Consumption Fluctuations and Expected Returns

Transcription

1 Consumption Fluctuations and Expected Returns Victoria Atanasov, Stig Vinther Møller, and Richard Priestley Abstract This paper introduces a new consumption-based variable, cyclical consumption, and examines its predictive properties for excess stock returns. Future expected stock returns are high when aggregate consumption falls relative to its past values and cyclical consumption is low. This empirical evidence ties consumption decisions of agents to time-variation in expected excess returns in a manner consistent with rational asset pricing. The predictive power of cyclical consumption is not confined to bad times and subsumes the predictability of almost all popular forecasting variables which track economic recessions. We also show that cyclical consumption fluctuations cannot anticipate future changes in cash-flow growth rates. In all, these results appear compatible with prominent explanations of asset prices based on time-varying risk premia such as models with habit formation mechanisms. JEL Classification: G10, G12, G17. Keywords: cyclical consumption fluctuations, time-varying expected stock returns, predictability. Chair of Finance, University of Mannheim, L9 1-2, Mannheim, Germany. atanasov@uni-mannheim.de, phone: CREATES, Aarhus University, Fuglesangs allé 4, DK-8210 Aarhus V., Denmark. svm@econ.au.dk, phone: Department of Finance, BI Norwegian Business School, Nydalsveien 37, N 0444 Oslo, Norway. richard.priestley@bi.no, phone:

2 1 Introduction Stock return predictability has been linked to the identification of good and bad times in the economy that might capture variation in investors preferences or the quantity of risk. Cochrane (2017) asks "just what are the bad times...in which investors are particularly anxious that their stocks do not fall? Well something about recessions is an obvious candidate." and further "But what is the feared event exactly? How do we measure the event?". Measuring recessions in the economy has been at the forefront of identifying bad times. 1 Perhaps the often reported diffi culty in finding consistent results regarding predictability (see, for example, Welch and Goyal (2008)) is due to the weakness we have in identifying bad times either because we empirically measure recessions poorly or because bad times are better described another way. In this paper, we take a novel and more direct approach to linking stock return predictability to bad economic times. This is the first paper that studies the role of cyclical fluctuations in consumption for predicting changes in stock market prices and therefore ties time-variation in returns directly to investors consumption decisions in a manner consistent with rational asset pricing. Cyclical consumption emerges as a strong predictor of excess stock returns both in-sample and out-of-sample. This finding is comforting because it relates expected return variation to macroeconomic fluctuations suggesting that asset prices are driven by primitive shocks and not other asset prices as is the case when using different measures of interest rate spreads, earnings and dividend yields or other price-to-fundamentals ratios. To extract the cyclical component of consumption, we employ a simple and robust linear projection method of Hamilton (2017). This procedure is advantageous in several 1 For example, the predictive ability of interest rates and term and default spreads (Fama and Schwert (1977), Fama (1981), Keim and Stambaugh (1986), Fama and French (1989), and Ang and Bekaert (2007)), dividend price ratios (Campbell and Shiller (1988) and Fama and French (1988)), and the output gap (Cooper and Priestley (2009)) has been advocated on grounds that these variables follow business cycle patterns (recessions) that might track time-variation in expected returns. 2

3 important respects. First, is ensures that the identified cyclical component is consistently estimated for a wide range of nonstationary processes. Second, it produces a series which is accurately related to the underlying economic fluctuations as opposed to, for instance, the popular Hodrick and Prescott (1997) filter which can spuriously generate dynamic relations. This feature is particularly appealing because it implies that the predictive ability of cyclical consumption reflects the true predictability rather than a statistical artifact. Finally, cyclical consumption fluctuations that we identify reveal stable out-ofsample properties. We explore a variety of alternative specifications based on different aggregates of consumer spending classified by the type of good and utilize other econometric procedures to isolate cyclical variation in consumption including polynomial time trends and backward-looking moving averages. Our choice of the detrending procedure of Hamilton (2017) as a benchmark specification provides a conservative and robust view of return predictability. We argue that the forecasting power of cyclical consumption arises as a result of rational variation in expected returns. When aggregate consumption increases relative to its past history, high cyclical component will lower the marginal utility of consumption and stimulate investment, forcing a rise in prices and a decline in future expected returns. Conversely, when aggregate consumption declines relative to its past values, low cyclical component will increase the marginal utility of consumption and prompt a rise in future expected returns to clear the markets. Intuitively, cyclical consumption should be useful in picking out bad and good times in the economy and hence likely to be informative about future returns, consistent with what we find. The empirical results we present confirm the idea that future expected stock returns are high (low) when cyclical consumption is low (high). Our findings appear consistent with consumption-based explanations of asset prices which generate time-varying risk premia. One prominent example is the habit formation 3

