An introduction to security returns

Are stock returns still mean-reverting?

Equity risk premiums are a central component of every risk and return model in finance and are a key input into estimating costs of equity and capital in both corporate finance and valuation. Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating equity risk premiums, historical returns are used, with the difference in annual returns on stocks versus bonds over a long time period comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums - the survey approach, where investors and managers ar asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. We also look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis. (In an addendum, we also look at equity risk premiums during the market crisis, starting on September 12, 2008 through December 31, 2008, and then track the shift the changes through September 30, 2009.)

Mean Reversion Expectations and the 1987 Stock Market Crash: An Empirical Investigation

We model and estimate equity premium in a general equilibrium setting. It is done by reframing the Merton's model (1974) in the context of general equilibrium models such as Ahn and Thompson (1988) and Bates (1991). Our approach is novel in its attempt to derive equity premium by evaluating the equity returns dynamics in equilibrium and to thereby estimate non‐risk convexity premium for equity as well as its risk premium. While risk premium is generally due to systematic risk, convexity premium is due to the option‐like feature of equity, and exists under returns discontinuity and risk neutrality. We model equity premium such that the convexity premium pays for the liquidity and information costs of equity. We calibrate our equity premium model and report that the convexity premium counts for about one third of our predicted equity premium. We find relevance for our non‐risk convexity premium in relation to the premium puzzle and anomalies in the stock market.

Forecasting the Equity Risk Premium: The Ups and the Downs

How does an economy behave if (1) fundamentals are truly hump-shaped, exhibiting momentum in the short run and partial mean reversion in the long run, and (2) agents do not know that fundamentals are hump-shaped and base their beliefs on parsimonious models that they fit to the available data? A class of parsimonious models leads to qualitatively similar biases and generates empirically observed patterns in asset prices and macroeconomic dynamics. First, parsimonious models will robustly pick up the short-term momentum in fundamentals but will generally fail to fully capture the long-run mean reversion. Beliefs will therefore be characterized by endogenous extrapolation bias and pro-cyclical excess optimism. Second, asset prices will be highly volatile and exhibit partial mean reversion--i.e., overreaction. Excess returns will be negatively predicted by lagged excess returns, P/E ratios, and consumption growth. Third, real economic activity will have amplified cycles. For example, consumption growth will be negatively auto-correlated in the medium run. Fourth, the equity premium will be large. Agents will perceive that equities are very risky when in fact long-run equity returns will co-vary only weakly with long-run consumption growth. If agents had rational expectations, the equity premium would be close to zero. Fifth, sophisticated agents--i.e., those who are assumed to know the true model--will hold far more equity than investors who use parsimonious models. Moreover, sophisticated agents will follow a counter-cyclical asset allocation policy. These predicted effects are qualitatively confirmed in U.S. data.(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was bo(This abstract was borrowed from another version of this item.)

In his seminal paper Samuelson (1965) argues that in an informationally efficient market — not to be confused with an allocationally or Pareto-efficient market — price changes must be unforecastable if they are properly anticipated. Prices follow a random walk and fully incorporate the information and expectations of all market participants. Fama's (1970a) dictum that "prices fully reflect all available information" has become a holy grail among the academic community and triggered virtually hundreds of empirical investigations on market efficiency since then. However, in the late 1980s several studies reported deviations of stock returns behavior from the random walk. Poterba/Summers (1988) and Fama/French (1988a) find significant negative autocorrelation in both real and excess long-horizon returns, while Lo/MacKinlay (1988) detect positive autocorrelation for weekly holding-period returns. The empirical evidence throughout this book has shown that stock returns are predictable to some extent on the basis of global instrument variables. It has been argued in chapter 4 that expected returns vary with the business cycle, and that appropriate instrument variables should be indicators for recent and/or future real activity. Similar to the previous literature, the results in chapter 5 strongly suggested that the time variation of economic risk premiums can explain a considerable fraction of the observed stock return predictability. This chapter attempts to put many things together into a unifying framework. Throughout this book it has been argued that predictability is far from being a symptom of inefficiency or irrationality. Now the focus is explicitly on the underlying economic forces in a general equilibrium model of asset pricing, namely reversion in the stochastic discount factor and consumption smoothing. Specifically, this chapter proposes a model in the spirit of LeRoy (1973) and Lucas (1978) to explain mean reversion and, hence stock return predictability in a consumption-based framework. The goal is to demonstrate empirically that the random walk hypothesis is neither a necessary nor a sufficient condition for rationally determined asset prices. In fact, unforecastable prices do not necessarily imply a well-functioning financial market with rational investors, and forecastable prices need not imply the opposite. While the original version of the efficient market hypothesis implicitly assumes constant expected returns, this is inappropriate because it does not account for time variation in risk.KeywordsBusiness CycleStock ReturnAsset PriceExcess ReturnConsumption GrowthThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Stock Return Predictability in a Production Economy

The U.S. equity risk premium using historical estimates of stocks and bonds is 6 to 8 percent. However, research has suggested that the risk premium should be much lower. An important stream of literature in this respect is using analysts’ earnings forecasts and reverse engineering the residual income valuation model to impute risk premium. The use of analysts’ earnings forecasts leads to an upward bias of the estimated risk premium. In this study, we implement methodology to measure equity risk premium without using analysts’ earnings forecasts. Our results provide evidence supporting a close to zero risk premium.

