Oil price increases and the predictability of equity premium

Journal of Banking and Finance 102 (2019) 43–58

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Journal of Banking and Finance journal homepage: www.elsevier.com/locate/jbf

Oil price increases and the predictability of equity premiumR Yudong Wang a, Zhiyuan Pan b,∗, Li Liu c, Chongfeng Wu d a

School of Economics and Management, Nanjing University of Science and Technology, Xiaolingwei 200, Xuanwu District, Nanjing 210094, China Institute of Chinese Financial Studies, Southwestern University of Finance and Economics; Collaborative Innovation Center of Financial Security, Liutai Avenue 555, Wenjiang District, Chengdu 611130, China c School of Finance, Nanjing Audit University, West Yushan Road 86, Pukou District, Nanjing 211815, China d Antai College of Economics and Management, Shanghai Jiao Tong University, China b

a r t i c l e

i n f o

Article history: Received 16 June 2018 Accepted 10 March 2019 Available online 12 March 2019 JEL classification: C11 C22 G11 G12

a b s t r a c t We show that increases in oil prices, rather than changes in oil prices, can predict stock returns. The revealed stock return predictability is both statistically and economically significant. The forecasting performance of oil price increases is not affected by changes in the choice of subsample, a considerable advantage over other popular predictors. We obtain greater forecasting gains by adding oil price increases as an additional predictor to univariate macro models. This forecasting improvement is also present when using multivariate information methods. The success of oil-macro models in forecasting stock returns is robust to a large battery of robustness tests. Oil price increases predict stock returns by affecting future industrial production and discount rates. © 2019 Elsevier B.V. All rights reserved.

Keywords: Oil price increases Stock returns Out-of-sample predictability Forecast combination Portfolio

1. Introduction Stock return predictability is of great interest to academics because it has important implications for topics such as asset pricing and risk management. Many studies report the predictive ability of some variables for stock returns. These predictors include dividend ratios (Fama and French, 1988, 1989; Goyal and Welch, 20 03; Lewellen, 20 04), stock variances (Guo, 20 06; Ludvigson and Ng, 20 07), interest rates (Fama and Schwert, 1977; Campbell, 1987; Ang and Bekaert, 2007), inflation (Campbell and Vuolteenaho, 2004) and the consumption-wealth ratio (Lettau and Ludvigson, 2001). However, an influential paper

R This work was supported by the Chinese National Science Foundation through grant numbers 71501095 and 71722015 (Yudong Wang), 71601161 (Zhiyuan Pan), 71771124 (Li Liu), 71320107002 and 71790592 (Chongfeng Wu) the National Social Science Fund of China through grant number 18VSJ073 (Zhiyuan Pan), and the State Scholarship Fund organized by the China Scholarship Council (CSC) through grant number 201806985006 (Zhiyuan Pan). ∗ Corresponding author. E-mail addresses: [email protected] (Y. Wang), [email protected] (Z. Pan), [email protected] (L. Liu), [email protected] (C. Wu).

https://doi.org/10.1016/j.jbankfin.2019.03.009 0378-4266/© 2019 Elsevier B.V. All rights reserved.

by Goyal and Welch (2008)1 shows that it is difficult to find a predictor that can predict stock returns out of sample. Recent studies propose several new return predictors, including short interest (Rapach, Ringgenberg and Zhou, 2016), variance risk premia (Bollerslev, Tauchen and Zhou, 2009), technical indicators (Neely, Rapach, Tu and Zhou, 2014), news-implied volatility (Manela and Moreira, 2017) and aligned investor sentiment (Huang, Jiang, Tu and Zhou, 2015). In this paper, we contribute to the literature by finding that a new predictor reflecting oil price increases has strong predictive content for monthly stock returns both in and out of sample. There are three reasons explaining our finding of return predictability by oil price increases. First, many macroeconomic papers document the important impacts of oil price changes on the real economy (Hamilton, 1983, 1996; Kilian, 2009). According to Campbell and Cochrane (1999) and Cochrane (2007), investors are more risk averse when economic conditions worsen and they demand higher risk premia. A number of studies also documents that the predictable component of stock returns can be related to

1 This paper won the Michael Brennan Award for Best Paper from the Review of Financial Studies in 2008.

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business cycle (e.g., Fama and French, 1989; Breen, Glosten and Jagannathan, 1990). Therefore, oil price increases could predict stock returns in the way that they change economic conditions, which is an important source of return predictability. Second, oil price changes influence the determinants of stock returns, including stock volatility (Arouri, Jouini and Nguyen, 2011; Schwert, 1989), interest rates (Bernanke, Gertler, Watson, Sims and Friedman, 1997; Bodenstein, Guerrieri and Kilian, 2012; Hamilton and Herrera, 2004), cash flows (Jones and Kaul, 1996) and inflation (Kilian, 2009). In this sense, oil prices contain some of the predictive information regarding some components of stock returns. Our empirical results also suggest that oil price increases affect future stock returns through their effects on the discount rate. Third, the investor underreaction hypothesis can also explain the predictive ability of oil price information for stock returns (Narayan and Sharma, 2011). Griffin and Tversky (1992) suggest that individuals might underreact to intermittent news, but overreact to a prolonged record of salient performance. This causes the fact that market investors underreact to new information in the short-term and overreact to new information in the long-term (Barberis, Shleifer and Vishny, 1998; Daniel, Hirshleifer and Subrahmanyam, 1998; Hong and Stein, 1999). Narayan and Sharma (2011) point out that as the public information concerned by investors, oil prices are observed in real time, leading to undereaction in financial markets. We use oil price increases to conduct a forecasting exercise for January 1927 through December 2016. The motivation for using price increases instead of price changes comes from Mork (1989), who finds that the effects of oil shocks on the real economy are significant when oil prices increase but insignificant when oil prices drop. However, Kilian and Vigfusson (2011a,b) fail to find this asymmetry in the relationship between oil prices and GDP. Charfeddine et al. (2018) find that the oil price increase measure of Mork (1989) does not capture the oil-GDP relationship. Herrera et al. (2011) pay close attention to the linkage between oil prices and U.S. industrial production because asymmetries are more likely to be apparent in industrial production data than in real GDP data. For example, if oil price changes lead to a costly reallocation of capital and labor, concentrating on real aggregate GDP might obscure the nature of the reallocative effect (Bresnahan and Ramey, 1993; Davis and Haltiwanger, 2001). Herrera et al. (2011) find strong evidence of an asymmetric relationship at the disaggregate level, especially for energy-related industries. Herrera et al. (2015) reject the null hypothesis of symmetry in the response to a one standard deviation change for G7 countries when using oil price increases, although they find little evidence of an asymmetry in most OECD countries. Because industries lead the stock market according to the gradual information diffusion hypothesis (Hong, Torous and Valkanov, 2007), we expect an asymmetry in the predictive relationship between oil price changes and aggregate market returns. Following Mork (1989), we construct the variable asymmetric oil return (AOR) that reflects oil price increases by truncating changes in oil prices at zero2 We find that this truncated variable significantly predicts stock returns in the full sample, with the in-sample R2 of the univariate AOR model greater than that of any univariate model using the popular predictors suggested by Goyal and Welch (2008). The predictive content of AOR does not overlap with other popular predictors.

2 For robustness, we use the other three measures capturing oil price increases and also find the existence of significant return predictability. For more details, one can see Section 6.2.

We perform out-of-sample analysis by evaluating the recursive forecasts between 1947 and 2016. The Sharpe ratio constraint, as defined by Pettenuzzo et al. (2014), is applied to our predictive regressions to improve return forecasts. We find that the univariate AOR model leads to an out-of-sample R2 (R2OoS ) of 0.361%, which is statistically significant at the 5% level. In terms of economic predictability, the univariate AOR model leads to CER gains of 57.2 basis points. The AOR model outperforms the benchmark model in the two subsamples of 1947 to 1983 and 1984 to 2016, whereas no model using a popular predictor achieves both economic and statistical forecasting gains over these two subperiods. Furthermore, we find that adding AOR to existing univariate macro models as an additional predictor can improve forecasting performance for all 14 cases. The average R2OoS improves from 0.219% to 0.504% after the incorporation of oil price increases into the predictive models. On average, the oil-macro bivariate models improve upon the univariate models by increasing the CER gains from 47.7 bps to 84.0 bps. Not surprisingly, there is quite a large body of literature on the predictive relationship between oil and stock prices (e.g., Kilian and Park, 2009; Sim and Zhou, 2015; Narayan and Gupta, 2015; Sadorsky, 1999). Smyth and Narayan (2018) perform a comprehensive literature review on oil prices and stock returns. They point out that one limitation of existing studies is that they do not clarify the practical implications of the statistical relationship between oil prices and stock returns. In the absence of this type of analysis, investors and policy makers do not know how useful oil information is. We address this limitation by explicitly showing how using oil price increases improves portfolio performance. Notably, Driesprong et al. (2008) find that oil prices strongly predict future stock returns in sample. Narayan and Sharma (2011) find the strong in-sample evidence that lagged oil price affects firm returns (i.e., in-sample predictability). However, it is well known that good in-sample performance does not imply good out-of-sample performance because of reasons such as estimation errors and model uncertainty (Avramov, 2002; Dangl and Halling, 2012; DeMiguel, Garlappi and Uppal, 2007). We contribute to the literature by revealing the out-of-sample statistical and economic predictability of stock returns using information on oil prices. Furthermore, we show that increases in oil prices, rather than changes in oil prices as commonly used in the literature, successfully predict stock returns. Chiang et al. (2015) estimate the latent oil factors from price information for stock and derivative markets. The authors find that these factors are important in explaining the cross-sectional behavior of asset prices. In contrast, we explicitly show the predictive relationship between oil price increases and aggregate market returns. Our work is closely related to that of Chiang and Hughen (2017), who explore stock return predictability by exploiting the cross-section of oil futures prices. They find strong evidence that the curvature factor of the oil futures curve predicts stock returns both in and out of sample. The curvature factor is the linear combination of oil futures returns at four maturities. In comparison with this curvature factor, the oil price increase measure we use is easier to observe in real time. Chiang and Hughen (2017) use oil futures data starting from 1983, when such data first became available. We improve on their work by using spot data and extending the sample period back to 1927. This makes the forecasting performance of our oil variable comparable with popular predictors that perform better during the earlier period (Goyal and Welch, 2008). Complementing Chiang and Hughen (2017), we find that using oil and economic information together generates more accurate return forecasts than using one type of information only. The improvement in return predictability from incorporating information on oil prices is also found when using

