In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962--1985) and for all subperiod for a variety of aggregate returns indexes and size-sorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.

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Abstract: This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of cross-sectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: 1) an increase in trading volume relative to trend over the prior six months; and 2) positive returns over the prior thirty-six months. The first finding is consistent with the model of Hong and Stein (1999), which predicts that negative asymmetries are more likely to occur when there are large differences of opinion among investors. The latter finding fits with a number of theories, most notably Blanchard and Watson’s (1982) rendition of stockprice bubbles. Analogous results also obtain when we attempt to forecast the skewness of the aggregate stock market, though our statistical power in this case is limited.

One of the central questions in financial economics is the determination of asset prices, such as the value of a stock. Over the past three decades, research on this topic has converged on a concept called the “state-price density”. However, a puzzle has arisen. On the one hand, Cox, Ingersoll, and Ross (1985) and others argue that the ratio of the state-price density to the statistical probability density, which is commonly known as the pricing kernel, should decrease monotonically as the aggregate wealth of an economy rises. On the other hand, recent empirical work on options on the S&P 500 index suggests that, for a sizable range of index levels, the pricing kernel is increasing instead of decreasing. We investigate theoretical explanations to this puzzle. Our existing work has ruled out some alternative hypotheses, such as data imperfections and methodological problems. The current paper focuses on the hypothesis of state-dependent utility. State-dependent utility can arise from diverse causes such as habit persistence, stochastic index volatility, or dependence on interest rates or other asset prices. In this paper we characterize a general relation between the index and the state variables that is required to explain the puzzle. However, it remains for us to provide economic reasoning to justify this relation. The existing literature is largely unsatisfactory with respect to this puzzle, and most research does not touch on the puzzle altogether.

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuoustime components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Lévy-driven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the high-frequency intraday data.

This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to measure ex post latent volatility imply that standard time series models of the conditional variance become variants of an AR-MAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under duration-dependent mixing. This process can capture large abrupt changes in the level of volatility, time-varying persistence, and time-varying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives.

Aggregate stock prices are driven by shocks with persistence levels ranging from daily intervals to several decades. To accommodate this, we introduce a parsimonious equilibrium with regime-shifts of heterogeneous durations in dividend news, and estimate specifications with up to 256 states on daily U.S. equity returns. The multifrequency equilibrium has significantly higher likelihood than the classic Campbell and Hentschel (1992) specification, while generating volatility feedback effects 10 to 40 times larger. Furthermore, Bayesian learning about volatility generates a novel tradeoff between skewness and kurtosis as information quality varies, which complements the traditional uncertainty channel (e.g., Veronesi, 1999). Economies with intermediate investor information best match the return data.

Business School, London, for helpful comments and suggestions. Further, we thank Mitch Haviv of GovPX for providing useful information on their data. Of course, all errors remain our sole responsibility. The most recent version of the paper can be downloaded from

this paper is that, for any finite number of data points, it is more likely than not that we will pick the worse of two specific models if we use the likelihood function to compare them. It turns out that maximum likelihood will lead to an

We analyze the pricing and informational efficiency of the Italian market for options written on the most important stock index, the MIB30. We find several indications inconsistent with the hypothesis that the Italian MIBO is an efficient market. We report that a striking percentage of the data consists of option prices violating basic no-arbitrage conditions. This percentage declines but never becomes negligible when we relax the no-arbitrage restrictions to accommodate for the presence of bid/ask spreads and other frictions. The result holds in general for all levels of moneyness and time to maturity. We also document abrupt changes of the implied volatility surface that can hardly be explained by changes in market beliefs. Finally we investigate the informational efficiency of the MIBO and conclude that option prices are poor predictors of the volatility of MIB30 returns. We wish to thank Alberto di Stefano from BSI (Banca della Svizzera Italiana) who has made available the data used in this paper. We have received valuable comments and encouragement from Andrea Beltratti and Wake Epps. We are also grateful to Paolo Mammola and Laura Cavallo and seminar participants at Bocconi