Model uncertainty and asset return predictability: an application of Bayesian model averaging

We investigate model uncertainty associated with predictive regressions employed in asset return forecasting research. We use simple combination and Bayesian model averaging (BMA) techniques to compare the performance of these forecasting approaches in short-vs. long-run horizons of S&P500 monthly excess returns. Simple averaging involves an equally-weighted averaging of the forecasts from alternative combinations of factors used in the predictive regressions, whereas BMA involves computing the predictive probability that each model is the true model and uses these predictive probabilities as weights in combing the forecasts from different models. From a given set of multiple factors, we evaluate all possible pricing models to the extent, which they describe the data as dictated by the posterior model probabilities. We find that, while simple averaging compares quite favorably to forecasts derived from a random walk model with drift (using a 10-year out-of-sample iterative period), BMA outperforms simple averaging in longer compared to shorter forecast horizons. Moreover, we find further evidence of the latter when the predictive Bayesian model includes shorter, rather than longer lags of the predictive factors. An interesting outcome of this study tends to illustrate the power of BMA in suppressing model uncertainty through model as well as parameter shrinkage, especially when applied to longer predictive horizons.     

Comparing linear and nonlinear forecasts for stock returns

We compare the out-of-sample performance of monthly returns forecasts for two indices, namely the Dow Jones (DJ) and the Financial Times (FT) indices. A linear and a nonlinear artificial neural network (ANN) model are used to generate the out-of-sample competing forecasts for monthly returns. Stationary transformations of dividends and trading volume are considered as fundamental explanatory variables in the linear model and the input variables in the ANN model. The comparison of out-of-sample forecasts is done on the basis of forecast accuracy, using the Diebold and Mariano test [J. Bus. Econ. Stat. 13 (1995) 253.], and forecast encompassing, using the Clements and Hendry approach [J. Forecast. 5 (1998) 559.]. The results suggest that the out-of-sample ANN forecasts are significantly more accurate than linear forecasts of both indices. Furthermore, the ANN forecasts can explain the forecast errors of the linear model for both indices, while the linear model cannot explain the forecast errors of the ANN in either of the two indices. Overall, the results indicate that the inclusion of nonlinear terms in the relation between stock returns and fundamentals is important in out-of-sample forecasting. This conclusion is consistent with the view that the relation between stock returns and fundamentals is nonlinear.     

South African stock return predictability in the context data mining: The role of financial variables and international stock returns

In this paper, we examine the predictive ability, both in-sample and the out-of-sample, for South African stock returns using a number of financial variables, based on monthly data with an in-sample period covering 1990:01 to 1996:12 and the out-of-sample period of 1997:01 to 2010:04. We use the t-statistic corresponding to the slope coefficient in a predictive regression model for in-sample predictions, while for the out-of-sample, the MSE-F and the ENC-NEW tests statistics with good power properties were utilised. To guard against data mining, a bootstrap procedure was employed for calculating the critical values of both the in-sample and out-of-sample test statistics. Furthermore, we use a procedure that combines in-sample general-to-specific model selection with out-of-sample tests of predictive ability to further analyse the predictive power of each financial variable. Our results show that, for the in-sample test statistic, only the stock returns for our major trading partners have predictive power at certain short and long run horizons. For the out-of-sample tests, the Treasury bill rate and the term spread together with the stock returns for our major trading partners show predictive power both at short and long run horizons. When accounting for data mining, the maximal out-of-sample test statistics become insignificant from 6-months onward suggesting that the evidence of the out-of-sample predictability at longer horizons is due to data mining. The general-to-specific model shows that valuation ratios contain very useful information that explains the behaviour of stock returns, despite their inability to predict stock return at any horizon. The model also highlights the role of multiple variables in predicting stock returns at medium- to long run horizons.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Drivers of expected returns in Istanbul stock exchange: Fama–French factors and coskewness