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the forecast combinations methods that have been demonstrated to work well in the literature (Rapach, Strauss and Zhou, 2010). Broadly, our work is related to the literature on the predictive relationship between commodity and financial asset prices. Chen et al. (2010) find that the exchange rates of currencies in major commodity-exporting countries predict the prices of the corresponding commodities but that commodity prices do not predict exchange rates. Ferraro et al. (2015) find evidence that oil price changes forecast the exchange rate of the Canadian dollar at a daily frequency but that the predictability disappears at a monthly frequency. We contribute to this literature by finding that the prices of a global commodity (crude oil) have significant predictive content for the returns of a typical financial asset (stock index). Jacobsen et al. (2018) find that the price movements of industrial metals such as copper and aluminum predict stock returns between 2001 and 2013. We complement their work by extending the data sample to 1927. Furthermore, we find that combining commodity prices and popular macro information leads to more accurate return forecasts than using one type of information alone. The remainder of this paper is organized as follows. Section 2 describes the data. Section 3 gives the results for in-sample predictive analysis. Section 4 reports out-of-sample forecasting results. We perform a series of extensions and robustness tests in Section 5. Section 6 discusses the implications of our results. The last section concludes the paper. 2. Data 2.1. Stock returns We forecast the returns of the S&P 500 index, including dividends, in excess of the risk-free rate. The return of the 3-month U.S. Treasury bill is taken as the risk-free rate. 2.2. Oil price data Crude oil plays an important role in the modern economy. The prices of three oils are always taken as the benchmark for world oil pricing. These are West Texas Intermediate (WTI) crude oil, Brent oil and Dubai oil. The spot price for WTI, which is traded in Cushing, Oklahoma, is the benchmark for domestic oil pricing in the U.S. and is closely linked to the U.S. economy. The refiner’s acquisition cost for imported crude oil (RAC), which is used in empirical macroeconomic papers on oil price shocks (Kilian, 2009; Kilian and Park, 2009), is also a good proxy for oil price fluctuations in global oil markets. However, the RAC price data are published with one to two months lags. Therefore, it is not possible to use RAC prices as a predictor of stock returns because portfolio allocations based on return forecasts are made in real time. Furthermore, monthly Brent, Dubai and RAC prices are unavailable before 1973, whereas WTI oil price can be obtained as early as 1875. To make the comparison with the popular predictors of stock returns suggested by Goyal and Welch (2008), we select WTI price data from December 1926 through December 2016 because most popular predictors begin after 1927. Our data are collected from Global Financial Data.3 Fig. 1 plots the WTI oil prices over the NBER-dated business cycles. Oil prices peak at the end of economic expansions or the beginning of economic recessions. Before 9 out of 15 recessions, oil price had experienced meaningful increases during a period of time. After the beginning of these recessions, oil price displayed a decreasing pattern and touched the local bottoms at the time close to the economic business troughs. Clearly, oil prices are closely linked to the real economy. This motivates us to investigate the

3

http://www.globalfinancialdata.com/.

45

ability of oil price changes to predict stock returns because the literature documents that stock returns depend on economic conditions (Campbell and Cochrane, 1999; Cochrane, 2007). We use an asymmetric oil return measure to predict stock returns, as suggested by Mork (1989). The motivation to use an asymmetric measure instead of the original return values comes from Mork (1989), who shows that the predictive relationship between oil price changes and the macroeconomic variables are asymmetric. Specifically, he shows that the economic responses to oil shocks are significant when oil prices increase but that this significance disappears when oil prices decrease. Asymmetric oil price returns (AOR) are obtained by applying a simple truncation method to the log differences: + oil rt,oil = max(log( poil t ) − log ( pt−1 ), 0 ).

(1)

Because the first observation of oil prices is not used when computing the log difference, we have oil price increase data from January 1927. As a robustness check, we also consider alternative measures of oil price increases in the empirical analysis. 2.3. Traditional predictors To relate our findings to the literature on forecasting stock returns, we compare the predictive ability of our oil variable to the predictive abilities of the 14 popular predictors suggested by Goyal and Welch (2008), the data for which are available at the website of Amit Goyal4 The brief descriptions of these predictors and the corresponding predicted sign for stock returns are listed in Table 1. The data for these popular predictors begin in January 1927, consistent with Goyal and Welch (2008), and are updated until December 2016. Following the literature (Campbell and Thompson, 2008; Dangl and Halling, 2012; Neely, Rapach, Tu and Zhou, 2014), we use monthly data. Kilian and Vigfusson (2011a,b) do not find an asymmetry in the oil-economy relationship using lower frequency data of GDP. As a result, we have a total of 1080 observations for each series. 3. Full-sample estimation results To examine stock return predictability, we use a standard univariate predictive regression to examine stock return predictability:

rt+1 = α + β xt + t+1 ,

for t = 1, 2, · · · , T − 1

(2)

where xt is a predictor variable for excess stock returns rt+1 (e.g., asymmetric oil returns or a popular predictor) and  t is the error term, which is assumed to be independent and identically distributed. The null hypothesis of no predictability by the predictor of interest for stock returns can be examined using the heteroskedasticity consistent t-statistic based on the NeweyWest standard errors. We execute one-sided tests for H0 : β ≥ 0 against the alternative H1 : β < 0 for AOR and four popular predictors: NTIS, TBL, LTY and INFL. For the remaining (Goyal and Welch, 2008) predictors, we use the null H0 : β ≤ 0 and the alternative hypothesis H1 : β > 0. Table 2 reports the in-sample estimation results for the predictive regressions, with all predictors standardized. We find that the β coefficients for 5 of the 14 popular predictors (EP, BM, NTIS, TBL and LTR) are significant. The β for AOR is significantly negative, consistent with the results of Driesprong et al. (2008). A standard deviation increase in this month’s AOR leads to a 5.277 decrease in next month’s excess stock returns in annualized value. This coefficient is also greater in magnitude than the coefficient for any 4

http://www.hec.unil.ch/agoyal.

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Fig. 1. This figure plots the log prices of WTI oil. “REC” denotes the NBER-dated economic recession period (shadowed areas). “Oil” is WTI oil price. Sample period: January 1927-December 2016. Table 1 Popular predictors for stock returns. Name

Abbreviation

Brief description

Predicted sign for stock returns

Dividend-price ratio Dividend yield Earning-price ratio Dividend-payout ratio Stock variance Book-to-market ratio

DP DY EP DE SVAR BM

Net equity expansion

NTIS

Treasury bill rate Long-term yield Term spread Long-term return Default yield spread Default return spread

TBL LTY TMS LTR DFY DFR

Inflation

INFL

The log of dividends on the S&P 500 Index minus the log of stock prices The log of dividends on the S&P 500 Index minus the log of lagged stock prices The log of earnings on the S&P 500 Index minus the log of stock prices. The difference between DP and EP The sum of squared daily returns on S&P 500 Index The ratio of book value at the end of the previous year divided by the end-of-month market value for the DJIA The ratio of a 12-month moving sum of net equity issues by NYSE-listed stocks to the total end-of-year market capitalization of NYSE stocks The second market rate of the 3-month U.S. Treasury bills The long-term government bond yields The difference between TBL and LTY The returns on long-term government bond The difference between Moody’s BAA- and AAA-rated corporate bond yields The difference between returns on long-term corporate bonds and returns on long-term government bonds The consumer price index (CPI) for all urban consumers

+ + + + + + + + + + -

Notes: This table lists the popular predictors for stock returns suggested by Goyal and Welch (2008). Sample period: January 1927-December 2016.

of the popular predictors. The in-sample R2 for the univariate AOR model is 0.650%, higher than that for any popular predictor model of excess returns. In summary, our results indicate that oil price increases have stronger predictive content for stock returns than popular predictors do. Sadorsky (1999) argues that the OLS estimator’s finite-sample properties can depart substantially from the standard regression setting if the regressor is highly persistent. For robustness, we use the methodology of Johnson (2017) with 10,0 0 0 simulations to obtain the parameters adjusted by the bias described by Sadorsky (1999). The adjusted slope coefficient for AOR is -5.307 and has a p-value of 0.005. Therefore, the revealed predictability of stock returns by AOR is not qualitatively affected by correcting for this possible bias. To investigate whether the predictive information from oil price increases overlaps with that from popular predictors, we consider an alternative regression that includes two predictors:

rt+1 = α +βmaroxt,macro+βoil xt,oil + t+1 ,

for t = 1, 2, · · · , T − 1, (3)

where xt,oil and xt,macro denote asymmetric oil returns and one of the 14 popular predictors, respectively. Intuitively, a significant β oil implies that oil price changes still predict stock returns after controlling for the effect of the macro variable of interest. Table 3 shows the estimation results of Eq. (3). The estimates of β oil are significant at least at the 5% level for all cases. The estimates are close across different models and between −4.642 and −6.205. The in-sample R2 of each bivariate model is also greater than the corresponding R2 of the corresponding univariate model. That is, oil price increases contain quite different predictive information from all popular predictors in our sample. New variables are often proposed to predict stock returns. We should recognize that our AOR variable might not outperform all newly developed predictors. Nevertheless, it is necessary for us to investigate whether the information provided by oil prices and these predictors overlap. If the information from these two sources does not overlap, combining different types of information can still improve forecasting performance (Rapach, Strauss and Zhou, 2010). For this purpose, we use the bivariate regression (3). We consider three newly developed predictors: newsimplied volatility (Manela and Moreira, 2017), short interest

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(Rapach, Ringgenberg and Zhou, 2016) and aligned investor sentiment (Huang, Jiang, Tu and Zhou, 2015). When using these three predictors as the control variable,5 the coefficient estimates for β oil in (3) are −5.491, −3.498 and −3.632 with p-values of 0.008, 0.043 and 0.036, respectively. That is, AOR cannot be replaced by the three predictors suggested by recent studies.

Table 2 In-sample estimation results: Univariate predictive regressions.

DP DY EP DE SVAR BM NTIS TBL LTY LTR TMS DFY DFR INFL AOR

β

t − stat

R2 (%)

2.865 3.502 4.187∗∗ −1.289 −2.693 4.221∗ −4.156∗ −3.117∗ −2.300 2.860∗∗ 2.480 0.740 2.813 −1.358 −5.277∗∗∗

1.079 1.278 1.709 −0.389 −0.586 1.394 −1.552 −1.612 −1.220 1.666 1.278 0.150 0.956 −0.392 −2.347

0.192 0.286 0.409 0.039 0.170 0.416 0.403 0.227 0.124 0.191 0.144 0.013 0.185 0.043 0.650

4. Out-of-sample results This section shows the out-of-sample results of return predictability using our measure of oil price increases. Although we have demonstrated in-sample return predictability, it is wellknown that a good in-sample performance does not guarantee a good out-of-sample performance. We first evaluate the statistical and economic predictability using univariate predictive regressions. Then, we investigate whether the incorporation of oil information is helpful for improving the forecasting performance of popular predictor models.

Notes: This table reports the in-sample estimation results for the univariate predictive regression RT +1 = α + β xt + t+1 , for t = 1, 2, · · · , T − 1, where xt is a predictor variable for excess stock return rt+1 and t+1 is the error term assumed to be independent and identically distributed. All the predictive variables are standardized. The parameter estimates and in-sample R2 in percentage are given. We execute onesided tests for H0 : β ≥ 0 against the alternative H1 : β < 0 for AOR and four popular predictors: NTIS, TBL, LTY and INFL. For the remaining Goyal and Welch (2008) predictors, we use the null H0 : β ≤ 0 and the alternative hypothesis H1 : β > 0. Such test is executed using the heteroskedasticity consistent t-statistic based on the Newey-West method. The asterisks ∗ , ∗∗ and ∗∗∗ denote significance at 10%, 5% and 1% levels, respectively.

