Testing the expectations hypothesis when interest rates are near integrated

Nominal interest rates are unlikely to be generated by unit-root processes. Using data on short and long interest rates from eight developed and six emerging economies, we test the expectations hypothesis using cointegration methods under the assumption that interest rates are near integrated. If the null hypothesis of no cointegration is rejected, we then test whether the estimated cointegrating vector is consistent with that suggested by the expectations hypothesis. The results show support for cointegration in 10 of the 14 countries we consider, and the cointegrating vector is similar across countries. However, the parameters differ from those suggested by theory. We relate our findings to existing literature on the failure of the expectations hypothesis and to the role of term premia.     

Multifrequency news and stock returns

Equity prices are driven by shocks with persistence levels ranging from intraday horizons to several decades. To accommodate this diversity, we introduce a parsimonious equilibrium model with regime shifts of heterogeneous durations in fundamentals, and estimate specifications with up to 256 states on daily aggregate returns. The multifrequency equilibrium has higher likelihood than the Campbell and Hentschel [1992. No news is good news: an asymmetric model of changing volatility in stock returns. Journal of Financial Economics 31, 281–318] specification, while producing volatility feedback 10 to 40 times larger. Furthermore, Bayesian learning about volatility generates a novel trade-off between skewness and kurtosis as information quality varies, complementing the uncertainty channel [e.g., Veronesi, 1999. Stock market overreaction to bad news in good times: a rational expectations equilibrium model. Review of Financial Studies 12, 975–1007]. Economies with intermediate information best match daily returns.     

The risk-return tradeoff: A COGARCH analysis of Merton's hypothesis

We analysed daily returns of the CRSP value weighted and equally weighted indices over 1953-2007 in order to test for Merton's theorised relationship between risk and return. Like some previous studies we used a GARCH stochastic volatility approach, employing not only traditional discrete time GARCH models but also using a COGARCH — a newly developed continuous-time GARCH model which allows for a rigorous analysis of unequally spaced data. When a risk-return relationship symmetric to positive or negative returns is postulated, a significant risk premium of the order of 7-8% p.a., consistent with previously published estimates, is obtained. When the model includes an asymmetry effect, the estimated risk premium, still around 7% p.a., becomes insignificant. These results are robust to the use of a value weighted or equally weighted index.The COGARCH model properly allows for unequally spaced time series data. As a sidelight, the model estimates that, during the period from 1953 to 2007, the weekend is equivalent, in volatility terms, to about 0.3-0.5 regular trading days.     

Are share prices still too high?

The current value of the dividend yield is at a historically low level. Since the end of the bear market in 2003 prices have rebounded strongly such that this yield is at a lower point than any previous in its history except at the height of the late 1990s bubble. The price-earnings ratio paints a similar picture and raises the issues of equity overvaluation and price falls. This paper resolves to examine whether prices are over-valued by arguing that such measures do not have a single attractor point and hence relying on historical means as a guide to mis-valuation is not a valid approach. In explaining why the higher equity prices relative to dividends are supported we provide evidence consistent with existing arguments that low and stable inflation is a particular driver to better equity valuation and note that the last decade has seen a period of historically low and stable inflation. Hence, the stable economic environment has led to more accurate valuation of stocks and lower required rates of return, thus supporting higher prices.     

Bubbles in the dividend–price ratio? Evidence from an asymmetric exponential smooth-transition model

Recent stock price movements have led to a re-examination of the present value model. An increasing belief is that although dividends and prices are indeed cointegrated, they may exhibit non-linear dynamics in the process of reversion. This paper implements an empirical model designed to capture two possible explanations for such non-linearity, namely transaction costs and noise traders. Utilising data from a number of countries we show that the dynamics of the log dividend yield are, first, characterised by an inner random walk regime, where the benefits of engaging in trade do not outweigh the costs and so the process moves randomly. Second, a reverting outer regime where the dynamics of reversion differ between positive and negative deviations, such that price rises greater than the level supported by dividends exhibit a greater degree of persistence than price falls relative to dividends.     

Maximum likelihood estimation of stochastic volatility models

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.     

Do jumps contribute to the dynamics of the equity premium?

This paper investigates whether risks associated with time-varying arrival of jumps and their effect on the dynamics of higher moments of returns are priced in the conditional mean of daily market excess returns. We find that jumps and jump dynamics are significantly related to the market equity premium. The results from our time-series approach reinforce the importance of the skewness premium found in cross-sectional studies using lower-frequency data; and offer a potential resolution to sometimes conflicting results on the intertemporal risk-return relationship. We use a general utility specification, consistent with our pricing kernel, to evaluate the relative value of alternative risk premium models in an out-of-sample portfolio performance application.     

