This paper identities five common risk factors in the returns on stocks and bonds. There are three stock-market factors: an overall market factor and factors related to firm size and book-to-market equity. There are two bond-market factors. related to maturity and default risks. Stock returns have shared variation due to the stock-market factors, and they are linked to bond returns through shared variation in the bond-market factors. Except for low-grade corporates. the bond-market factors capture the common variation in bond returns. Most important. the five factors seem to explain average returns on stocks and bonds. 1.

The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.l) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation. This property is then used to derive a partial differential equation for bond prices. The solution to that equation is given in the form of a stochastic integral representation. An interpretation of the bond pricing formula is provided. The model is illustrated on a specific case.

Market e#ciency survives the challenge from the literature on long-term return anomalies. Consistent with the market e#ciency hypothesis that the anomalies are chance results, apparent overreaction to information is about as common as underreaction, and post-event continuation of pre-event abnormal returns is about as frequent as post-event reversal. Most important, consistent with the market e#ciency prediction that apparent anomalies can be due to methodology, most long-term return anomalies tend to disappear with reasonable changes in technique. # 1998 Elsevier Science S.A. All rights reserved.

We model a market populated by two groups of boundedly rational agents: “newswatchers” and “momentum traders.” Each newswatcher observes some private information, but fails to extract other newswatchers’ information from prices. If information diffuses gradually across the population, prices underreact in the short run. The underreaction means that the momentum traders can profit by trendchasing. However, if they can only implement simple (i.e., univariate) strategies, their attempts at arbitrage must inevitably lead to overreaction at long horizons. In addition to providing a unified account of under- and overreactions, the model generates several other distinctive implications.

We examine how the evidence of predictability in asset returns affects optimal portfolio choice for investors with long horizons. Particular attention is paid to estimation risk, or uncertainty about the true values of model parameters. We find that even after incorporating parameter uncertainty, there is enough predictability in returns to make investors allocate substantially more to stocks, the longer their horizon. Moreover, the weak statistical significance of the evidence for predictability makes it important to take estimation risk into account; a long-horizon investor who ignores it may overallocate to stocks by a sizeable amount. ONE OF THE MORE STRIKING EMPIRICAL FINDINGS in recent financial research is the evidence of predictability in asset returns. 1 In this paper we examine the implications of this predictability for an investor seeking to make sensible portfolio allocation decisions. We approach this question from the perspective of horizon effects: Given the evidence of predictability in returns, should a long-horizon investor allocate his wealth differently from a short-horizon investor? The motivation for thinking about the problem in these terms is the classic work of Samuelson ~1969! and Merton ~1969!. They show that if asset returns are i.i.d., an investor with power utility who rebalances his portfolio optimally should choose the same asset allocation, regardless of investment horizon. In light of the growing body of evidence that returns are predictable, the investor’s horizon may no longer be irrelevant. The extent to which the horizon does play a role serves as an interesting and convenient way of thinking about how predictability affects portfolio choice. Moreover, the results may shed light on the common but controversial advice that investors with long horizons should allocate more heavily to stocks. 2

This study investigates whether market-wide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. Over a 34-year period, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 % annually, adjusted for exposures to the market return as well as size, value, and momentum factors.

This paper studies the role of fluctuations in the aggregate consumption–wealth ratio for predicting stock returns. Using U.S. quarterly stock market data, we find that these fluctuations in the consumption–wealth ratio are strong predictors of both real stock returns and excess returns over a Treasury bill rate. We also find that this variable is a better forecaster of future returns at short and intermediate horizons than is the dividend yield, the dividend payout ratio, and several other popular forecasting variables. Why should the consumption–wealth ratio forecast asset returns? We show that a wide class of optimal models of consumer behavior imply that the log consumption–aggregate wealth ~human capital plus asset holdings! ratio summarizes expected returns on aggregate wealth, or the market portfolio. Although this ratio is not observable, we provide assumptions under which its important predictive components for future asset returns may be expressed in terms of observable variables, namely in terms of consumption, asset holdings and labor income. The framework implies that these variables are cointegrated, and

We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describt tbe process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: 1) positive correlation between conditional volatility and volume, 2) large price movements are followed by high volume, 3) conditioning on lagged volume substantially attenuates the "leverage " effect, and 4) after conditioning on lagged volume, there is a positive risk/return relation.

The value premium in U.S. stock returns is robust. The positive relation between average return and book-to-market equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers. A three-factor risk model explains the value premium better than the hypothesis that the book-tomarket characteristic is compensated irrespective of risk loadings. Firms with high ratios of book value to the market value of common equity have higher average returns than firms with low book-to-market ratios (Rosenberg, Reid, and Lanstein (1985)). Because the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) does not explain this pattern in average returns, it is typically called an anomaly. There are four common explanations for the book-to-market (BE/ME) anomaly. One says that the positive relation between BE/ME and average return (the so-called value premium) is a chance result unlikely to be observed out of sample (Black (1993), MacKinlay (1995)). Out-of-s...

Value stocks have higher returns than growth stocks in markets around the world. For the period 1975 through 1995, the difference between the average returns on global portfolios of high and low book-to-market stocks is 7.68 percent per year, and value stocks outperform growth stocks in twelve of thirteen major markets. An international capital asset pricing model cannot explain the value premium, but a two-factor model that includes a risk factor for relative distress captures the value premium in international returns. INVESTMENT MANAGERS CLASSIFY FIRMS that have high ratios of book-to-market equity ~B0M!, earnings to price ~E0P!, or cash flow to price ~C0P! as value stocks. Fama and French ~1992, 1996! and Lakonishok, Shleifer, and Vishny ~1994! show that for U.S. stocks there is a strong value premium in average returns. High B0M, E0P, or C0P stocks have higher average returns than low B0M, E0P, or C0P stocks. Fama and French ~1995! and Lakonishok et al. ~1994! also show that the value premium is associated with relative distress.