4.1. Forecasting methodology We use the recursive estimation window method to produce return forecasts. The observations during the initial M months are used to estimate parameters. The forecasts in the (M + 1)-th month from a given predictor xi,t (i.e., oil or macro predictors) is given by

rˆi,M+1 = αˆ i,M+1 + βˆi,M+1 xi,M ,

Table 3 In-sample estimation results: bivariate predictive regressions.

DP DY EP DE SVAR BM NTIS TBL LTY LTR TMS DFY DFR INFL

1.688 2.351 3.251∗ −1.728 −2.564 3.339 −5.252∗∗ −2.812∗ −1.808 2.620∗ 2.825∗ 0.973 3.136 −1.065

tmacro 0.596 0.794 1.323 −0.491 −0.550 1.066 −1.895 −1.426 −0.938 1.542 1.445 0.198 1.057 −0.306

β oil ∗∗

−4.869 −4.701∗∗ −4.618∗∗ −5.418∗∗ −5.214∗∗ −4.642∗∗ −6.205∗∗∗ −5.109∗∗ −5.103∗∗∗ −5.155∗∗ −5.456∗∗∗ −5.320∗∗∗ −5.463∗∗∗ −5.217∗∗

(4)

where αˆ i,M+1 and βˆi,M+1 are the parameter estimates subject to the Sharpe ratio restriction of Pettenuzzo et al. (2014) (PTV hereafter). PTV argues that reasonable return forecasts should satisfy the condition that the expectation of the annualized Sharpe ratio is larger than 0 but smaller than 1.6 The PTV method performs much better out of sample than either an unrestricted regression or a regression using the Campbell and Thompson (2008) restriction for most variables does. This restriction can be written as

0≤

β macro

47

toil

R2 (%)

−1.964 −1.865 −2.036 −2.317 −2.326 −1.963 −2.658 −2.258 −2.238 −2.278 −2.431 −2.370 −2.419 −2.303

0.712 0.771 0.886 0.719 0.803 0.901 1.273 0.834 0.725 0.810 0.835 0.672 0.878 0.676

Notes: This table reports the in-sample estimation results for the predictive regression with two predictive variables rt+1 = α + βmacro xt,macro + βoil xt,oil + t+1 , for t = 1, 2, · · · , T − 1, where xt,oil and xt,macro denote the asymmetric oil return and one of the 14 popular predictors under consideration. The error term t+1 is assumed to be independent and identically distributed. All the predictive variables are standardized. The parameter estimates and insample R2 in percentage are given. We execute one-sided tests for H0 : β ≥ 0 against the alternative H1 : β < 0 for AOR and four popular predictors: NTIS, TBL, LTY and INFL. For the remaining Goyal and Welch (2008) predictors, we use the null H0 : β ≤ 0 and the alternative hypothesis H1 : β > 0. Such test is executed using the heteroskedasticity consistent t-statistic based on the NeweyWest method. The asterisks ∗ , ∗∗ and ∗∗∗ denote significance at 10%, 5% and 1% levels, respectively.

√ αˆ i,M+1 + βˆi,M+1 xi,M H ≤ 1, σˆ i,M+1

(5)

where H is the number of observations per year (i.e., H = 12 with monthly data). We use the approach of weighted OLS suggested by Johnson (2017) to estimate the parameters under the PTV conM−1 M−1 straint by regressing {rt+1 }t=1 on a constant and {xi,t }t=1 . Similarly, return forecasts in the (M + 2)-th month are given by

rˆi,M+2 = αˆ i,M+2 + βˆi,M+2 xi,M+1 ,

(6)

M on a where αˆ i,M+2 and βˆi,M+2 are obtained by regressing {rt+1 }t=1 M constant and {xi,t }t=1 according to the PTV constraint. Continuing like this, we generate a series of return forecasts for each predictor.

4.2. Statistical predictability 4.2.1. Forecast evaluation A standard approach to evaluating the performance of return forecasts is the out-of-sample R2 (R2OoS ) (Campbell and Thompson, 2008; Ferreira and Santa-Clara, 2011). This measure mirrors the well-known in-sample R2 and is computed as

R2OoS = 1 −

MSP Emodel , MSP Ebench

(7)

5 We use the first-order difference of news-implied volatility, detrended short interest and the original values of aligned investor sentiment. The sample periods are January 1927 to December 2015, January 1973 to December 2015 and July 1965 to December 2015, respectively. 6 Tests that we do not report indicate that the parameter estimates subject to the PTV constraint fluctuate less than the traditional OLS estimates, reducing the volatility of the forecast errors.

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Table 4 Out-of-sample forecasting results of univariate models: R2OoS .

DP DY EP DE SVAR BM NTIS TBL LTY LTR TMS DFY DFR INFL AOR AVERAGE

Panel A: 1947–2016

Panel B: 1947–1983

Panel C: 1984–2016

0.422∗∗ 0.687∗∗∗ 0.461∗∗ −0.358 0.052 0.061 0.021 0.641∗∗∗ 0.759∗∗∗ 0.075 0.252∗ −0.17 0.117 0.044 0.361∗∗ 0.219

1.159∗∗∗ 1.519∗∗∗ 0.211∗ −0.828 −0.074 0.365 0.128 1.368∗∗∗ 1.668∗∗∗ −0.095 0.622∗∗ −0.174 −0.167 0.151∗∗ 0.433∗ 0.418

−0.281 −0.106 0.700∗ 0.091 0.173∗ −0.230 −0.082 −0.053 −0.108 0.238 −0.101 −0.166 0.387 −0.058 0.292∗ 0.029

Notes: This table reports the out-of-sample performance of univariate models. The forecasts rˆt are produced by the model rt+1 = α + β xt + t+1 , where xt is a predictor variable for excess stock return rt+1 . We apply the Sharpe ratio restriction of Pettenuzzo et al. (2014) to each model in the procedure of parameter estimation. The forecast quality is evaluated by the out-of-sample R2 (R2OoS ) defined by the percent reduction of MSPE of the given model relative to the benchmark model of historical mean, given by,

R2OoS = 1 −

MSPEmodel MSPEbench

1 T 1 T 2 2 where MSPEmodel = T −M and MSPEmodel = T −M t=M+1 (rt − rˆt ) t=M+1 (rt − r¯t ) , where rˆt , r¯t and rt are the return forecasts from the model of interest, prevailing mean forecasts and the realized return values, respectively. The full sample period is from January 1927 through December 2016 and the out-of-sample period starts in January 1947 (i.e., M=240). We multiply the R2OoS figure by 100 to denote percentage values. For the positive R2OoS , we measure the statistical significance relative to the prevailing mean model using the Clark and West (2007) test statistic. The 2nd -15th rows show the performance of popular predictors suggested by Goyal and Welch (2008). The 16th row displays the forecasting results of asymmetric oil return (AOR). The last row gives the average R2OoS of popular predictors. The asterisks ∗ , ∗∗ and ∗∗∗ denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.

where MSPEmodel and MSPEbench are the mean squared predictive errors of the model of interest and the benchmark model, respec1 T 2 tively. That is, MSP Emodel = T −M t=M+1 (rt − rˆt ) and MSP Ebench =  T 1 2 ¯ t=M+1 (rt − rt ) , where rt is the realized monthly return. The T −M forecasts from the given model and the benchmark model are denoted by rˆt and r¯t , respectively. The historical average of the  stock returns, r¯t = t−1 j=1 r j , is taken as the natural benchmark. Such benchmark forecasts are also available by regressing returns on a constant. Intuitively, a positive R2OoS indicates that the model forecasts have lower MSPE than the benchmark forecasts, suggesting the existence of return predictability. To check whether the return predictability is significant, we follow the literature in using the Clark and West (2007) (CW) test. The null hypothesis of the CW test is that the MSPE of the benchmark forecasts is less than or equal to the MSPE of the given model. In comparison with the Diebold and Mariano (1995) test, this corrected test is more suitable for nested models. 4.2.2. Forecasting results The 2nd column of Table 4 reports the evaluation results of the univariate models over the out-of-sample period from January 1947 through December 2016. We find that the AOR model leads to an out-of-sample R2 of 0.361%, which is statistically significant at the 5% level. This suggests significant return predictability of AOR for stock returns. For comparison, we also show the performance of popular predictors. 6 of the 14 predictors have significantly positive R2OoS values (DP, DY, EP, TBL, LTY and TMS). This is not consistent with the finding of Goyal and Welch (2008) that individual univariate models struggle to predict stock returns successfully.

The reason for this is that we apply the Sharpe ratio constraint to the predictive regressions, improving forecasting performance. Similarly, PTV finds significant return predictability using the same four predictors (DP, DY, TBL and LTY), although it uses a different out-of-sample period lasting only until December 2010. More importantly, the R2OoS of the AOR model is greater than the R2OoS of the models for 9 of the 14 popular predictors, implying that the asymmetric oil price measure has more predictive content than most macro variables. The average R2OoS of the models using popular predictors is 0.219%, lower than the R2OoS of the AOR model. To look at forecasting performance over time, we divide the whole evaluation period into two subperiods. The first subperiod spans January 1947 to December 1983. The second starts in 1984, corresponding to the great moderation when the volatility of oil prices significantly decreased. The motivation of choosing December 1983 as the breakpoint is from Goyal and Welch (2008). The authors find that the predictive ability of economic variables becomes much worse after the “Great Moderation” in mid-1980s. Similarly, Pettenuzzo et al. (2014) also split the whole sample period into two halves to look at the changes of return predictability over time.7 The 3rd and 4th columns of Table 4 report the forecasting results for the univariate models in these two subsamples. We find that the predictive abilities of the univariate macro models change greatly across two subperiods. Only one of the popular predictors significantly beats the historical average benchmark in both subsamples. For example, the models using DP and DY have R2OoS values of 1.159% and 1.519% in the first subsample, respectively. In sharp contrast, these models have negative R2OoS values in the second subsample, implying underperformance relative to the benchmark model. The only exception is the model using EP, which significantly outperforms the benchmark model in both subsamples, with R2OoS values of 0.211% and 0.700% in the two periods. Interestingly, the AOR model leads to significant return predictability in both evaluation periods. Its R2OoS is 0.433% in the first subsample, statistically significant at 5% level. In the second subsample, the R2OoS is 0.292%, weakly significant at 10% level. That is, the model using our AOR measure is less affected by sample period selection than models using most popular predictors. In the first subsample, the average R2OoS of the univariate macro models is 0.418%, slightly lower than the R2OoS of the AOR model. Notably, the average R2OoS is only 0.029% in the second subsample. Therefore, the superiority in forecasting performance of our AOR measure compared to that of macroeconomic variables is greater in the more recent subperiod. 4.3. Economic predictability To evaluate the economic value of oil market information for stock index investments, we follow the literature (e.g., Campbell and Thompson, 2008; Ferreira and Santa-Clara, 2011; Neely et al., 2014) and imagine an investor with mean-variance utility who allocates his or her wealth between the stock index security and a risk-free Treasury bill. In this framework, the investor should exante determine the optimal weight on the stock index according to

ωt∗ =

1 rˆt+1

2 γ σˆ t+1

,

(8)

7 Indeed, this looks a bit arbitrary. We detect the structural break in the predictive relationship between oil price increases and stock returns using the Bai and Perron (2003) method. The test results indicate the existence of a break occurred in December 1973, referring to a large oil price shock. The subsample results based on this alternative breakpoint are reported in the appendix. We find that they are highly consistent with our main results reported in the paper. Furthermore, because the time of structural break is actually ex-ante unknown for forecasters, we do not give more details about these subsample results.