We investigate the impact of coskewness on the variation of portfolio excess returns in Istanbul Stock Exchange (ISE) over the period July 1999 to December 2005. We form portfolios according to size, industry, size and book-to-market ratio, momentum and coskewness and compare alternative asset pricing models. The traditional capital asset pricing model (CAPM) and the three-factor model of Fama and French are tested in the multivariate testing procedure of Gibbons–Ross–Shanken (1989). Coskewness is introduced as a fourth factor and its incremental effect over CAPM and Fama–French factors is examined both in multivariate tests and in cross-sectional regressions. The findings reveal that coskewness is able to explain the size premium in ISE. Hence, the basic two-moment CAPM without the coskewness factor would underestimate the expected return of size portfolios. Multivariate test results indicate that coskewness reduces the pricing bias, albeit insignificantly. Cross-sectional analysis uncovers that coskewness has a significant additional explanatory power over CAPM, especially for size and industry portfolios. However, coskewness does not have a significant incremental explanatory power over Fama–French factors in ISE.     

International sign predictability of stock returns: The role of the United States

We study the directional predictability of monthly excess stock market returns in the U.S. and ten other markets using univariate and bivariate binary response models. We introduce a new bivariate (two-equation) probit model that allows us to examine the benefits of predicting the signs of returns jointly, focusing on the predictive power originating from the U.S. to foreign markets. Our in-sample and out-of-sample forecasting results indicate superior predictive performance of the new model over competing univariate binary response models, and conventional predictive regressions, by statistical measures and market timing performance. This highlights the importance of predictive information from the U.S. to the other markets providing also practical improvement in investors' market timing decisions.     

The pricing of time-varying beta

We generalize an asset pricing model based on the Arbitrage Pricing Theory (APT) allowing beta to be time-varying. Making beta a random variable adds flexibility to the model because permits a non-linear relation between individual returns and the set of factors, and accounts for the effect of possible omitted variables. We integrate the conditional APT with a general linear stochastic process for beta. We analyze the behavior of the conditional expected return, the conditional variance and conditional covariance of individual asset returns as functions of the conditional moments of beta. On considering time-varying betas we introduce another source of uncertainty (risk) independent of the factors. We need to disentangle if this extra risk is systematic or non-systematic. To this end, we introduce a modified conditional APT model that rationalizes why the time variation of beta may represent extra systematic risk. For a sample of individual stocks, we test the hypothesis of time-varying beta and the feasibility of the modified conditional APT. We present a test for time-varying beta based on the conditional second moments of returns. We find that there is strong evidence against constancy of betas in favor of a random coefficient model, and that the time variation of beta is due to non-systematic behavior of the firms and investors should be able to diversify this risk away.     

资产的理性定价模型和非理性定价模型的比较研究--基于中国股市的实证分析

本文以 1 995年 2月— 2 0 0 2年 6月深沪两市A股上市公司为样本 ,考察和对比三个定价模型———CAPM、三因素模型和特征模型。实证研究发现 :(1 )中国股市存在显著的“账面市值比效应”(BMEffect)和“规模效应”(SIZEEffect) ,但对于小公司则不存在“1月份效应” ;(2 )三因素模型比CAPM能更好地描述股票横截面收益的变化 ;(3 )基于“股票横截面收益是由公司特征决定”的非理性定价理论的特征模型不成立 ,而基于“股票横截面收益是由风险因素决定”的理性定价理论的三因素模型成立。这些发现说明 ,账面市值比和公司规模这二个变量代表的是一种“风险因素” ,并非“特征因素” ,因此中国股票横截面收益的变化取决于风险因素 ,而非特征因素。作者认为 ,导致上述结果的主要原因是中国股市长期的同涨同跌特征。     

Systematic skewness in asset pricing: an empirical examination of the Taiwan stock market

This paper is an empirical study of asset pricing with the systematic skewness in the pricing model. We adopt the Fama-French three-factor model, which incorporates the firm-size and book-to-market ratio in asset pricing as the base case, and then includes the skewness factor used by Harvey and Siddique in the pricing model. The evidence shows that systematic skewness is significant and might be important in asset pricing when portfolios are formed by industry, firm-size, book-to-market, or momentum strategies. When portfolios are constructed by momentum or coskewness strategies, lower momentum, or lower coskewness portfolios exhibit higher skewness and higher kurtosis. When portfolios are grouped by excess returns, it is seen that the average excess return is positively correlated with size and coskewness. Thus the systematic skewness is closely related to firm size. And the relationship between systematic skewness and excess return is obscured by the reverse firm-size effect.     