4 model of Campbell and Cochrane (1999) in which time-variation in expected stock returns is driven by shocks to the current level of consumption that move consumption in relation to its past realization (see also, Cochrane (2017)). In the model, habit acts as a trend for consumption: As consumption declines relative to the trend in a recession, people become more risk-averse, stock prices fall, and future expected returns rise. Cyclical consumption analogously describes deviations of actual consumption from its hypothesized value which is determined by past consumption realizations. We also find that virtually none of the variation in expected cash-flow growth can be attributed to consumption fluctuations. This result is interesting and reminds of another central feature of the habit model where aggregate consumption and dividends are assumed to follow a random walk. While this circumstance renders a danger that detrended consumption is spurious, econometrically, it is a challenging task to distinguish between a purely i.i.d. process and one which incorporates a small persistent component in finite samples. While we do not exclude the possibility of sizable effects of fluctuations in expected growth and aggregate economic uncertainty on asset valuations as emphasized for example by long-run risk models in Bansal and Yaron (2004), we argue that the channel of time-varying price of market risk can by itself go a long way to help understand market movements. We perform a battery of robustness checks and address a number of econometric concerns surrounding predictive regressions with persistent predictors (Nelson and Kim (1993) and Stambaugh (1999)). Both a novel IVX testing approach of Kostakis, Magdalinos, and Stamatogiannis (2015) that robustifies the inference to the degree of regressor s persistence, and an advanced bootstrap procedure that accounts for the regressor s timeseries properties indicate strong evidence of predictability at the one-quarter horizon which extends to horizons of about five years. Robust patterns of predictability exist across U.S. decile portfolios sorted on industry and fifteen various financial characteris- 4

5 tics including size, several price-to-fundamentals ratios, momentum, reversal, operating profitability, investment, accruals, net share issues and variance and in all the remaining G7 countries. The predictability does not vanish during the recent post-oil-crisis period in which standard popular business cycle indicators have proven dismal as predictive variables (Welch and Goyal (2008)). Further, we show that the predictive power of cyclical consumption is not confined to times of crisis and, therefore, unlikely to reflect only negative shocks based on institutional or intermediation factors that have been emphasized in the literature as an explanation of the recent sub-prime financial crisis. Cyclical consumption seems hence to provide a consistent description of how positive and negative macroeconomic events affect stock markets. These results are notable because they stand in stark contrast to Henkel, Martin, and Nardari (2011) and Golez and Koudijs (2018) who find that popular predictor variables are successful only in bad times as defined by economic recessions, while there is essentially no evidence of predictability in good times, that is, during business cycle expansions. Generally, there is not much evidence in favor of returns being predictable from aggregate consumption. Perhaps the most prominent consumption-based predictive variable is Lettau and Ludvigson s (2001) consumption-wealth ratio. If valid, a log-linearized approximation to an aggregate budget constraint implies that an empirical analogue to the consumption-wealth ratio can be obtained as a residual from a cointegrating relation between consumption, financial asset wealth, and labor income. 2 We find that cyclical consumption contains predictive information which goes clearly over and above that of many well-recognized variables that track economic recessions, including the consumption-wealth ratio of Lettau and Ludvigson (2001), the ratio of labor income to consumption of Santos and Versonesi (2006), and conditional volatility of consumption 2 Byrne and Davis (2003) and Rudd and Whelan (2006) cast doubts about the precision of this approximation and the out-of-sample properties of the consumption-wealth ratio and question its robustness to the use of theoretically consistent aggregate data. 5

6 of Bansal, Khatchatrian, and Yaron (2005). We consider nineteen alternative recessionbased economic variables from the extant literature and find that only two of them reveal a significant out-of-sample predictive power which is complementary to that of cyclical consumption. Our work relates also to a number of recent papers that attempt to reconcile the failure of the standard consumption-based capital asset pricing model (CCAPM) of Lucas (1978) and Breeden (1979) to explain the equity premium and return predictability which stands as a central stylized fact in the macro-finance literature. Since the early contribution of Hansen and Singleton (1983), many have argued that these deficiencies are related to imperfections in the measurement of consumption. In this vein, Savov (2011) advocates more recently the use of the municipal solid waste as a stand-in for consumption in empirical asset pricing tests. Kroencke (2017) argues that a simple model of the filter process which removes the persistent component of aggregate consumption matches well the equity premium with plausible risk aversion preferences and considerably improves the fit of the habit model. The paper proceeds as follows. Section 2 explains how we construct cyclical consumption. Section 3 presents the benchmark results from our predictive analysis. A number of robustness tests are summarized in Section 4. Section 5 compares the forecasting ability of alternative predictor variables to that of cyclical consumption. Section 6 concludes. 2 Extracting cyclical consumption To measure consumption, we use aggregate seasonally adjusted consumption expenditures on nondurables and services from the National Income and Product Accounts (NIPA) Table 7.1 constructed by the Bureau of Economic Analysis (BEA) in the Department of Commerce of the United States. The data are quarterly, in real per capita terms, 6