Rationality of Survival, Market Segmentation and Equity Premium Puzzle

I. INTRODUCTION The consumption-based capital asset pricing model (CCAPM) has become the dominant paradigm in asset pricing theory because of its intuitive characterization of asset risk. That is, unlike expectations-based asset pricing theories (e.g. the present value model of stock prices) which inherently assume risk neutrality, the CCAPM is predicated upon risk-averse agents attempting to achieve a smooth consumption profile through the trading of assets. From this perspective, the risk of an asset is captured by the covariance of the asset's return with agents' marginal utility of consumption, or, more broadly, agents' intertemporal marginal rate of substitution of wealth. With this characterization, the CCAPM extends the results of the standard CAPM, i.e. the risk of an asset is reflected in the covariance of the asset's return with the market portfolio, to a general equilibrium setting. However, this intuitively appealing theory has not found much empirical support. Perhaps the most famous demonstration of inconsistency between the theory and data was Rajnish Mehra and Edward Prescott's [1985] analysis of the equity premium, i.e. the difference between the average return on equity and that on government bonds. Using calibration methods rather than a formal statistical approach, they showed that a standard CCAPM severely underpredicts the size of the risk premium on equity. The important implication of this finding is that the basic CCAPM incorrectly models the covariance structure between the return on equity and asset holders' intertemporal marginal rate of substitution. Economists' response to this empirical rejection has been to either identify new sources of risk (e.g., that implied by a particular monetary environment as in Labadie [1989]) or define alternative preferences toward risk (e.g., the use of non-expected utility theory as presented in Weil [1989] and Epstein and Zin [1989]). The potential for this research was illustrated recently by George Constantinides's [1990] resolution of the equity premium puzzle in a model that included habit formation in consumption. By relaxing the standard CCAPM's assumption of time-separable preferences, Constantinides demonstrated that a relatively smooth consumption profile and large risk premium on equity are consistent with equilibrium in a complete markets, rational-expectations framework.(1) I use this insight to study another risk premium puzzle; specifically the behavior of the nominal term premium. The existence of a nominal term premium puzzle was demonstrated in papers by Backus, Gregory, and Zin [1989] and Salyer [1990] in which the term structure implications within a Lucas [1982] type cash-in-advance (CIA) economy were studied. While some equilibrium characteristics of this model were consistent with the data, both papers demonstrated that the model predicts the wrong sign of the term premium: the theory implies the term premium should be negative while, based on quarterly data for yields of three- and six-month U.S. Treasury Bills over the period 1959.1-1989.4, the observed term premium is positive. Similar to the equity premium puzzle as posed by Mehra and Prescott [1985], the prediction of a negative average term premium signals a critical discrepancy between the risk associated with nominal bonds as perceived by market participants and as captured by the models. Moreover, this term premium puzzle is in some sense a stronger rejection of the underlying asset pricing model than that embodied by the equity premium puzzle. To see this, recall that within the consumption-based asset pricing model, the sign of the risk premium on any asset depends on the sign of the covariance between the marginal utility of consumption and that asset's return. Applying this reasoning to the case of the equity premium suggests that, while the discrepancy in size between the observed equity premium and that generated within the model is troubling, the model's prediction of a positive equity premium implies that the basic payout structure of equity within the model is consistent with that in the data (e. …

The Comovement of US and UK Stock Markets

The Portuguese Equity Risk Premium

PurposeThis paper aims to investigate the performance of various return forecasting variables and methods in Saudi Arabia and Malaysia. The authors document that market excess returns in Saudi Arabia are predicted by changes in oil prices, the dividend yield and inflation, whereas the equity premium in Malaysia is predicted only by the US market excess returns. In both countries, the authors find that the diffusion index is the best forecasting method and stock return predictability is stronger in expansions than in recessions. To interpret the findings, the authors perform two tests. The empirical results suggest irrational pricing in Malaysia and rationally time-varying expected returns in Saudi Arabia.Design/methodology/approachThe authors apply the state-of-the-art in-sample and out-of-sample forecasting techniques to predict stock returns in Saudi Arabia and Malaysia.FindingsThe Saudi equity premium is predicted by oil prices, dividend yield and inflation. The Malaysian equity premium is predicted by the US market excess returns. In both countries, the authors find that the diffusion index is the best forecasting method. In both countries, predictability is stronger in expansions than in recessions. The tests suggest irrational pricing in Malaysia and rationality in Saudi Arabia.Practical implicationsThe empirical results have some practical implications. The fact that stock returns are predictable in Saudi Arabia makes it possible for policymakers to better evaluate future business conditions, and thus to take appropriate decisions regarding economic and monetary policy. In Malaysia, the results of this study have interesting implications for portfolio management. The fact that the Malaysian market seems to be inefficient suggests the presence of strong opportunities for sophisticated investors, such as hedge and mutual funds.Originality/valueFirst, there are no papers that have studied the return predictability in Saudi Arabia in spite of its importance as an emerging market. Second, the methods that combine all predictive variables such as the diffusion index or the kitchen sink methods have not been implemented in emerging markets. Third, this paper is the first study to deal with time-varying short-horizon predictability in emerging countries.

Limited stock market participation and the equity premium