Country and industry factors in tests of Capital Asset Pricing Models for partially integrated emerging markets

Existing literature has produced broadly inconclusive evidence about the asset pricing model which best fits partially integrated markets. This paper examines whether industry and country factors are independent factors helping to determine returns in emerging stock markets, or are derived from the stocks’ risk-return characteristics. We link the country-industry decomposition framework to the local and the Global CAPM in a new and more direct way. The results show that country factors are additional independent sources of cross-sectional variation in stock returns before 1996 particularly under the Global CAPM. After 1996, the results suggest partial integration: industry and country factors are both additional independent determinants of cross-sectional variations in stock returns. .     

Sentiment dynamics and stock returns: the case of the German stock market

We use weekly survey data on short-term and medium-term sentiment of German investors in order to study the causal relationship between investors’ mood and subsequent stock price changes. In contrast to extant literature for other countries, a trivariate vector autoregression for short-run sentiment, medium-run sentiment, and stock index returns allows to reject exogeneity of returns. Depending on the chosen VAR specification, returns are found to either follow a feedback process caused by medium-run sentiment, or returns form a simultaneous systems together with the two sentiment measures. An out-of-sample forecasting experiment on the base of estimated subset VAR models shows significant exploitable linear structure. However, trading experiments do not yield convincing evidence of significant economic gains from the VAR forecasts, and it appears that predictability of returns from sentiment decreases during the recent market gyrations.     

The predictability of aggregate Japanese stock returns: Implications of dividend yield

This paper explores the implications of a dividend yield model for predicting aggregate Japanese stock returns using long time-series data from 1949 to 2009. In addition to one-period return tests, we conduct statistical tests based on dividend growth forecasts and long-horizon return forecasts implied by one-year regressions to provide significant evidence for the predictability of aggregate Japanese stock returns. Our findings therefore strengthen the international evidence for the role of dividend yield in predicting returns. However, we find that direct long-horizon regressions are not a powerful way of testing the null hypothesis of no return predictability. Moreover, we find that current cash flow is a more important driving force than future cash flow in the stock market fluctuations, although the dominant force is attributed to expected future returns.     

CAPM and the changing distribution of historical returns

Three statistical tests reject the capital asset pricing model (CAPM) assumption of a constant distribution of returns over time, for three different aggregate stock indices over various holding periods since 1950. These findings further undermine the reliability of CAPM applied to historical data for choosing optimal portfolio allocations.     

The capital asset pricing model in economic perspective

The capital asset pricing model (CAPM) is theoretically incomplete in its demand-side focus, risk-averse investors and internally inconsistent homogeneous beliefs; is not conclusively supported empirically; and yet it legitimizes a notion that investors can earn higher returns by bearing undiversifiable risk. Our article does not merely extend the CAPM with more realistic assumptions, it completes its original framework by including (1) risk-taking investors in the investor population, (2) investors who can have heterogeneous expectations or beliefs – an overlooked but required condition for the CAPM to be an internally consistent and meaningful model of competitive financial asset pricing under uncertainty and (3) a positive-sloped short-run supply curve based on a reasonable interpretation of the nature of financial asset trade. Upon a complete economic interpretation, it is shown that the equilibrium (systematic) risk-rate of return relationship depends on whose aggregate trading activity dominates, risk-averse or risk-taking investors’. There is no universal, or even general, positive relationship between systematic risk and rate of return. This has far-reaching implications for investors and investment advisors who serve them.     

Rolling Regression Analysis of the Pástor-Stambaugh Model: Evidence from Robust Instrumental Variables

The capital asset pricing model (CAPM), Fama-French (FF), and Pástor-Stambaugh (PS) factor models are examined using a new dynamic rolling regression version of the generalized method of moments (GMM) method. This rolling regression framework not only allows us to investigate phases of the business cycle, but also permits regression estimates to vary through time due to changes in the development and efficiency of the sectors. The principal reasons for using the dynamic GMM with robust instruments is that some of these factors are measured with errors and the disturbances may be non-spherical. The CAPM appears as the most parsimonious model to explain the FF sector returns. Furthermore, the rolling GMM approach is clearly more sensitive to dynamic financial episodes than the ordinary least squares approach. In particular, liquidity has some anticipatory power, as it is able to forecast the 2007–2009 crises with heightened volatility starting in late 2005.     