7 measured in 2009 chain weighted dollars, and span the period from the first quarter of 1947 to the fourth quarter of To extract the cyclical component of consumption, we employ a simple and robust linear projection method of Hamilton (2017) and regress the log of real aggregate consumption series, c t, on a constant and four lagged values of c as of date t k: c t = b 0 + b 1 c t k + b 2 c t k 1 + b 3 c t k 2 + b 4 c t k 3 + e t, (1) where the residual measures cyclical consumption, cc: cc t = c t b 0 b 1 c t k b 2 c t k 1 b 3 c t k 2 b 4 c t k 3. (2) Hamilton (2017) notes that this procedure has two important advantages. First, it ensures that the identified cyclical component is consistently estimated for a wide range of nonstationary processes. Second, it offers a reasonable model-free way to construct a time series which is accurately related to the actual economic fluctuations as opposed to, for instance, the Hodrick and Prescott (1997) filter which spuriously generates series with dynamics that have no relation to the underlying data-generating process. This property is appealing because it guarantees that the predictive ability of cc for the future values of another variable reflects the true predictability rather than a statistical artifact. 3 An empirical implementation of Equation (1) requires a choice of k. Given that our goal is to capture a slowly moving but transient variation in the risk premium along the lines of the habit formation model of Campbell and Cochrane (1999), we follow the recommendation of Hamilton (2017) and compute cc using a value of six years (k = 24). 4 3 While the OLS coeffi cients in Equation (2) rely on future observations, this influence vanishes asymptotically. Although there exist a number of modern treatments of nonlinear filters, linear filtering theory is generally better understood (see also, Stock and Watson (1999)). 4 We investigated the forecasting power of cyclical consumption for future stock returns at various horizons k ranging from one quarter up to ten years (k = 1, 2,..., 40) and found that the results are generally robust toward other choices of k in the interval of 5-10 years. 7

8 Figure 1 shows a plot of cc along with recession dates as defined by the NBER. Cyclical consumption has an unconditional mean of zero by construction, a standard deviation of 3.74%, and a first order autocorrelation of 0.97 corresponding to a half-life of about 6 years, which implies highly persistent expected returns in the return forecasting regressions in line with Campbell and Cochrane (1999), Pastor and Stambaugh (2009), and van Binsbergen and Koijen (2010). 5 The figure illustrates that cc exhibits significant fluctuations in the postwar period: It typically reaches its highest values some time before the onset of recessions, and falls throughout economic contractions. 3 Predictive regression analysis We investigate the forecasting ability of cyclical consumption for stock returns on the S&P 500 index and the CRSP value-weighted index. Excess returns are computed by subtracting the return on the 30-day Treasury-bill rate from the actual stock return. To calculate real returns, we deflate nominal returns with the U.S. inflation rate, measured by the growth rate of the aggregate consumer price index (CPI) from the Bureau of Labor Statistics. For the in-sample analysis, we use the most recently available finally revised consumption figures and full-sample parameter estimates in Equation (1). For out-ofsample tests, we use real-time consumption vintages and ensure that the estimate of cc at time t is based on data and parameter estimates which were available to the investor at time t. 6 5 For comparison, Lettau and Ludvigson (2013) identify a risk aversion shock with a half-life of over four years. 6 We also consider a scenario when the predictive regression is estimated recursively, but cc is computed over the full sample. This estimation procedure trades-off effi ciency gains against the "look-ahead-bias" (Lettau and Ludvigson (2001) and Welch and Goyal (2008)). 8

9 3.1 Basic return predictive regressions We test the ability of cyclical consumption to capture time-variation in expected returns by estimating the following predictive regression model: r t+h = α + βcc t 1 + ε t+h, (3) where h denotes the horizon in quarters, r t+h is h-quarter log stock market return, and cc t 1 is two-quarter lagged cyclical consumption. We include a second lag of cc in the regression to account for delays in macroeconomic releases. 7 To test the significance of β in Equation (3), we use the Newey and West (1987) heteroskedasticity- and autocorrelationrobust t-statistic (truncated at lag h; our results are robust towards other choices of truncation lags). Table 1 reports our benchmark findings. It shows the OLS estimates of β, the corresponding t-statistics (in parentheses), and the adjusted R 2 s, R2, (in square brackets) from simple forecasting regressions of log stock returns on the two-quarter lagged values of cyclical consumption, cc. When considering the results for excess returns in Panel A of Table 1, we find that the sign of the estimated coeffi cient on cc is significantly negative at standard levels of significance across all values of h. Thus, expected returns are low when cyclical consumption is high in economic upswings, and expected returns are high when cyclical consumption is low in economic downturns. This result is consistent with investors responding rationally to countercyclical variation in the price of consumption risk over time: A fall in consumption relative to its past history indicates bad times of high marginal utility of consumption and high future expected returns. The predictive 7 The U.S. Bureau of Economic Analysis (BEA) at the Department of Commerce typically releases the "advance", "second", and "third" estimates of NIPA consumption expenditure for quarter t near the end of the first, second, and third months of quarter t + 1, respectively. Annual revisions, which generally cover the quarters of the three most recent calendar years, are usually carried out each summer and incorporate newly available major annual source data. Comprehensive revisions are carried out at about five-year intervals and incorporate major periodic source data and changes in concepts and methods. 9