Y. Wang, Z. Pan and L. Liu et al. / Journal of Banking and Finance 102 (2019) 43–58 Table 6 Out-of-sample performance of univariate models: CER gains.

Table 5 Out-of-sample performance of univariate models: Sharpe ratio gains.

DP DY EP DE SVAR BM NTIS TBL LTY LTR TMS DFY DFR INFL AOR AVERAGE

Panel A: 1947–2016

Panel B: 1947–1983

Panel C: 1984–2016

0.006 0.054 0.043 0.013 0.016 −0.018 0.017 0.111 0.139 0.044 0.063 −0.022 0.036 0.001 0.039 0.036

0.103 0.152 −0.014 0.003 −0.007 0.016 0.006 0.249 0.333 0.035 0.115 −0.018 −0.005 0.010 0.051 0.070

−0.150 −0.103 0.189 0.027 0.043 −0.006 0.029 0.020 0.007 0.054 0.017 −0.027 0.087 −0.009 0.023 0.013

DP DY EP DE SVAR BM NTIS TBL LTY LTR TMS DFY DFR INFL AOR AVERAGE

Notes: This table reports the out-of-sample performance of univariate models. The forecasts rˆt are produced by the model rt+1 = α + β xt + t+1 , where xt is a predictor variable for excess stock return rt+1 . We apply the Sharpe ratio restriction of Pettenuzzo et al. (2014) to each model in the procedure of parameter estimation. Each period a mean-variance investor allocates wealth between stock and Tbill based on return and volatility forecasts. In this framework, the stock index is assigned the weight,

where γ denotes the risk aversion degree. We use a 5-year rolling window volatility forecasts and use γ = 3. The optimal weight of stock is restricted between 0 and 1.5. The portfolio performance is evaluated based on the Sharpe ratio (SR). We show the difference between the SR of the given√portfolio and that of the benchmark portfolio. This difference is multiplied by 12 to denote annualized value. The full sample period is from January 1927 through December 2016 and the outof-sample period starts in January 1947. The 2nd -15th rows show the performance of popular predictors suggested by Goyal and Welch (2008). The 16th row displays the forecasting results of asymmetric oil return (AOR). The last row gives the average SR gains of popular predictors.

2 where rˆt+1 and σˆ t+1 are the forecasts of the return and variance, respectively, of the stock index security. A weight 1 − ωt∗ is assigned to the risk-free Treasury bill. We use the risk aversion parameter γ = 3, following (Rapach et al., 2010; Dangl and Halling, 2012).8 For the variance forecasts, we follow (Campbell and Thompson, 2008) in using the sample variance computed from a five-year rolling window of historical returns. We follow the suggestions of the related literature (e.g., Rapach and Zhou, 2013) and restrict the optimal weight on the stock security to be between 0 and 1.5 to preclude either short selling and having more than 50% financial leverage.9 The portfolio return is given by,

(9)

where Rf,t is the risk-free rate. We use two popular criteria to evaluate portfolio performance, including Sharpe ratio (SR) and the certainty equivalent return (CER). Table 5 reports the portfolio performance of the univariate models evaluated by SR. We show the SR gains defined as the SR of the given portfolio minus√that of the benchmark portfolio. This difference is multiplied by 12 to arrive at an annualized value. We find that the AOR model results in an SR gain of 0.039, suggesting that the improvement in return predictability is economically significant. This value is higher than the SR gains of 8 macro models

8

As a robustness check, we also consider other risk aversion coefficients. As a robustness check, we consider different restrictions on the optimal stock weights. 9

Panel A: 1947–2016

Panel B: 1947–1983

Panel C: 1984–2016

0.089 0.672 0.655 −0.002 0.257 −0.222 0.102 1.542 1.740 0.660 0.957 −0.342 0.566 0.008 0.572 0.477

1.459 2.199 −0.656 −0.312 −0.101 −0.057 −0.049 2.665 3.136 0.536 1.785 −0.279 −0.090 0.165 0.781 0.743

−1.464 −1.061 2.147 0.324 0.671 −0.405 0.258 0.277 0.156 0.804 0.015 −0.406 1.323 −0.173 0.324 0.176

Notes: This table reports the out-of-sample performance of univariate models. The forecasts rˆt are produced by the model rt+1 = α + β xt + t+1 , where xt is a predictor variable for excess stock return rt+1 . We apply the Sharpe ratio restriction of Pettenuzzo et al. (2014) to each model in the procedure of parameter estimation. Each period a mean-variance investor allocates wealth between stock and Tbill based on return and volatility forecasts. In this framework, the stock index is assigned the weight,

ωt∗ =

1 rˆt+1 ω = 2 γ σˆ t+1 ∗ t

R p,t+1 = ωt∗ rt+1 + R f,t ,

49

1 rˆt+1

2 γ σˆt+1

where γ denotes the risk aversion degree. We use a 5-year rolling window volatility forecasts and use γ = 3. The optimal weight of stock is restricted between 0 and 1.5. The portfolio performance is evaluated based on the certainty equivalent return (CER). We show the difference between the CER of the given portfolio and that of the benchmark portfolio. This difference is multiplied by 1200 to denote annualized percent value. The full sample period is from January 1927 through December 2016 and the out-of-sample period starts in January 1947. The 2nd -15th rows show the performance of popular predictors suggested by Goyal and Welch (2008). The 16th row displays the forecasting results of asymmetric oil return (AOR). The last row gives the average CER gains of popular predictors.

and close to the average SR gains of the macro models. Subsample analysis indicates that the superior performance of the AOR model over the models using popular predictors is concentrated in the second subsample. Consistent with the statistical evaluation results, we find that the AOR model has positive SR gains in both subsamples. A similar result is found for only 6 of the 14 popular predictors (DE, NTIS, TBL, LTY, LTR and TMS). We compute the CER gains of different forecasting strategies, defined as the difference between the CER of the given portfolio and that of the benchmark portfolio. The results are reported in Table 6. This difference is multiplied by 1200 to obtain an annualized percent value. These CER differences can be also interpreted as the annualized performance fees that an investor would be willing to pay to switch from using the benchmark forecasts to using the return forecasts generated using the model of interest. Using the univariate oil model of stock returns, we obtain CER gains of 57.2 basis points in the full sample, confirming the economic significance of the return predictability. Subsample analysis finds that the superior performance of the AOR model over the models using popular predictors is more prominent during the second subperiods. The oil model has CER gains of 32.4 bps in the second subsample, whereas the models using popular predictors have CER gains of only 17.6 bps on average in the second subsample. We conclude that AOR predicts stock returns out of sample with both statistical and economic significance. The predictability by asymmetric oil returns of stock returns is significant in both subsamples. However, the forecasting performance of popular predictors depends on the evaluation period and evaluation framework heavily. No popular predictor achieves both economic and statistical forecasting gains in both subperiods.

50

Y. Wang, Z. Pan and L. Liu et al. / Journal of Banking and Finance 102 (2019) 43–58 Table 7 Forecasting results of bivariate predictive regressions. Panel A: Out-of-sample R2

DP DY EP DE SVAR BM NTIS TBL LTY LTR TMS DFY DFR INFL AVERAGE

Panel B: CER gains

Panel C: Sharpe ratio gains

1947-2016

1947-1983

1984-2016

1947-2016

1947-1983

1984-2016

1947-2016

1947-1983

1984-2016

0.543∗∗ 0.971∗∗∗ 0.469∗∗ −0.040 0.454∗∗ 0.239∗ 0.300∗ 1.214∗∗∗ 1.088∗∗∗ 0.268∗ 0.625∗∗ 0.264 0.309∗ 0.353∗∗ 0.504

1.584∗∗∗ 2.146∗∗∗ 0.189∗ −0.423 0.402 0.424 0.423 2.347∗∗∗ 2.210∗∗∗ 0.118 1.259∗∗∗ 0.438 0.134 0.508∗ 0.840

−0.451 −0.150 0.736∗∗ 0.325 0.505∗∗ 0.062 0.182 0.133 0.018 0.410∗ 0.021 0.097 0.477∗ 0.205 0.184

0.005 0.834 0.514 0.332 0.765 0.484 0.649 2.237 1.921 1.179 1.046 0.167 1.012 0.613 0.840

1.351 2.379 −0.637 0.106 0.726 0.666 0.580 3.733 3.459 1.428 1.624 0.298 0.694 0.964 1.241

−1.527 −0.924 1.819 0.565 0.803 0.285 0.704 0.536 0.170 0.889 0.383 0.018 1.368 0.201 0.378

−0.004 0.061 0.036 0.030 0.050 0.032 0.051 0.153 0.146 0.077 0.069 0.012 0.066 0.041 0.059

0.085 0.156 −0.013 0.022 0.048 0.061 0.047 0.282 0.323 0.090 0.102 0.021 0.047 0.062 0.095

−0.147 −0.090 0.134 0.040 0.053 0.063 0.056 0.036 0.009 0.059 0.036 0.003 0.090 0.016 0.026

Notes: This table reports the out-of-sample performance of bivariate models. The forecasts rˆt are produced by the model rt+1 = α + βmacro xt,macro + βoil xt,oil + t+1 , for t = 1, 2, · · · , T − 1, where xt,oil and xt,macro denote the asymmetric oil return and one of the 14 popular predictors under consideration. We apply the Sharpe ratio restriction of Pettenuzzo et al. (2014) to each model in the procedure of parameter estimation. The forecast quality is evaluated by the out-of-sample R2 (R2OoS ) defined by the percent reduction of MSPE of the given model relative to the benchmark model of historical mean,

R2OoS = 1 −

MSPEmodel , MSPEbench

1 T 1 T 2 2 where MSPEmodel = T −M t=M+1 (rt − rˆt ) and MSPEmodel = T −M t=M+1 (rt − r¯t ) , where rˆt , r¯t and rt are the return forecasts from the model of interest, prevailing mean forecasts and the realized return values, respectively. Each period a mean-variance investor allocates wealth between stock and T-bill based on return and volatility forecasts. In this framework, the stock index is assigned the weight

ωt∗ =

1 rˆt+1

2 γ σˆt+1

,

where γ denotes the risk aversion degree. We use a 5-year rolling window volatility forecasts and use γ = 3. The optimal weight of stock is restricted between 0 and 1.5. The portfolio performance is evaluated based on the Sharpe ratio (SR) and the certainty equivalent √ return (CER). We show the difference between the SR of the given portfolio and that of the benchmark portfolio. This difference is multiplied by 12 to denote annualized value. We show the difference between the CER of the given portfolio and that of the benchmark portfolio. This difference is multiplied by 1200 to denote annualized percentage value. The full sample period is from January 1927 through December 2016 and the out-of-sample period starts in January 1947. The 3nd -16th rows show the performance of popular predictors suggested by Goyal and Welch (2008). The 17th row displays the forecasting results of asymmetric oil return (AOR). The last row reports the average performance of popular predictors. The numbers in bolds denote that the bivariate model with a macro variable and AOR performs better than the corresponding univariate model without AOR. For the positive R2OoS , we measure the statistical significance relative to the prevailing mean model using the Clark and West (2007) test statistic. The asterisks ∗ , ∗∗ and ∗∗∗ denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.

