasters have identified a predictable component of time-varying term premia.     

Inflation risk premia and the expectations hypothesis

We study the properties of the nominal and real risk premia of the term structure of interest rates. We develop and solve the bond pricing implications of a structural monetary version of a real business cycle model, with taxes and endogenous monetary policy. We show the relation of this model with the class of essentially affine models that incorporate an endogenous state-dependent market price of risk. We characterize and estimate the inflation risk premium and find that over the last 40 years the ten-year inflation risk premium has been has averaged 70 basis points. It is time-varying, ranging from 20 to 140 basis points over the business cycle and its term structure is sharply upward sloping. The inflation risk premium explains 23% (42%) of the time variation in the five (ten)-year forward risk premium and it plays an important role in help explain deviations from the expectations hypothesis of interest rates.     

Pockets of Predictability

For many benchmark predictor variables, short-horizon return predictability in the U.S. stock market is local in time as short periods with significant predictability (“pockets”) are interspersed with long periods with no return predictability. We document this result empirically using a flexible time-varying parameter model that estimates predictive coefficients as a nonparametric function of time and explore possible explanations of this finding, including time-varying risk premia for which we find limited support. Conversely, pockets of return predictability are consistent with a sticky expectations model in which investors slowly update their beliefs about a persistent component in the cash flow process.     

Out-of-sample density forecasts with affine jump diffusion models

We conduct out-of-sample density forecast evaluations of the affine jump diffusion models for the S&P 500 stock index and its options’ contracts. We also examine the time-series consistency between the model-implied spot volatilities using options & returns and only returns. In particular, we focus on the role of the time-varying jump risk premia. Particle filters are used to estimate the model-implied spot volatilities. We also propose the beta transformation approach for recursive parameter updating. Our empirical analysis shows that the inconsistencies between options & returns and only returns are resolved by the introduction of the time-varying jump risk premia. For density forecasts, the time-varying jump risk premia models dominate the other models in terms of likelihood criteria. We also find that for medium-term horizons, the beta transformation can weaken the systematic effect of misspecified AJD models using options & returns.     

Belief Dispersion in the Stock Market

We develop a dynamic model of belief dispersion with a continuum of investors differing in beliefs. The model is tractable and qualitatively matches many of the empirical regularities in a stock price and its mean return, volatility, and trading volume. We find that the stock price is convex in cash‐flow news and increases in belief dispersion, while its mean return decreases when the view on the stock is optimistic, and vice versa when pessimistic. Moreover, belief dispersion leads to higher stock volatility and trading volume. We demonstrate that otherwise identical two‐investor heterogeneous‐beliefs economies do not necessarily generate our main results.     

Banks,maturity transformation,and monetary policy

Banks engage in maturity transformation and the term premium compensates them for bearing the associated interest rate risk. Consistent with this view, I show that banks’ net interest margins and term premia have comoved in the United States over the last decades. On monetary policy announcement days, bank equity falls more sharply than nonbank equity following an increase in expected future short-term rates, but also responds more positively if term premia increase. These effects are reflected in bank cash-flows and amplified for banks with a larger maturity mismatch. The results reveal that banks are not immune to interest rate risk.