10 impact of cyclical consumption is economically large: the point estimate of β in the quarterly regression on the S&P 500 index (first row, first column in Table 1) is -1.6 in annual terms. This figure implies that a fall in cc by one standard deviation below its mean leads to a rise in the expected return of about 6 percentage points at an annual rate. The estimate of the coeffi cient is strongly statistically significant and the associated R 2 is 3.07%. The R 2 statistics tend to increase with the horizon. The results for real and actual returns and for the broader CRSP value-weighted index are qualitatively similar. A general concern with predictability regressions is that their reliability can be undermined by the uncertainty regarding the order of integration of the predictor variable. Statistical inference can be unreliable when the predictor variable is persistent and its innovations are highly correlated with returns (Nelson and Kim (1993) and Stambaugh (1999)). Modelling the predictive variables as local-to-unity processes can lead to invalid inference if the regressor contains stationary or near-stationary components (Valkanov (2003), Lewellen (2004), Campbell and Yogo (2006), and Hjalmarsson (2011)). We address these econometric concerns in two ways. First, we compute empirical p-values for the slope estimates from a wild bootstrap procedure that accounts for the persistence in regressors and correlations between equity stock return and predictor innovations, and allows for general forms of heteroskedasticity. This simulation produces an empirical distribution that better approximates the finite sample distribution of the slope estimates in Equation (3). 8 Second, we employ a novel IVX testing approach of Kostakis, Magdalinos, and Stamatogiannis (2015) that is robust to the regressor s degree of persistence (including unit root, local-to-unit root, near-stationary or stationary persistence classes) and has good size and power properties. This approach alleviates practical concerns about 8 In fact, since cc is a purely macroeconomic variable, its innovations have lower correlation with the innovations in returns, which almost eliminates the small sample bias. For more powerful tests, we follow the recommendation of Inoue and Kilian (2004) and calculate p-values for a one-sided alternative hypothesis (see also, Neely, Rapach, Tu, and Zhou (2014) and Rapach, Ringgenberg, and Zhou (2016)). We summarize the details of the bootstrap algorithm in the appendix. 10

11 the quality of inference under possible misspecification of the (generally unobservable) time-series properties of the regressor in long-horizon predictive regressions. Table 2 reports the results using their IVX estimator to test the significance of β. We find that the null hypothesis of no predictability can be usually rejected at the 1% level. In summary, we show that stock returns are predictable by cyclical consumption fluctuations at various business cycle horizons over the period. Expected returns are high when consumption falls relative to its past history and marginal utility of consumption increases. In bad times, investors want to consume more and require a higher expected premium as a compensation for bearing risk. These findings constitute new evidence of time-varying risk premia which ties stock return predictability directly to fluctuations in consumption as in investors first order conditions in the classical consumption-based capital asset pricing model (CCAPM) of Lucas (1978) and Breeden (1979). Our results also relate to a number of more recent contributions which argue that the dismal performance of the standard CCAPM can be attributed to our poor ability to measure consumption appropriately (Savov (2011) and Kroencke (2017)). 3.2 Alternative detrending methods Since there is no a priori theoretical guideline regarding a choice of an appropriate econometric procedure to isolate a cyclical component of consumption, it is instructive to compare the predictive ability of cc with other measures of cyclical consumption. In the following, we consider five such definitions. First, we follow a voluminous literature in macroeconomics and finance and assume a secular linear upward trend in consumption: c t = b 0 + b 1 t + e t, (4) where the residual measures the cyclical consumption, cc. A second technique extends a linear trend formulation to allow for a breakpoint. This procedure makes it possible to 11

12 account for a well-known fall in the macroeconomic risk, or the volatility of the aggregate economy, at the beginning of the 1990s 9 : c t = b 0 + b 1 t + e t for t t 1, c t = b 0 + b 1 t + b 2 (t t 1 ) + e t for t > t 1, (5) where the breakpoint t 1 corresponds to the first quarter of 1992 (see also, Lettau, Ludvigson, and Wachter (2008)). Essentially, Equation (5) presents a piecewise OLS regression which fits two separate lines to the disconnected data around the break date. Next, we allow for higher order time polynomials such as a quadratic time trend model which conveniently accounts for slowly changing trends by establishing a quadratic exposure estimate b 2 that can intensify or diminish the linear time trend: c t = b 0 + b 1 t + b 2 t 2 + e t, (6) and a cubic representation: c t = b 0 + b 1 t + b 2 t 2 + b 3 t 3 + e t. (7) Finally, we follow Campbell (1991) and Hodrick (1992) and calculate a "stochastically detrended" consumption series as a backward-looking moving average based on a five-year window, where cc in quarter t is equal to the difference between the natural logarithm of consumption in quarter t and the average of the natural logarithm of consumption in quarters t-20 to t The six measures of cyclical consumption that we identify display cross-correlations of 0.39 to 0.92 with autoregressive coeffi cients in the range from An extensive body of the macroeconomic literature finds evidence of a regime shift to lower volatility of real macroeconomic activity occuring in the last two decades of the 20th century (see e.g. McConnell and Perez-Quiros (2000) and Stock and Watson (2002)). 10 We obtain similar results for windows of three or four years. 12