4.4. Combining oil and macro information Oil and popular predictors provide different predictive information regarding future stock returns. Furthermore, the results of a Harvey et al. (1998) test (which we do not report) indicates that oil-based return forecasts are not duplicates of forecasts based on popular predictors such as DP, DY, EP, LTY and LTR. This implies that forecasting performance can be improved by combining oil and macro information. We compare the forecasting accuracy of the bivariate predictive regression (3) with the oil variable and the corresponding univariate regression (2) without the oil variable. To maintain consistency, the Sharpe ratio constraint of PTV (2014) is applied to both types of predictive models. We note that the bivariate model does not necessarily outperform the univariate models in an out-of-sample exercise. The incorporation of irrelevant predictors in a model can result in worse out-of-sample forecasting performance because of estimation errors. More parameters can also lead to more volatile forecasts and therefore cause higher forecasting variance. An example of this is that the “kitchen sink” model with all potential predictors displays much worse forecasting accuracy than the historical average benchmark (Goyal and Welch, 2008; Rapach, Strauss and Zhou, 2010). Panel A of Table 7 reports the statistics of the forecasting performance of the bivariate models. Compared with the univariate model results in Table 4, the inclusion of asymmetric oil return leads to higher R2OoS values for all 14 cases in the full sample. The

inclusion of oil information leads to increases in the R2OoS values of the three ratio variables DP, DY and EP from 0.422% to 0.543%, from 0.687% to 0.971% and from 0.461% to 0.469%, respectively. The R2OoS values of the two interest predictors TBL and LTY also improve from 0.641% to 1.214% and from 0.759% to 1.088%, respectively. The predictability of stock returns by 6 popular predictors (SVAR, BM, NTIS, LTR, DFR and INFL) changes from being insignificant to being statistically significant. The average R2OoS of the bivariate models is 0.514%, more than twice that of the univariate models (0.219%). Notably, we find that bivariate models with different popular predictors and AOR significantly outperform the historical average benchmark for 12 of the 14 cases, implying the existence of universal return predictability. Subsample analysis indicates that the predictive ability of the bivariate models weakens in the more recent period for 9 of the 14 popular predictors. Nevertheless, the bivariate models with a macro variable and AOR perform better than the univariate macro models for most cases in both subsamples. Accounting for oil information improves the average R2OoS from 0.418% to 0.840% and from 0.029% to 0.184% in the first and second subsamples, respectively. Panel B of Table 7 shows the CER gains of portfolios formed by bivariate model forecasts. All bivariate models have positive CER gains in the full sample. Compared with the corresponding univariate model results in Table 6, the incorporation of AOR results in greater CER gains in 12 of the 14 cases. For example, the CER gain for the TBL model increases by 69.5 bps, from 154.2 bps to

Y. Wang, Z. Pan and L. Liu et al. / Journal of Banking and Finance 102 (2019) 43–58

223.7 bps. The CER gains of three popular predictors (DE, BM and DFY) switch from being negative to positive after including oil information. The average CER gains improve from 47.7 bps to 84 bps. The results by subsample are similar. The average CER gains increase from 74.3 bps to 124.1 bps in the first subsample and from 17.6 bps to 37.8 bps in the second subsample. The portfolio performance of bivariate models as evaluated by SR is given in Panel C of Table 7. Overall, the results are highly consistent. Most macroeconomic models of stock returns benefit from adding AOR as an additional predictor.

4.5. Forecast combinations We have shown that accounting for oil information improves the forecasting accuracy of univariate macroeconomic models. However, the inferior performance of univariate models could be caused by model uncertainty rather than the lack of enough predictive information. Recently, multivariate approaches such as forecast combination (Rapach et al., 2010; Dangl and Halling, 2012) and diffusion index (Ludvigson and Ng, 2007; Kelly and Pruitt, 2013; Neely et al., 2014) have been suggested as powerful tools in dealing with model uncertainty. Rapach et al. (2010) find that a combination of univariate models can provide reliable return predictability even if none of the individual models significantly outperform the historical average benchmark. Motivated by this finding, we investigate whether a forecast combination for bivariate models with AOR (FC-BV) generates more accurate return forecasts than the combination for univariate models without AOR (FC-UV). Note that the two combination strategies use the same set of macroeconomic information. The only difference is the FC-BV strategy uses AOR while the FC-UV does not. The usefulness of oil information for improving stock return forecasts is made clear by the comparison of the forecasting performances of these two strategies. The combination methods take the weighted average of forecasts from a set of individual models. The combined forecasts are computed using the equation

rˆt,comb =

N 

ω j,t rˆ j,t ,

(10)

j=1

where rˆ j,t denotes the return forecast produced by the j-th model and N is the total number of predictive models. Because we have a total of 14 popular predictors, N = 14. After obtaining the individual model forecasts rˆ j,t , the key procedure of the combination strategy is to determine the weights ωj,t ex-ante. Here, we use 5 different weighting schemes to combine the individual forecasts. The first is the naive scheme that assigns an equal weight to each individual model forecast (i.e, ω j,t = 1/N). Although this equal-weighted combination (EWC) is simple, the empirical evidence given by Stock and Watson (2004) and the simulations done by Claeskens et al. (2016) suggest that it performs as well as more advanced combination strategies in out-of-sample forecasting exercises. The second weighting method is the trimmed mean combination (TMC). This strategy excludes the model with the worst past performance in the previous period (i.e., the greatest MSPE at time t − 1), assigning an equal weight to each of the remaining forecasts. The model excluded from the pool can differ across time. The last three weighting methods compute the ex-ante weights based on various transformations of MSPE. Stock and Watson (2004) develop a discounted MSPE (DMPSE) in which the weight of individual model j is given by

φ −1 ω j,t = N j,t−1−1 , i=1 φi,t−1

(11)

51

where the summation of the discounted MSPE is given by φ j,t = t t−k (r − rˆ )2 . We consider two discounting factors, δ = k j,k k=1 δ 1 and δ = 0.9, and call the corresponding combinations DMSPE (1) and DMSPE (0.9), respectively. When δ = 1, this method is equivalent to the inverse MSPE suggested by Baumeister and Kilian (2015). Yang (2004) argues that large variability in the ex-ante estimates of combination weights can cause the linear forecast combination to perform much worse than the best individual model. In its place, the author proposes a nonlinear weighting scheme that uses the exponential transformation of MSPE given by

   2  π j exp −λ t−1 k=1 rk − rˆ j,k    ω j,t =  2  . N t−1 ˆ π exp − λ r − r i k i,k i=1 k=1

(12)

For simplicity, the weighting parameters λ and π are set to 1. Table 8 reports the forecasting results for the 5 forecast combinations. The 5 combinations have similar out-of-sample performances. This is consistent with existing findings of the equalweighted combination performing well (Stock and Watson, 2004; Claeskens et al., 2016). In the full sample, FC-UV leads to R2OoS values of 0.5% to 0.517%, statistically significant at the 1% level. The finding of return predictability can be treated as a successful replication of Rapach et al. (2010) using updated data. More importantly, we find that the FC-BV strategy has R2OoS values of 0.758% to 0.819%, higher than those of the related FC-UV strategies. The superior performance of the bivariate model combinations is also evident in both subsamples. In the first subsample, the average R2OoS of the combination strategies improves from 0.80% to 1.20% after the incorporation of oil information. In the second subsample, the FC-UV strategies have an average R2OoS value of 0.21%, which is not statistically significant. In contrast, the FC-BV methods increase the R2OoS values by 0.33%; these forecasting gains are significant at the 10% level or better. In summary, accounting for oil information improves the forecasting performance of the combination methods and makes them more robust to the choice of evaluation period. 5. Extension analysis This section performs two extension analyses. We first analyze the forecasting performance the business cycle. Then, the AOR is employed to predict characteristic portfolio returns. 5.1. Forecasting performance over business cycle The predictability of stock return is dependent of business condition (Cochrane, 1999, 2007). Specifically, the predictive ability of economic variables displays a counter-cyclical behavior which become stronger when the economy turns from an expansion to a recession. Therefore, it is worth for us to analyze the usefulness of oil market information for stock return prediction over business cycle. The R2OoS during the business recession and expansion periods is defined as follow:

T

(rt − rˆt )2 Itc , 2 c t=M+1 (rt − r¯t ) It

M+1 R2c = 1 − t= T

for

c = E X P, REC,

(13)

where ItEXP (ItREC ) is an indicator variable which takes the value of unity when the economy in the month t belongs to an NBER dated expansion (recession). Table 9 presents the R2OoS values of univariate macro models, as well as those of bivariate models with AOR, over the business cycle. We find that for 10 out of 14 popular predictors the R2OoS values are indeed higher during the recession period than those

52

Y. Wang, Z. Pan and L. Liu et al. / Journal of Banking and Finance 102 (2019) 43–58 Table 8 Out-of-sample performance of forecast combinations.

Mean Trimmed Mean DMSPE(0.9) DMSPE(1) Yang

Panel A: 1947–2016

Panel B: 1947–1983

Panel C: 1984–2016

Macro

Oil-Macro

Macro

Oil-Macro

Macro

Oil-Macro

0.501∗∗∗ 0.517∗∗∗ 0.500∗∗∗ 0.511∗∗∗ 0.501∗∗∗

0.758∗∗∗ 0.819∗∗∗ 0.758∗∗∗ 0.769∗∗∗ 0.758∗∗∗

0.803∗∗∗ 0.838∗∗∗ 0.803∗∗∗ 0.817∗∗∗ 0.804∗∗∗

1.204∗∗∗ 1.288∗∗∗ 1.206∗∗∗ 1.223∗∗∗ 1.206∗∗∗

0.212 0.211 0.211 0.218 0.211

0.333∗ 0.371∗∗ 0.331∗ 0.336∗ 0.331∗

Notes: This table reports the out-of-sample performance of forecast combinations. The forecasts are produced by the univariate model rt+1 = α + βmacro xt,macro + t+1 , and the corresponding bivariate model with oil, rt+1 = α + βmacro xt,macro + βoil xt,oil + t+1 for t = 1, 2, · · · , T − 1, where xt,oil and xt,macro denote the asymmetric oil return and one of the 14 popular predictors under consideration. Then, the weighted average of the individual forecasts from the univariate macro models (bivariate oil-macro models) are taken as the combination forecasts of macro (oil-macro) strategy. We apply the Sharpe ratio restriction of Pettenuzzo et al. (2014) to each model in the procedure of parameter estimation. The forecast quality is evaluated by the out-of-sample R2 (R2OoS ) defined by the percent reduction of MSPE of the given model relative to the benchmark model of historical mean, given by,