Are survey forecasts of individual and institutional investor sentiments rational?

We examine the effects of rational risk factors on investor sentiments. We find that institutional investor sentiments are more rational than individual investor sentiments. There are significant positive effects of, market return and dividend yield and negative effect of inflation on both types of sentiments. These risk factors have stronger effects on institutional than individual investor sentiments. Also, there are significant effects of term spread and HML on the institutional investor sentiments. The evidence suggests that linkages between sentiments and stock return stems from a combination of rational outlook and noise i.e. expectations that are not fully justified by information.     

The relationship between risk and expected return in Europe

We employ MIDAS (mixed data sampling) to study the risk–expected return trade-off in several European stock indices. Using MIDAS, we report that in most indices there is a significant positive relationship between risk and expected return. This strongly contrasts with the result we obtain when we employ both symmetric and asymmetric GARCH models for conditional variance. We also find that asymmetric specifications of the variance process within the MIDAS framework improve the relationship between risk and expected return. As an additional application, we analyze the extent to which European stock markets are integrated, which is a particularly relevant issue, especially following the launch of the Euro in January 1999. Finally, we propose a bivariate MIDAS specification to test the pricing significance of the hedging component within an intertemporal risk–return trade-off with multiple European market indices.     

The components of the illiquidity premium: An empirical analysis of US stocks 1927–2010

This paper implements a conditional version of the liquidity adjusted CAPM (LCAPM). The conditional LCAPM allows for a time-varying decomposition of the total illiquidity premium into a level component and three risk components. The estimated average annual total illiquidity premium for US stocks 1927–2010 is 1.74–2.08%, which is substantially lower than in most previous studies. The contributions from illiquidity level and illiquidity risk are 1.25–1.28% and 0.46–0.83%, respectively. Of the three illiquidity risk components, risk related to the hedging of wealth shocks is the most important, while commonality risk is the least important. The illiquidity premia are clearly time-varying, with peaks in downturns and crises, but with no general tendency to decrease over time. The level premium and the risk premium are significantly positively correlated, at around 0.35; indicating that in periods of turbulence both illiquidity cost and illiquidity risk premia tend to be high.     

The leverage effect puzzle: Disentangling sources of bias at high frequency

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation to be negative. To better understand the sources of the puzzle, we analyze the different asymptotic biases that are involved in high frequency estimation of the leverage effect, including biases due to discretization errors, to smoothing errors in estimating spot volatilities, to estimation error, and to market microstructure noise. This decomposition enables us to propose novel bias correction methods for estimating the leverage effect.     

The risk return tradeoff in the long run: 1836–2003

Previous studies typically find a statistically insignificant relation between the market risk premium and its expected volatility. Further, several of these studies estimate a negative risk return tradeoff, contrary to the predictions of mainstream theory. Using simulations, I demonstrate that even 100 years of data constitute a small sample that may easily lead to this finding even though the true risk return tradeoff is positive. Small-sample inference is plagued by the fact that conditional volatility has almost no explanatory power for realized returns. Using the nearly two century history of U.S. equity market returns from Schwert [1990. Indexes of United States stock prices from 1802 to 1987. Journal of Business 63, 399–426], I estimate a positive and statistically significant risk return tradeoff. Finally, exploratory analysis suggests a role for a time-varying relation linked to the changing nature of the U.S. economy.     

Political regimes,business cycles,seasonalities, and returns

This paper provides a method for testing for regime differences when regimes are long-lasting. Standard testing procedures are generally inappropriate because regime persistence causes a spurious regression problem – a problem that has led to incorrect inference in a broad range of studies involving regimes representing political, business, and seasonal cycles. The paper outlines analytically how standard estimators can be adjusted for regime dummy variable persistence. While the adjustments are helpful asymptotically, spurious regression remains a problem in small samples and must be addressed using simulation or bootstrap procedures. We provide a simulation procedure for testing hypotheses in situations where an independent variable in a time-series regression is a persistent regime dummy variable. We also develop a procedure for testing hypotheses in situations where the dependent variable has similar properties.     

Efficient tests of stock return predictability

Conventional tests of the predictability of stock returns could be invalid, that is reject the null too frequently, when the predictor variable is persistent and its innovations are highly correlated with returns. We develop a pretest to determine whether the conventional t-test leads to invalid inference and an efficient test of predictability that corrects this problem. Although the conventional t-test is invalid for the dividend–price and smoothed earnings–price ratios, our test finds evidence for predictability. We also find evidence for predictability with the short rate and the long-short yield spread, for which the conventional t-test leads to valid inference.