13 to Table 3 reports estimation results for the predictive regression in Equation (3) for alternative measures of cc. Cyclical consumption displays stable and robust predictive power. Compared to the results in Table 1, the breaking and cubic detrending methods in Table 3 yield systematically higher R 2 statistics at any forecasting horizon. These results demonstrate that our choice of the linear projection procedure of Hamilton (2017) as our benchmark specification provides a conservative view of return predictability. Further, the question regarding which method should be employed to isolate cyclical variation in consumption appears largely irrelevant since all methods reveal substantial return predictability. 3.3 Out-of-sample analysis Welch and Goyal (2008) show that in-sample predictability does not necessarily imply that investors can benefit from a better portfolio allocation and that most variables that have been used to predict stock returns in the extant literature perform poorly out-ofsample. There are two reasons that can cause out-of-sample forecasts to differ from in-sample forecasts. First, in out-of-sample forecasts, the coeffi cients in the predictive model could change over time. Second, the macroeconomic time series available today could differ from those which were available in real time due to ongoing data revisions. To address these concerns, we construct a real-time data set for cc based on vintage data from the Archival Federal Reserve Economic Data (ALFRED) database of the Bureau of Economic Analysis at the Federal Reserve Bank of St. Louis with data observations from each vintage starting in 1947Q1. Because vintage data on population estimates of the Bureau of Economic Analysis can be downloaded only for the period after 1999, we use total consumption expenditure for nondurable goods and services in the out-of-sample calculations. Following Møller and Rangvid (2015) we assume that the 13

14 real-time practitioner uses the final estimates from each vintage which typically become available in the last month of each quarter. To gauge the situation of an investor operating in real time, we reestimate the parameters in cc recursively every period, based upon an expanding window and data available at the time of the forecast. At a cost of a larger sampling error in the early estimation recursions, this technique provides a means to circumvent a so-called "look-ahead" bias (Brennan and Xia (2005) and Lettau and Ludvigson (2005)) Out-of-sample test statistics To guard against a possibility that our conclusions are affected by any particular period, we consider three different out-of-sample forecast evaluation periods: , , and We follow Welch and Goyal (2008) and Campbell and Thompson (2008) and choose the first sub-sample to start in The second sub-period corresponds to the sample studied by Rapach, Ringgenberg, and Zhou (2016). Finally, we evaluate a recent post-2000 period for purposes of comparison with Rapach, Strauss, and Zhou (2010). For nested forecast comparison tests, we specify a model of constant expected returns, that is, a benchmark model where a constant is the sole explanatory variable. The constant expected return model is a restricted nested version of an unrestricted model of time-varying expected returns which includes both a constant and cc as predictive variables. Accordingly, we evaluate whether our return predictions are more precise than predictions from the prevailing mean model. For example, Welch and Goyal (2008) show that the historical average forecast is a very stringent out-of-sample benchmark Starting the out-of-sample evaluation in 1980Q1 provides a reasonably long initial in-sample period for reliably estimating the parameters used to generate the first predictive regression forecast. For consistency with the in-sample analysis, we take publication lags into account and use a two-quarter lagged value of cc in out-of-sample calculations. The results for one-quarter-ahead returns are qualitatively similar. 12 We find that an autoregressive model that includes a constant and lagged dependent variable with lag 14

15 The assessment of out-of-sample predictability involves four metrics. The first statistic we report is the powerful ENC-NEW statistic of Clark and McCracken (2001) which extends the encompassing test of Harvey, Leybourne, and Newbold (1998) by deriving a nonstandard asymptotic distribution of this test statistic under the null of nested forecasts. The ENC-NEW statistic tests the null hypothesis that the restricted forecasting model encompasses the unrestricted forecasting model; the alternative is that the timevarying expected return model contains information that could be used to significantly improve the forecast of the constant expected return model. The second is the MSE-F statistic of McCracken (2007) which tests the null hypothesis that the restricted forecasting model has a mean squared error (MSE) that is less than or equal to that of the unrestricted forecasting model; the alternative is that the unrestricted model has smaller MSE. The third test is the out-of-sample R 2 OOS statistic of Campbell and Thompson (2008) which measures the proportional reduction (or increase) in the MSE of the unrestricted model relative to the MSE of the prevailing mean benchmark forecast. The ROOS 2 statistic is measured in units that are comparable to the in-sample R 2. The ROOS 2 takes positive (negative) values when the predictive regression model predicts better (worse) than the historical mean. The critical values for these statistics are obtained from the bootstrap procedure described in the appendix. Finally, to measure the economic value of the equity premium forecasts, we follow Campbell and Thompson (2008) and compute the certainty equivalent return (CER) for an investor with mean-variance preferences who allocates across stocks and risk-free bills using the time-varying expected returns model relative to the historical mean return forecast. At the end of each quarter t, we calculate the optimal weight of equities in quarter t + 1: length selection based on AIC and BIC information criteria does not improve, and often even degrades the out-of-sample predictive power of a regression that uses just a constant term. Hence, we show comparison tests with the more parsimonious model of a constant expected return as a benchmark. 15