R2OoS = 1 −

MSPEmodel , MSPEbench

1 T 1 T 2 2 where MSPEmodel = T −M t=M+1 (rt − rˆt ) and MSPEmodel = T −M t=M+1 (rt − r¯t ) , where rˆt , r¯t and rt are the return forecasts from the model of interest, prevailing mean forecasts and the realized return values, respectively. The full sample period is from January 1927 through December 2016 and the out-ofsample period starts in January 1947. The numbers in bolds denote that the combination for bivariate models with a macro variable and AOR perform better than the combination for univariate models without AOR. For the positive R2OoS , we measure the statistical significance relative to the prevailing mean model using the Clark and West (2007) test statistic. The asterisks ∗ , ∗∗ and ∗∗∗ denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.

during the expansion period. When the economy is recession, bivariate models perform better than the univariate counterparts for 9 out of 14 cases. The average R2OoS increases slightly from 0.412% to 0.504% after accounting for oil information. When the economy is expansion, the inclusion of asymmetric oil return in the righthand side of univariate predictive regression results in higher R2OoS for all 14 cases. 10 out of 14 bivariate models can outperform the benchmark model significantly. In particular, the significance of return predictability emerges after the incorporation of AOR in the univariate models of SVAR, TMS and DFR. Oil information makes the average R2OoS improve from 0.149% to 0.504% during the expansion period. In summary, our analysis indicates the helpfulness of oil information for improving stock return predictability over business changes. 5.2. Forecasting characteristic portfolio returns In this subsection, we investigate whether asymmetric oil return can predict returns of portfolio formed based on industry, size, book-to-market and momentum. This analysis is useful for us to demonstrate the robustness of our main finding. It also helps us to further understand the predictive ability of oil for stock returns. The characteristic portfolio returns data are available at Kenneth French’s Data Library10 Panel A of Table 10 reports the estimation results for industry returns. We find the significant predictive relationship running from the asymmetric oil return (AOR) to 8 out of 10 industry returns by observing the estimates of β . The in-sample R2 changes between 0.327% and 0.825% across these 8 industries. We perform a Wald test for the equality of slope coefficients for different industries. Our results significantly reject the null hypothesis, indicating that the effects of oil price increases on future industry returns are different across various industries. AOR cannot predict returns of energy or utilities industries. The plausible explanation is that the companies of these two industries such as oil refiners and 10

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

transportation companies may hedge oil risk by some ways since oil price is a core determinant of refining cost and transportation cost. The hedging behavior makes the stock prices of the industries insensible to oil price increases. The absence of predictability from oil returns to energy-related industry returns is also consistent with the results in Driesprong et al. (2008) and Chiang and Hughen (2017). Panels B, C and D of Table 10 shows the predictive analysis results for portfolios formed by momentum, firm size and bookto-market ratio, respectively. We find the strong evidence about the significant return predictability from AOR to returns of characteristics portfolios. In particular, some regular patterns are also found by looking at the regression coefficient β . Stocks that are small (small size), distressed (high book-to-market ratio), with high growth opportunity (low book-to-market ratio), or past losers are more predictable by AOR. This pattern is also consistent with Huang et al. (2015) who develop a new investor sentiment measure to predict returns of characteristics portfolios. The R2 varies between 0.280% and 0.665%, between 0.317% and 0.658% and between 0.253% and 0.789% when the momemtun, size and book-tomarket characteristics change, respectively. However, using a Wald test on seeming unrelated regressions, we cannot reject the equality of slope coefficients for any of these three characteristic portfolios. Therefore, the effects of oil price increases on future stock returns have no structural differences for portfolios formed by size, book-to-market ratio or momentum.

6. Discussion of results 6.1. Economic explanations about the return predictability We have found that oil price increase, rather than the symmetric oil return suggested by Driesprong et al. (2008) can successfully predict stock returns. Another important finding is that the predictive ability of AOR for stock returns becomes weaker during the more recent period after 1983. In this section, we try to give the economic explanations about these empirical findings.

Y. Wang, Z. Pan and L. Liu et al. / Journal of Banking and Finance 102 (2019) 43–58 Table 10 Analysis of predictive relationship from oil to characteristic portfolio returns.

Table 9 Business cycle results.

DP DY EP DE SVAR BM NTIS TBL LTY LTR TMS DFY DFR INFL AVERAGE

Recession periods

Expansion periods

Macro

Oil-Macro

Macro

Oil-Macro

1.260∗∗ 1.637∗∗ −0.264 −0.760 0.233 0.548 −0.890 1.211∗ 1.479∗∗ 0.884∗ 0.531 −0.170 0.192 −0.117 0.412

1.009∗∗ 1.707∗∗∗ −0.466 −0.274 0.505∗ 0.527 −0.798 1.616∗∗ 1.806∗∗ 0.844∗ 0.553 −0.110 0.096 0.046 0.504

0.120∗ 0.344∗∗ 0.723∗∗ −0.212 −0.013 −0.116 0.350∗∗ 0.435∗∗ 0.499∗∗ −0.217 0.151 −0.170 0.090 0.102∗∗ 0.149

0.374∗ 0.705∗∗ 0.806∗∗ 0.044 0.436∗∗ 0.135 0.697∗∗ 1.069∗∗∗ 0.829∗∗∗ 0.059 0.652∗∗ 0.399 0.386∗ 0.464∗∗ 0.504

β

NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth Utils Other

for c = E XP, REC,

Panel Growth 2 3 4 5 6 7 8 9 Value

6.1.1. Explanations based on economic activity A potential explanation about the predictive ability of oil price increases for stock returns is that oil price increases drive future economic activity (Kilian, 2009; Hamilton, 1983), which is an important determinant of stock returns (Fama, 1981). To investigate whether this hypothesis holds, we use industrial production as a proxy for economic activity. Then, we use a simple predictive regression to detect the predictive ability of oil prices for economic activity:

x = AOR, SOR,

−3.518∗∗ −7.480∗∗ −4.709∗∗ −2.141 −7.575∗∗∗ −3.170∗ −6.386∗∗∗ −4.749∗∗ −3.075 −6.050∗∗∗

Panel C: Forecasting Small −6.766∗∗ 2 −6.754∗∗ 3 −6.732∗∗ 4 −7.148∗∗∗ 5 −6.336∗∗ 6 −6.257∗∗∗ 7 −4.756∗∗ 8 −4.935∗∗ 9 −4.749∗∗ Large −4.946∗∗

where ItEXP (ItREC ) is an indicator variable which takes the value of unity when month t is an NBER dated expansion (recession). rˆt , r¯t and rt are the return forecasts from the model of interest, prevailing mean forecasts and the realized returns, respectively. The full sample period is from January 1927 through December 2016 and the out-of-sample period starts in January 1947. The numbers in bolds denote that the bivariate models with a macro variable and AOR perform better than the related univariate models without AOR. The 3nd -16th rows show the performance of popular predictors suggested by Goyal and Welch (2008). The 17th row displays the forecasting results of asymmetric oil return (AOR). The last row reports the average performance of popular predictors. For the positive R2OoS , we measure the statistical significance relative to the prevailing mean model using the Clark and West (2007) test statistic. The asterisks ∗ , ∗∗ and ∗∗∗ denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.

ipt+1 = μ + θ1 ipt + θ2 xt + t+1 ,

R2 (%)

−1.744 −2.301 −1.848 −0.891 −2.632 −1.576 −2.666 −2.239 −1.173 −2.341

0.404 0.648 0.388 0.085 0.746 0.327 0.825 0.497 0.212 0.606

Panel B: Forecasting returns of momentum portfolios −1.978 0.532 Loser −8.589∗∗ −2.124 0.614 2 −7.587∗∗ −2.178 0.665 3 −6.849∗∗ −2.167 0.507 4 −5.441∗∗ −1.880 0.433 5 −4.714∗∗ −1.668 0.290 6 −3.763∗∗ −1.964 0.424 7 −4.310∗∗ ∗ −1.548 0.280 8 −3.396 −2.015 0.372 9 −4.125∗∗ −2.180 0.453 Winner −5.244∗∗

T

(rt − rˆt )2 Itc , 2 c t=M+1 (rt − r¯t ) It

t − stat

Panel A: Forecasting returns of industry portfolios

Notes: This table reports the out-of-sample performance over the business cycle. The forecasts are produced by the univariate model rt+1 = α + βmacro xt,macro + t+1 , and the corresponding bivariate model with oil, rt+1 = α + βmacro xt,macro + βoil xt,oil + t+1 for t = 1, 2, · · · , T − 1, where xt,oil and xt,macro denote the asymmetric oil return and one of the 14 popular predictors under consideration. We apply the Sharpe ratio restriction of Pettenuzzo et al. (2014) to each model in the procedure of parameter estimation. The forecast quality is evaluated by the out-of-sample R2 (R2OoS ) defined by the percent reduction of MSPE of the given model relative to the benchmark model of historical mean, given by, M+1 R2c = 1 − t= T

53

returns of size portfolios −1.936 0.317 −1.983 0.410 −2.184 0.490 −2.518 0.634 −2.208 0.554 −2.366 0.582 −1.866 0.376 −1.931 0.443 −2.033 0.460 −2.495 0.658

D: Forecasting returns of BM portfolios −2.696 0.789 −6.112∗∗∗ −2.564 0.716 −5.418∗∗∗ ∗ −1.599 0.349 −3.832 −1.697 0.253 −3.599∗∗ −1.932 0.398 −4.338∗∗ −2.143 0.490 −5.083∗∗ −1.899 0.395 −4.878∗∗ −2.270 0.440 −5.380∗∗ −2.228 0.454 −6.244∗∗ ∗∗ −2.218 0.433 −7.328

Notes: This table reports the in-sample estimation results for the univariate predictive regression rt+1 = α + β xt + t+1 , for t = 1, 2, · · · , T − 1, where xt is the asymmetric oil return (AOR) and t+1 is the error term assumed to be independent and identically distributed. We analyze the predictive regression for characteristic portfolio returns, the name of which are listed in the first column. All the predictive variables are standardized. The parameter estimates and in-sample R2 in percentage are given. We perform one-sided test for H0 : β ≥ 0 against the alternative H1 : β < 0 for asymmetric oil return (AOR). Such test is executed using the heteroskedasticity consistent tstatistic based on the Newey-West method. The asterisks ∗ ∗∗ , and ∗∗∗ denote significance at 10%, 5% and 1% levels, respectively.