Improving the predictability of the oil–US stock nexus: The role of macroeconomic variables

In this study, we revisit the oil–stock nexus by accounting for the role of macroeconomic variables and testing their in-sample and out-of-sample predictive powers. We follow the approaches of Lewellen (2004) and Westerlund and Narayan (2015), which were formulated into a linear multi-predictive form by Makin et al. (2014) and Salisu et al. (2018) and a nonlinear multi-predictive model by Salisu and Isah (2018). Thereafter, we extend the multi-predictive model to account for structural breaks and asymmetries. Our analyses are conducted on aggregate and sectoral stock price indexes for the US stock market. Our proposed predictive model, which accounts for macroeconomic variables, outperforms the oil-based single-factor variant as well as the constant returns (historical average) model for both in-sample and out-of-sample forecasts. We find that it is important to account for structural breaks in our proposed predictive model, although asymmetries do not seem to improve predictability. In addition, we show that it is important to pre-test the predictors for persistence, endogeneity, and conditional heteroscedasticity, particularly when modeling with high-frequency series. Our results are robust to different forecast measures and forecast horizons and are useful for making effective hedging decisions in the US stock market.     

Performance of value- and size-based strategies in the Italian stock market

This paper investigates the performance of size- and value-based strategies in the Italian stock market in the period 2000–2018. Previous research argued the impossibility to define properly value-sorted portfolios due to the inaccuracy of book-to-market ratios available for Italian listed stocks. Using more accurate data, we implement portfolios sorting based on value and growth stocks, to assess the relevance of the value factor in the Italian stock market. We find that the capital asset pricing model fails to explain the cross-section of returns on the different strategies while the Fama and French three-factor model provides a better fit. The results show that all three factors are significant in explaining Italian stock returns during the sample period. Unlike previous studies, which either found no value effect at all or no clear-cut results when testing the book-to-market variable, we find that the value factor is statistically significant and the associated risk premium is of a considerable size.     

QARMA-Beta-t-EGARCH versus ARMA-GARCH: an application to S&P 500

Statistical performance and out-of-sample forecast precision of ARMA-GARCH and QARMA-Beta-t-EGARCH are compared. We study daily returns on the Standard and Poor’s 500 (S&P 500) index and a random sample of 50 stocks from the S&P 500 for period May 2006 to July 2010. Competing models are estimated for periods before and during the US financial crisis of 2008. Out-of-sample point and density forecasts are performed for periods during and after the US financial crisis. The results provide evidence of the superior in-sample statistical and out-of-sample predictive performance of QARMA-Beta-t-EGARCH.     

On the predictive power of ARJI volatility forecasts for Bitcoin

Motivated by the recent literature on cryptocurrency volatility dynamics, this paper adopts the ARJI, GARCH, EGARCH, and CGARCH models to explore their capabilities to make out-of-sample volatility forecasts for Bitcoin returns over a daily horizon from 2013 to 2018. The empirical results indicate that the ARJI jump model can cope with the extreme price movements of Bitcoin, showing comparatively superior in-sample goodness-of-fit, as well as out-of-sample predictive performance. However, due to the excessive volatility swings on the cryptocurrency market, the realized volatility of Bitcoin prices is only marginally explained by the GARCH genre of employed models.     

Can the Consumption Capital Asset Pricing Model Account for Traders' Expected Currency Returns?

This study uses survey data on traders' exchange rate forecasts to test whether their expected excess returns are related to the covariance between the exchange rate and consumption; as predicted by the consumption capital asset pricing model (CCAPM). The covariance is measured through the novel use of rolling windows of the realized covariance (both forward and backward looking) and testing is conducted with the cointegrated VAR. The model is able to account for expected returns with more plausible degrees of risk aversion, but only when using sufficiently long, backward‐looking measures of the covariance. This suggests that market participants assess risk, in part, based upon the pro‐cyclicality of returns, and infer it from experience in the recent past. There is also evidence that inclusion of the real exchange rate improves the plausibility of the estimates and the model fit.