16 w t,h = 1 r t+h γ σ 2, (8) t+h where r t+h is a forecast of h-quarter excess return, σ 2 t+h is a forecast of its variance, and γ is the risk aversion coeffi cient. The share 1 w t,h is allocated to risk-free bills, and the respective portfolio return is given by r p,t+h = w t,h r t+h + r f,t+h. (9) We use a rolling ten-year window of past returns to estimate the variance, constrain w t,h to lie between 0 and 1.5, i.e. preventing investors from shorting stocks or taking more than 50% leverage, and assume a risk aversion aversion coeffi cient of two. The portfolio CER can then be computed as CER p = µ p 0.5γ σ 2 p, (10) where µ p and σ 2 p are the mean and variance, respectively, for the investor s portfolio over the forecast evaluation period. The CER gain is the difference between the CER for an investor who uses a predictive regression forecast and the CER for an investor who uses the historical average forecast. We multiply this difference by 400, so that it can be interpreted as the percentage portfolio management fee that an investor would be willing to pay each year to have access to the predictive regression forecast in place of a prevailing mean forecast Baseline out-of-sample results In Table 4, we show results of out-of-sample predictions of the log excess return on the S&P 500 index over various horizons ranging from one quarter to five years. We generally 16

17 find that the unrestricted model generates significantly better forecasts than the restricted model. For instance, the ENC-NEW encompassing test rejects the null hypothesis that the forecasts from the constant expected return model encompass the forecasts from the time-varying expected return model at the 1% level for all horizons and all forecasting periods that we consider. The MSE-F test significantly rejects the null hypothesis that the MSEs from the unrestricted model are bigger than or equal to those from the historical average return. The out-of-sample R 2 OOS statistics in Table 4 are all positive, meaning that cc delivers a lower average forecasting error than the historical average forecast. For example, at the one-quarter horizon, the R 2 OOS is 3.73% when we forecast from 1990, 5.08% when we forecast from 1990, and 6.43% when we forecast from Campbell and Thompson (2008) show that the correct way to judge the magnitude of the out-of-sample R 2 is to compare it with the squared Sharpe ratio for the portfolio that is predicted. A ratio of the two provides an estimate of the increase in return that can be obtained for a mean-variance investor if this investor relies on information contained in the predictive variable when making portfolio decisions. The out-of-sample R 2 is 3.73% when predicting next quarter log S&P 500 excess return over the post-1980 period; the respective squared Sharpe ratio is 2.86%. This implies that a mean-variance investor would increase the average quarterly portfolio return by about 30% if relying on return forecast generated by cc. The absolute increase in portfolio return depends on risk aversion, but is about 15% per year for an investor with a unity risk aversion, and about 7.5% per year for an investor with a risk aversion of two. This return enhancement for a market timer who allocates his investment optimally between the stock market and the risk-free asset comes in part from taking on greater risk. The associated welfare gain for a mean-variance investor with relative risk aversion of three is provided in Table 4 in the row labeled "CER gain". We find reliably positive and sizable CER gains for each time horizon. These gains tend to increase up to time 17

18 horizons of two years and decline thereafter. 13 We draw broadly consistent conclusions regarding out-of-sample predictability from a series of robustness checks. For instance, we conduct additional tests based on fixed fullsample parameter values or when relying on today-available, i.e. revised, consumption data. Similar conclusions emerge also from tests with one-quarter lagged value of cc, tests with autoregressive benchmark model, tests with the CRSP index return, and tests with actual and real returns. To summarize, our results show that cyclical consumption fluctuations that we identify display statistically significant out-of-sample predictive power for aggregate stock market returns. This is the case if an investor started a forecast in 1980, 1990, or These results are in contrast to Welch and Goyal (2008) who accentuate that a long list of popular business cycle predictor variables have been unsuccessful out-of-sample in the last few decades. 3.4 Predicting stock returns in good and bad times Several popular predictor variables are successful in bad times as defined by recessions but turn out disappointing in good times, that is, during business cycle expansions (Rapach, Strauss, and Zhou (2010), Henkel, Martin, and Nardari (2011), Dangl and Halling (2012), and Golez and Koudijs (2018)). Cujean and Hasler (2017) develop a theoretical mechanism with heterogeneous agents that causes stock return predictability to concentrate in bad times. In general, explanations that emphasize the role of financial institutions and intermediation coupled with frictions and market segmentation since the sub-prime financial crisis might be useful in capturing a propagation of a shock in bad times, but they are less likely to rationalize stock market behavior in normal and good 13 Differences between CER gains and out-of-sample R 2 statistics are at least partly due to the estimated variance of stock return that is necessary to calculate the CER gains. The utility gains reported in Table 4 are limited by the leverage constraint but do not take into account transaction costs. 18