(14)

where ipt denotes the changes in industrial production. AOR and SOR denote the asymmetric oil return, and symmetric oil return, respectively. One-month lag of industrial production is taken as an explanatory variable to control the effect of the autocorrelation. We collect the monthly data for industrial production from the Federal Reserve Bank at Saint Louis. The estimate of the coefficient θ 2 for AOR is -0.021 with the Newey-West adjusted t-statistic equals −1.704, indicating the significance at 5% level based on onesided test. This result indicates that higher asymmetric oil return in the current month cause worse economic condition in the next

month. Therefore, the role of economic activity in the pass-through of oil to stock returns is confirmed accordingly. In contrast, the slope coefficient of symmetric oil return (SOR) on ipt+1 is 0.001 with the t-statistic equals 0.158, implying the insignificant predictive ability. AOR provides useful information regarding future economic activity, whereas SOR fails to do so. This is the reason why SOR suggested by Driesprong et al. (2008) cannot predict stock returns. Furthermore, we estimate Eq. (14) using the subsample after 1983. Unfortunately, we find no evidence on the impact of oil price

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measures on the industrial production. The diminishing ability of oil price increases for predicting future economic condition leads to its weaker predictive ability for stock returns. 6.1.2. Explanations based on information efficiency The classical valuation models suggest that asset prices should equal discounted cash flows. Therefore, discount rate and expected cash flow are the two core determinants of stock prices. From this perspective, the stock return predictability from asymmetric oil return (AOR) may be attributed to the lagged responses of discount rate or cash flow, or both to oil price increase information. For this consideration, we investigate the source of the stock return predictability from the channels of discount rate and cash flow. Prior to investigate whether the discount rate or cash flow channel matters, we should use the proxies for these two variables. Following (Cochrane, 2008, 2011), the dividend price ratio is considered as the primary proxy to capture the dynamics of discount rates. Recently, Huang et al. (2015) also took dividend price ratio as a proxy for discount rate to analyze the source of return predictability from a new investor sentiment measure. We also use the returns to long-term government bonds (LTR) as an alternative proxy for discount rate. The motivation is from the argument of Campbell and Ammer (1993) and Campbell et al. (2010) that government bond return predictability should be driven by timevarying discount rates alone because the nominal cash flows of government bold are fixed. We use the growth rate of the aggregate dividend to measure the cash flows, following the majority of the literature (Chen et al., 2012; Koijen and Van Nieuwerburgh, 2011; Kelly and Pruitt, 2013; Garrett and Priestley, 2012). Because the dividends are subject to smoothing (Fama and French, 2001), we also examine an alternative proxy of cash flow, aggregate earning growth, in addition to the dividend growth. Our analysis of the information channel is based on Campbell and Shiller (1988) approximate present value identity (Cochrane, 2008, 2011; Campbell, Polk and Vuolteenaho, 2010),

rt+1 ≈ DGt+1 − ρ DPt+1 + DPt ,

(15)

where rt+1 is the aggregate returns from t to t + 1, DGt+1 is the log aggregate dividend growth rate, DPt+1 is the log dividend price ratio, and ρ is a positive log-linearization constant. The Eq. (15) implies that if a variable can predict stock returns rt+1 beyond the information provided by DPt , it must predict DPt+1 or DGt+1 . Because DPt+1 and DGt+1 are separate proxies for the discount rate and cash flow, the ability of the AOR to forecast DPt+1 and DGt+1 can refer to the discount rate channel and cash flow channel, respectively. We use the following predictive regression to investigate the roles of the two information channels:

yt+1 =

α + β xt + ϕ yt + ξt , x = AOR, SOR; and

y = DP, LT R, DG, EG,

(16)

where DP, LTR, DG, and EG are the dividend price ratio of the S&P 500 index, long-term government bond return, dividend growth rate of the S&P 500 index, and earning growth rate of the S&P 500 index, respectively. The estimation results of (16) are reported in Table 11. We also take the post-1983 subsample as an example to analyze why the predictive ability of oil increase information weakens over time. We find that the in-sample R2 is very high for almost all cases. This is expectable because all dependent variables have strong persistence. In the full sample, the slope of AOR on DPt+1 is significantly positive at 5% level based on one-sided test with the tstatistic is 1.681. An increase in AOR leads to an increase in DPt+1 . Keeping the dividend constant, an increase in DPt+1 suggests that stock price Pt+1 declines at time t + 1, implying the deterioration

in market condition. This is consistent with our main finding that AOR negatively predicts stock returns. As the consistence, we also find that the slope of AOR on LT Rt+1 is also highly significant. The slope coefficients of two oil variables on DGt+1 or EGt+1 are not significant. In summary, the existence of positive predictive ability of AOR for DPt+1 and LT Rt+1 , and the absence of predictive ability for DGt+1 or EGt+1 jointly indicate that the negative predictive ability of AOR for stock returns comes from the discount rate channel, rather than from the cash flow information channel. Jones and Kaul (1996) argue that the significant lagged effect of oil prices on stock returns indicate that either oil shocks induce some variation in expected stock returns or that stock market is inefficient. Our results indicate that the variation in expected stock returns responds to oil price increase information. The significant return predictability from oil price increase does not necessarily imply the stock market inefficiency. When AOR is replaced by SOR as the predictor of discount rate variables DPt+1 and LT Rt+1 , the significance of slope coefficient becomes weaker. This evidence can partly explain why the predictive ability of symmetric oil return (SOR) is weaker than the asymmetric oil return (AOR) for stock returns. In the post-1983 subsample, we find that the slope coefficients of oil variables on DP are not significant. In comparison with the full sample results, the significance of oil variable coefficients for LTR in this subsample is also weaker. In other words, during the more recent period, the role of discount channel for information transmission from oil price increase to stock returns is less prominent. This causes the weaker predictability of stock returns from oil information over time. 6.1.3. Explanations based on learning We now examine whether there is evidence that investors gradually learning of the predictive ability of oil price increases over time. The motivation is from McLean and Pontiff (2016) that the predictive ability of a number of variables becomes weaker over time after they are considered as return predictors in academic publications. The important impacts of oil price shocks on stock market and the real economy have caused much attention by academics, practitioners and policy makers. The weakening predictive ability of oil price increases for stock returns may be because people are more aware of it over time. Following (Bakshi et al., 2013; Jacobsen et al., 2018), we investigate whether there as evidence of such learning, using the equation

rt+1 = α + (β + β trend T rend )AORt + t+1 ,

(17)

where the trend is a variable calculated from an observation number series (i.e., a linear trend). Because we have found that the slope coefficient of AOR, β , is significantly negative, there would be evidence of learning if β trend is significant and positive. We obtain the coefficient β -0.348 and Newey-West t-statistic is -2.072. The estimate of β trend is 0.0 0 03, with the t-statistic is 1.727. Both β and β trend are significant but have opposite signs. This evidence indicates that the negative predictive power of AOR is weaker over time because of investor learning. 6.2. Different oil price increase measures As a robustness check, we consider alternative measures of oil price increases to confirm our finding that oil price increases contain meaningful predictive content for stock returns. The first alternative measure is the sign of oil returns, defined as

SignORt = I (rt,oil > 0 ),

(18)

where I( · ) is an indicator function that equals 1 when the condition in parenthesis is satisfied and zero otherwise.

Y. Wang, Z. Pan and L. Liu et al. / Journal of Banking and Finance 102 (2019) 43–58

55

Table 11 Forecasting discount rates and cash flows with oil returns. Full sample

Post-1983 subsample

AOR

SOR

β DP LTR DG EG

R2 (%) ∗∗

0.081 (1.681) 0.004∗∗∗ (2.363) −0.002 (-0.855) 0.018 (1.083)

98.553 99.244 74.540 58.533

AOR

β ∗

0.047 (1.408) 0.004∗∗ (2.256) 0.002 (0.845) 0.026 (1.195)

SOR

R2 (%)

β

R2 (%)

β

R2 (%)

98.552

0.041 (0.882) 0.005∗∗ (2.119) −0.001 (-0.663) 0.024 (0.817)

98.539

0.028 (0.868) 0.004∗∗ (2.156) 0.001 (0.300) 0.034 (1.230)

98.541

99.239 74.543 58.655

98.771 87.642 55.493

98.782 87.632 55.692

Notes: This table reports the in-sample estimation results for the predictive regression

yt+1 = α + β xt + ϕ yt + ξt ,

x = AOR, SOR,

and

y = DP, LT R, DG, EG,

where DP, LTR, DG, and EG are the dividend price ratio of the S&P 500 index, long-term government bond return, dividend growth rate of the S&P 500 index, and earning growth rate of the S&P 500 index, respectively. AOR and SOR denote the asymmetric oil return, and symmetric oil return, respectively. We report the slope coefficients for oil variables β and in-sample R2 . The numbers in parentheses are the Newey-West t-statistics. The asterisks ∗ , ∗∗ and ∗∗∗ denote significance at 10%, 5% and 1% significance levels, respectively.

Table 12 In-sample predictive ability of alternative oil return measures.

Hamilton (1996, 2003) finds that the impact of oil price changes on GDP is significant only when the price of oil exceeds recent peaks. Accordingly, he recommends looking at net oil price increases, defined as

α AOR

(19) where n is the length of the look-back period. Here, we define the net oil price increases using a look-back period of a year (i.e., n = 12). The third measure of oil price increases comes from Lee et al. (1995). They argue that oil price changes have greater impacts on real GNP when oil prices are stable than when oil prices are volatile. Based on this argument, they normalize oil price changes by the conditional standard deviation, leading to the measure

Panel B: Symmetric 5.974∗∗∗ (2.855) NOR 5.975∗∗∗ (2.863)

SOR

(20)

(21)

Table 12 reports the estimation results for the univariate oil model of stock returns using regression (2) for each of the three alternative measures. For comparison, we also include the results for two symmetric oil returns measures, rt,oil and ς t,oil , and reproduce the results from the AOR model. The slope coefficients β for all measures of asymmetric oil returns are significant at the 5% level, implying that the predictability by oil price increases of stock returns is robust to different measures of oil price increases. Mork (1989)’s AOR model has a greater R2 than the competing asymmetric oil models, signaling its better insample performance. In contrast, we find that the symmetric oil return measure suggested by Driesprong et al. (2008) has insignificant predictive ability using the updated data. This differs from Driesprong et al. (2008), who find predictability using symmetric oil returns. The first explanation for this inconsistency is that oil price increases have bigger impacts on stock returns than oil price decreases do. We decompose symmetric oil returns into its positive + component rt,oil = max(rt,oil , 0 ) (i.e., AOR) and negative component − rt,oil = min(rt,oil , 0 ) and then perform the bivariate regression given

0.650 0.284 0.198 0.404

WTI oil return −3.380 0.267 (-1.284) −2.883∗ 0.194 (-1.302)

Panel C: Alternative oil return (1985–2016) −2.250 0.183 SOR, Dubai 6.908∗∗∗ (2.579) (-0.836) −3.840∗ 0.530 AOR, Dubai 6.893∗∗∗ (2.578) (-1.424) ∗∗∗ −0.581 0.012 SOR, Brent 6.916 (2.580) (-0.216) −2.434 0.214 AOR, Brent 6.904∗∗∗ (2.578) (-0.903)

where σˆ t,oil denotes the conditional standard deviation of oil returns implied by the GARCH model of Bollerslev (1986). Similarly, we use the positive normalized oil return,

P NORt = max(ςt,oil , 0 ).

