Prediction of stocks: a new way to look at it.

While the traditional $R^{2}$ value is useful to evaluate the quality of a fit, it does not work when it comes to evaluating the predictive power of estimated financial models in finite samples. In this paper we introduce a validated $R_{V}^{2}$ value that is Taylor made for prediction. Based on data from the Danish stock market, using this measure we find that the dividend-price ratio has good predictive power for time horizons between one year and five years. We explain how the $R_{S}^{2}$ s for different time horizons could be compared, respectively, how they must not be interpreted. For our data we can conclude that the quality of prediction is almost the same for the five different time horizons. This is in contradiction to earlier studies based on the traditional $R^{2}$ value, where it has been argued that the predictive power increases with the time horizon up to a horizon of about five or six years. Furthermore, we find that while inflation and interest rate do not add to the predictive power of the dividend-price ratio then last years excess stock return does

The Abnormal Performance of Bond Returns

This article studies the link between the predictability of futures returns and the business cycle. Modelling the relationship between the variation through time in expected futures returns and economic activity should give us some insight as to whether the predictable movements in futures returns result from rational variation in the returns required by investors over time. With this in mind, the paper investigates three hypotheses that are consistent with weak-form market efficiency. First, it tests whether the time-varying risk premia identified in futures markets move in tandem. Second, it examines if the information variables predict futures returns because of their ability to proxy for change in the business cycle. Third, it analyses whether the pattern of forecastability in futures markets is consistent with the evidence from the stock and bond markets and with traditional theoretical explanations of the trade-off between risk and expected returns.Predictability, Business cycle, countercyclical and procyclical futures

Conditional variance forecasts for long-term stock returns

In this paper, we apply machine learning to forecast the conditional variance of long-term stock returns measured in excess of different benchmarks, considering the short- and long-term interest rate, the earnings-by-price ratio, and the inflation rate. In particular, we apply in a two-step procedure a fully nonparametric local-linear smoother and choose the set of covariates as well as the smoothing parameters via cross-validation. We find that volatility forecastability is much less important at longer horizons regardless of the chosen model and that the homoscedastic historical average of the squared return prediction errors gives an adequate approximation of the unobserved realised conditional variance for both the one-year and five-year horizon

Stock and Bond Returns with Moody Investors

We present a tractable, linear model for the simultaneous pricing of stock and bond returns that incorporates stochastic risk aversion. In this model, analytic solutions for endogenous stock and bond prices and returns are readily calculated. After estimating the parameters of the model by the general method of moments, we investigate a series of classic puzzles of the empirical asset pricing literature. In particular, our model is shown to jointly accommodate the mean and volatility of equity and long term bond risk premia as well as salient features of the nominal short rate, the dividend yield, and the term spread. Also, the model matches the evidence for predictability of excess stock and bond returns. However, the stock-bond return correlation implied by the model is somewhat higher than in the data.

A parsimonious macroeconomic model for asset pricing

I study asset prices in a two-agent macroeconomic model with two key features: limited stock market participation and heterogeneity in the elasticity of intertemporal substitution in consumption (EIS). The model is consistent with some prominent features of asset prices, such as a high equity premium; relatively smooth interest rates; procyclical stock prices; and countercyclical variation in the equity premium, its volatility, and in the Sharpe ratio. In this model, the risk-free asset market plays a central role by allowing non-stockholders (with low EIS) to smooth the fluctuations in their labor income. This process concentrates non-stockholders' labor income risk among a small group of stockholders, who then demand a high premium for bearing the aggregate equity risk. Furthermore, this mechanism is consistent with the very small share of aggregate wealth held by non-stockholders in the US data, which has proved problematic for previous models with limited participation. I show that this large wealth inequality is also important for the model's ability to generate a countercyclical equity premium. When it comes to business cycle performance the model's progress has been more limited: consumption is still too volatile compared to the data, whereas investment is still too smooth. These are important areas for potential improvement in this framework.Wealth ; Stock market

Risk, Uncertainty and Asset Prices

We identify the relative importance of changes in the conditional variance of fundamentals (which we call %u201Cuncertainty%u201D) and changes in risk aversion (%u201Crisk%u201D for short) in the determination of the term structure, equity prices and risk premiums. Theoretically, we introduce persistent time-varying uncertainty about the fundamentals in an external habit model. The model matches the dynamics of dividend and consumption growth, including their volatility dynamics and many salient asset market phenomena. While the variation in dividend yields and the equity risk premium is primarily driven by risk, uncertainty plays a large role in the term structure and is the driver of counter-cyclical volatility of asset returns.

Dividend predictability around the world

© Michael G. Foster School of Business, University of Washington 2015. We show that dividend-growth predictability by the dividend yield is the rule rather than the exception in global equity markets. Dividend predictability is weaker, however, in large and developed markets where dividends are smoothed more, the typical firm is large, and volatility is lower. Our findings suggest that the apparent lack of dividend predictability in the United States does not uniformly extend to other countries. Rather, cross-country patterns in dividend predictability are driven by differences in firm characteristics and the extent to which dividends are smoothed

Expected Returns and Expected Dividend Growth

We investigate a consumption-based present value relation that is a function of future dividend growth. Using data on aggregate consumption and measures of the dividend payments from aggregate wealth, we show that changing forecasts of dividend growth make an important contribution to fluctuations in the U.S. stock market, despite the failure of the dividend-price ratio to uncover such variation. In addition, these dividend forecasts are found to covary with changing forecasts of excess stock returns. The variation in expected dividend growth we uncover is positively correlated with changing forecasts of excess returns and occurs at business cycle frequencies, those ranging from one to six years. Because positively correlated fluctuations in expected dividend growth and expected returns have offsetting affects on the log dividend-price ratio, the results imply that both the market risk-premium and expected dividend growth vary considerably more than what can be revealed using the log dividend-price ratio alone as a predictive variable.

Asset pricing with adaptive learning

We study the extent to which self-referential adaptive learning can explain stylized asset pricing facts in a general equilibrium framework. In particular, we analyze the effects of recursive least squares and constant gain algorithms in a production economy and a Lucas type endowment economy. We find that recursive least squares learning has almost no effects on asset price behavior, for either model, since the algorithm converges fast to rational expectations. At the other end, constant gain learning may sometimes contribute towards explaining the stock price volatility and the predictability of excess returns in the endowment economy. However, in the production economy the effects of constant gain learning are mitigated by the persistence induced by capital accumulation. We conclude that, contrary to popular belief, standard self-referential learning alone cannot resolve the asset pricing puzzles observed in the dataAsset pricing, adaptive learning, excess returns, predictability.