19 times. To examine whether the relationship between future returns and cyclical consumption is only present in bad economic times, we estimate a linear two-state predictive regression model similar in a spirit to Boyd, Hu, and Jagannathan (2005): r t+h = α + β bad I bad cc t + β good (1 I bad ) cc t + ε t+h, (11) where I bad denotes the state indicator that equals one during recessions and zero otherwise, β bad and β good are the slope coeffi cients which measure the return predictability in bad and good times, respectively, and cc t is one-quarter lagged cyclical consumption. We follow Henkel, Martin, and Nardari (2011) and use the NBER-dated chronology of expansions and recessions to identify good and bad times ex post. For consistency with our previous analysis, Table 5 presents the results for excess, real, and actual returns. We find consistent predictability patterns across different horizons. Similar to Henkel, Martin, and Nardari (2011) and Dangl and Halling (2012), our estimates suggest that the expected returns adjust more during recessions than during expansions. 14 However, in contrast to these studies, we find that the estimated slope coeffi cient is negative and statistically significant both in recessions and expansions. We find a coherent pattern in the β bad and β good estimates which increase (in absolute values) steadily with the horizon. The R 2 statistics in Table 5 climb from around 2-3% for quarterly returns to levels of around 20-30% at horizons of five years. The results we present point toward a further notable property of cyclical consumption, namely, its ability to meaningfully capture time-variation in expected risk premiums independently of the economic state. This feature is important because it re-establishes the predictive ability of cyclical consumption in contrast to numerous traditional predictor 14 Over the full sample period, the NBER s Business Cycle Dating Committee identifies 222 quarters as expansions and the remaining 34 quarters as recessions (contractions). 19

20 variables whose forecastability is usually confined to bad economic times. 3.5 Cash-flow predictability In the previous analysis, we argue that the predictive ability of cyclical consumption for future stock returns is consistent with basic insights of structural asset pricing models which generate cyclical variation in the price of risk. One prominent example is the habit formation framework of Campbell and Cochrane (1999) which emphasizes a positive effect of today s consumption on tomorrow s marginal utility of consumption. Briefly, a fall in consumption relative to its recent history signals bad times when marginal utility of consumption and future required stock returns are high. This section aims to examine the behavior of cyclical consumption from a perspective of another essential feature of the habit model, namely, nonpredictability of cash-flow growth rates. In the habit model, log consumption is assumed to follow a random walk mirroring the observation that most countries do not have highly predictable consumption or dividend growth rates (Campbell (1999)). 15 To address this question we estimate simple predictive regressions of the form: y t+h = α + βcc t + ε t+h, (12) where y t+h denotes h-quarter log growth rate in aggregate consumption, total dividends or earnings, and cc t is one-quarter lagged cyclical consumption. The results in Table 6 indicate absence of cash-flow predictability in the postwar U.S. data in statistical terms. This result applies to all three cash-flow measures that we consider at any time horizon between one quarter and five years. We find R 2 statistics 15 By contrast, the long-run risk model of Bansal and Yaron (2004) highlights the role of persistent movements in consumption growth and volatility for asset prices and implies predictabile varation in cash flows. 20

21 which are negative or close to zero. The fact that future cash flows are not predictable out of cyclical consumption is interesting and fits well with the return predictability that we documented above. In particular, both findings appear consistent with explanations of asset prices where changes in consumption in relation to its past and current values generate changes in the risk attitude of agents and thus yield predictable movements in excess stock returns (Campbell and Cochrane (1999)). 4 Robustness tests In this section, we investigate the predictive ability of cyclical consumption from a crosssectional perspective, explore the robustness of our results to changes in the length of the sample period and alternative empirical measures of consumption, and examine international evidence. 4.1 Stock portfolios sorted on characteristics In the preceding analysis, we have assessed the predictability of stock returns by means of two commonly used stock market indices that give a broad view of the behavior of the aggregate equity premium. In what follows, we investigate how well our predictor variable can forecast U.S. portfolios of stocks sorted on industry SIC codes and 15 various financial characteristics including market equity, book-to-market equity, earnings-price and cashflow-price ratios, dividend yield, momentum, short-term and long-term reversals, operating profitability, investment, accruals, market beta, net share issues, and total and residual variances. 16 Table 7 reports the estimation results from in-sample univariate predictive regressions for each of the 10 decile portfolios sorted across the 16 alternative criteria. The tests are 16 The portfolio data are from Ken French s homepage. 21

22 conducted over the longest possible sample period, that is, starting in the first quarter of 1954 or the third quarter of 1963 depending on data availability. A general result is that cyclical consumption fluctuations strongly negatively predict the entire cross-section of returns and hence further reinforce our benchmark results. We find that only two of the 160 estimated coeffi cients are not statistically significant at the 5% level according to bootstrap p-values. These results emphasize that time-varying expected rates of return across a large number of portfolio sorts contain a common macroeconomic component. 4.2 Temporal stability of estimates Welch and Goyal (2008) and Campbell and Thompson (2008) highlight that many business cycle predictor variables have performed particularly poorly both in-sample and out-of-sample after the oil price crisis in the 1970s. To address this point, Table 8 reexamines the empirical evidence of predictability over the post-1980 period which includes the great equity bull market at the end of the twentieth century. Our estimates reveal that the predictive ability of cyclical consumption in the latter part of the sample is comparable to and often stronger than that over the full sample. The estimates in Table 8 show statistical significance for returns at various horizons and R 2 values which are often well beyond those reported in Table 1. This observation stands in contrast to many other predictor variables which record a reduction in the extent of predictability in the post-oil-price-crisis of the mid 1970s. We obtain similar results in three other episodes of the economic history: in the post-1965 data (see also, Welch and Goyal (2008)); a period predating the global financial crisis; and a sample which omits the data in the aftermath of the run-up in prices in the early 2000s. The explanatory ability of cyclical consumption fluctuations is not confined to any particular period and is not concentrated in sub-samples with severe crises, a pattern often found in the literature. We also study the temporal stability of the β estimates in Equation (3) to structural 22