R2 (%)

Panel A: Asymmetric oil return −5.277∗∗∗ 5.970∗∗∗ (2.870) (-2.347) −3.487∗∗ SignOR 5.973∗∗∗ (2.858) (-1.841) −2.923∗∗ NOP 5.970∗∗∗ (2.884) (-1.975) −4.157∗∗ PNOR 5.974∗∗∗ (2.874) (-1.995)

oil oil oil NOPt = max{log(Ptoil ) − max[log(Pt−1 ), log(Pt−2 ), · · · , log(Pt−n )] , 0 } ,

ςt,oil = rt,oil /σˆ t,oil ,

β

Notes: This table reports the in-sample estimation results for the univariate predictive regression rt+1 = α + β xt + t+1 , for t = 1, 2, · · · , T − 1, where xt is an oil return measure and t+1 is the error term assumed to be independent and identically distributed. All the predictive variables are standardized. The parameter estimates and insample R2 in percentage are given. We perform one-sided test for H0 : β ≥ 0 against the alternative H1 : β < 0. Such test is executed using the heteroskedasticity consistent t-statistic based on the Newey-West method. The asterisks ∗ , ∗∗ and ∗∗∗ denote significance at 10%, 5% and 1% levels, respectively.

by + − rt+1 = α + β + rt,oil + β − rt,oil + t .

(22)

β+

The p-value for the null hypothesis = 0 against the alternative hypothesis β + < 0 is 0.009. However, the p-value for the null hypothesis β − = 0 against the alternative hypothesis β − < 0 is 0.803. The insignificant predictive ability of the negative compo-

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− nent of oil returns (rt,oil ) dilutes the predictive ability of the pos-

+ itive component (rt,oil ) for stock returns, leading to an overall insignificant impact of symmetric oil returns. The second explanation for the change in the predictive ability of oil prices comes from changes in oil market fundamentals. Jiang et al. (2018) extend the data of Driesprong et al. (2008) to December 2015 and find that the overall predictive ability of oil prices decreases dramatically over the sample period. They use two structural vector autoregressive models to decompose oil price changes into oil supply shocks, global demand shocks and oilspecific demand shocks. The authors show that oil supply shocks and oil-specific demand shocks predict stock returns with a negative slope, whereas global demand shocks positively predict stock returns. From 2003 to mid-2008, higher demand from emerging economies instead of global oil production drives oil price changes (Kilian, 2009; Hamilton, 2009). Our subsample analysis shows that the predictive ability of oil price increases weakens after 1983. We also decompose oil price changes into three types of shocks using the traditional structural VAR methodology of Kilian (2009). Here, global oil production and Kilian (2009)’s index for global economic activity are taken as the proxies of supply and global demand, respectively. During the sample period after January 1974, we find that the impacts of oil supply shock or global demand shock on future stock returns are not significant. This result is slightly different from those reported in Table 4 of Jiang et al. (2018) who show that the predictive ability of oil supply shock is not significant, while that of the global demand shock is highly significant. Such inconsistent results may be caused by different data sample and different stock index we use. More importantly, we find that the slope coefficient of other oil-specific demand shock for stock return is -0.052 with the t-statistic is -1.703. This result is consistent with the finding in Jiang et al. (2018) that oil-specific demand shock negatively predict stock returns. Furthermore, we also analyze the predictive relationship between positive component of other oil-specific demand shock and stock returns. Our evidence reveals even stronger predictive ability that the slope coefficient is -0.083 and the t-statistic is -1.986. In summary, the predictive ability of oil price increases for stock returns comes from the impacts of positive other oil-specific demand shock. We also examine whether the predictability from oil to stock returns hold for Brent or Dubai oil. Especially, WTI and Brent decoupled in the more recent period since 2010, it is possible that the predictive power of these two oil price is different. Table 12 shows the estimation results when using AOR and SOR of two alternative oils11 Due to the data availability, the sample period for these two oil prices is from January 1985 through December 2016. We find that neither of the symmetric oil returns can significantly predict stock returns. The AOR of Dubai oil shows weak significance of predictive ability for stock returns, with the t-statistic equals −1.424. This result confirms our previous finding that AOR of WTI oil reveals weak stock return predictability after 1983. Interestingly, we find that the slope coefficient of Brent oil AOR is not significant. That is, WTI and Dubai AORs can predict stock returns of the US, but Brent oil AOR fails to do so. The plausible explanation is that WTI and Dubai oil prices are more relevant to the US economy. WTI and Dubai prices are the separated benchmarks for oils extracted in the North America and Persian Gulf. Domestic oil can satisfy about 60% of the US oil consumption in 201612 . The primary of the remaining imported oil also comes from these two regions. For example, according to the statistics of Energy Information Administration (EIA), the imports from the

11

We collect these oil price data from World Bank. These data are computed based on the BP statistical review of world energy 2017 12

Saudi Arabia and Canada account for 40.3% and 11.0% of the total imported oil to the US, respectively. 6.3. The effect of model misspecification Model misspecification is a potential problem affecting forecasting results (Meese and Rogoff, 1983; Carrasco and Rossi, 2016). Following the return forecasting literature (e.g., Goyal and Welch, 2008; Campbell and Thompson, 2008), we use simple predictive regressions that assume a linear predictive relationship to detect return predictability. It should be recognized that nonlinearity is likely to exist in the oil-GDP relationship (Charfeddine, Klein and Walther, 2018) and the oil-stock relationship (Jiang, Skoulakis and Xue, 2018). Nonlinear models can capture more complex relationships and perform better than simple linear models in-sample. However, whether nonlinear models outperform linear models out of sample is still undecided in the literature. For example, several studies find significant return predictability using nonlinear models such as regime switching regressions (Zhu and Zhu, 2013; Henkel, Martin and Nardari, 2011). Other studies document that linear models are good enough for out-of-sample forecasting (Racine, 20 01; Maasoumi and Racine, 20 02). A plausible explanation for this is that nonlinear models have more parameters that need to be estimated, increasing the scope for estimation errors that impair forecasting performance. We use a regime switching model with oil returns to predict stock returns but find a negative R2OoS value of -0.673%. Furthermore, in practice, forecasters face the problem of how to choose the appropriate specifications for nonlinear models ex-ante. Structural breaks are an important source of model misspecification. Besides regime switching models, time-varying parameter (TVP) models are also used to deal with structural breaks (e.g., Dangl and Halling, 2012). The TVP specification nests a specific process to capture the dynamics of the slope parameter. However, the TVP model can lead to overfitting because the predictive relationship is unlikely to change at every point in time. Broadly, Bacchetta et al. (2009) find that TVP models do not beat a random walk in exchange rate forecasting. The constant coefficient model with a rolling estimation window is another popular way to handle the problem of structural breaks. However, both TVP models and the rolling window method increase the variance of the parameter estimates. As pointed out by Clark and McCracken (2009), this increase in variance maps into larger forecast errors and causes the mean square forecast error to increase. The linear regression with nonlinear oil returns (AOR) already accounts for the nonlinearity in the oil-stock relationship. The AOR + measure rt,oil is obtained by truncating oil returns at zero. Therefore, the forecasts from the univariate AOR model of stock returns exhibit regime switching behavior. They are close to the forecasts from using symmetric oil returns (rt,oil ) when oil prices increase and close to the historical average benchmark when oil prices decrease. We find significant return predictability using linear regression with such a nonlinear predictor. Therefore, forecasters need to think more about whether nonlinear predictors or nonlinear models are more suitable for return forecasting. We leave this as an issue for future work. 7. Conclusions The relationship between crude oil prices and stock market activity is well studied. However, whether oil prices predict stock returns out of sample draws much less attention in the literature. Using monthly data from 1927 to 2016, we find that increases in WTI oil prices successfully predict aggregate market returns both in and out of sample. The return predictability revealed by oil market information is of statistical and economic significance. We use

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a simple bivariate regression model with oil and a popular predictor to generate return forecasts. Such oil-macro bivariate models outperform the corresponding univariate models. Incorporating oil information also improves forecast improvement for multivariate information methods. Our results survive a series of robustness tests including alternative information combining methods, business cycle analysis, different risk aversion coefficients and various constraints on the weight placed on stocks in the portfolio. Further analysis indicates that oil price increases provide predictive information for industrial production and interest rates, both of which influence stock returns. Our findings have meaningful implications for market participants and policy makers. First, we find that oil price increases negatively predict aggregate market returns, but oil price returns fail to do so. Investors should be aware of oil price increases rather than oil price changes as they reduce the diversification effect of portfolios with many stocks. Large institutions which may invest in stocks index (e.g., pension and insurance companies) are suggested using some financial instruments such as oil derivatives to hedge oil risk. Individuals can put the energy industry stocks in the portfolio to reduce risk because they are less affected by oil price increase. Second, policy makers should pay more attention to oil price increases than to oil price decreases. There is room for policy intervention to mitigate the adverse effects of high oil prices. We have found that oil price increases lead to decline in stock returns through a channel of economic activity. This result implies that any macroeconomic policies aiming to stimulate the economic activity are interpreted as good news by investors in the short horizon. Our evidence shows that oil price increases also affect future stock return through another channel of discount rate rather than the channel of cash flow. Therefore, monetary policy for reducing interest rate is a useful tool to mitigate the adverse effect of persistent increases in oil prices on stock market activity. Some policies such as relieving the fiscal burden and/or at easing the credit crunch, which contributes to improve future cash flows and investment profitability, may be less helpful. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jbankfin.2019.03.009. References Ang, A., Bekaert, G., 2007. Stock return predictability: is it there? Rev. Financ. Stud. 20 (3), 651–707. Arouri, M.E.H., Jouini, J., Nguyen, D.K., 2011. Volatility spillovers between oil prices and stock sector returns: implications for portfolio management. J. Int. Money Finance. 30 (7), 1387–1405. Avramov, D., 2002. Stock return predictability and model uncertainty. J. Financ. Econ. 64 (3), 423–458. Bacchetta, P., Van Wincoop, E., Beutler, T., 2009. Can parameter instability explain the meese-rogoff puzzle? In: NBER International Seminar on Macroeconomics, 6. JSTOR, pp. 125–173. Bai, J., Perron, P., 2003. Computation and analysis of multiple structural change models. J. Appl. Econom. 18 (1), 1–22. Bakshi, G., Panayotov, G., Skoulakis, G., 2013. In Search of explanation for the predictive ability of the baltic dry index for global stock returns, commodity returns, and global economic activity. University of Maryland Working Paper. Barberis, N., Shleifer, A., Vishny, R., 1998. A model of investor sentiment. J. Financ. Econ. 49 (3), 307–343. Baumeister, C., Kilian, L., 2015. Forecasting the real price of oil in a changing world: a forecast combination approach. J. Bus. Econ. Stat. 33 (3), 338–351. Bernanke, B.S., Gertler, M., Watson, M., Sims, C.A., Friedman, B.M., 1997. Systematic monetary policy and the effects of oil price shocks. Brook. Pap. Econ. Act. 1997 (1), 91–157. Bodenstein, M., Guerrieri, L., Kilian, L., 2012. Monetary policy responses to oil price fluctuations. IMF Econ. Rev. 60 (4), 470–504. Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. J. Econom. 31 (3), 307–327. Bollerslev, T., Tauchen, G., Zhou, H., 2009. Expected stock returns and variance risk premia. Rev. Financ. Stud. 22 (11), 4463–4492.

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