23 breaks as prescribed by Elliott and Müller (2006). Their proposed qll test statistic for the hypothesis that β t = β for all t and any h is particularly useful in the context of predictive regressions because it is asymptotically effi cient for a wide range of data-generating processes, has superior size properties in small samples than other popular statistics, and is simple to construct. Moreover, the simulation analysis in Paye and Timmermann (2006) shows that the test of Elliott and Müller (2006) possesses excellent finite sample size properties even in the presence of highly persistent lagged endogenous predictors. We find that the qll statistics for our benchmark estimates are never significant at any horizon (not reported). 4.3 Alternative consumption measures As explained in Section 2, our main empirical analysis conventionally focuses on real per capita NIPA expenditure on nondurable goods and services as a proxy of aggregate consumption. In this section, we consider the predictive ability of cyclical consumption extracted from various subcategories of personal consumption expenditure (PCE) including i) nondurable goods (NON), ii) services (SERV), iii) durable goods (DUR), iv) the stock of durable goods (SDUR) constructed from the year-end estimates of the chained quantity index for the net stock of consumer durable goods published by the Bureau of Economic Analysis (BEA) following Yogo (2006), v) nondurable and durable goods (GOODS), and vi) total aggregate PCE. Table 9 shows results from our benchmark regression (3) applied to the log excess return on the S&P 500 index. The predictive power of cyclical consumption varies across expenditure aggregates. This is result reinforces Wilcox (1992) who recommends to treat expenditures for goods and services separately in empirical work. 17 Another noticeable pattern is the strong performance of nondurable goods in terms of coeffi cient magnitudes, 17 Relatedly, Kroencke s (2017) filter model shows that NIPA nondurables suffer less from measurement errors than NIPA services. 23

24 statistical significance, and R 2 measures. Further, at horizons of two years and above, we often find stronger predictability based on alternative PCE categories in Table 9 than in Table 1 and this further highlights the conservative nature of our benchmark results derived from nondurables and services. 4.4 International evidence The empirical ability of U.S. financial indicators to predict foreign excess returns is well documented since Bekaert and Hodrick (1992), Campbell and Hamao (1992) and Ferson and Harvey (1993). More recently, Rapach, Strauss, and Zhou (2013) show that lagged U.S. returns significantly predict returns in numerous industrialized countries. Motivated by these studies, we ask whether U.S. cyclical consumption can anticipate time-variation in excess returns in the remaining G7 countries: Canada, France, Germany, Italy, Japan, and the United Kingdom. To answer this question, we follow Solnik (1993), Ang and Bekaert (2007), Hjalmarsson (2010), and Rapach, Strauss, and Zhou (2013) and collect international total return indexes in national currency from Morgan Stanley Capital International (MSCI) available since Quarterly excess return series are calculated by subtracting the local short-term interest rates from the OECD database. For the G7 index, we use the three-month interbank rate for Germany as a short-term rate. Table 10 presents international evidence regarding stock return predictability over the period. To facilitate comparisons, we also include results for the United States over this shorter sample and for the aggregate G7 index for which the MSCI data are recorded since the beginning of We generally find a stable negative relation between cyclical consumption and future stock returns in each country as well as for the aggregate G7 index. The consistency of the estimated sign, its size, and statistical significance provide evidence that cyclical consumption is useful in tracking future movements in local market equity returns. These results are consistent with our benchmark findings for 24

25 the U.S. and they suggest that our conclusions are probably not caused by overfitting or data snooping (Lo and MacKinley (1990) and Bossaerts and Hillion (1999)). 5 Alternative predictor variables Is the information contained in cyclical consumption independent of other well known predictor variables that have been rationalized by their ability to track business cycle conditions? To address this question, we consider a set of out-of-sample tests with alternative popular business cycle variables in the extant literature. The forecasting variables that we consider include fifteen predictors studied by Welch and Goyal (2008), 18 the consumption-aggregate wealth ratio of Lettau and Ludvigson (2001), the share of labor income to consumption of Santos and Veronesi (2006), the consumption volatility of Bansal, Khatchatrian, and Yaron (2005), and the output gap of Cooper and Priestley (2009). We download the data on the consumption-wealth ratio from the website of Martin Lettau, compute the share of labor income to consumption using the definition of labor income in Lettau and Ludvigson (2001) following Santos and Versonesi (2005), calculate the consumption volatility following Bansal, Khatchatrian, and Yaron (2005) ( J as σ c,t 1,J log η c,t j ), where η c,t is the residual from an AR(1) process of log j=1 growth rate in real per capita nondurables and services and J = 4, and construct the output gap from industrial production data available at the Federal Reserve Bank of St. Louis following Cooper and Priestley (2009). This gives us a total of nineteen alternative predictor variables: 1. Log dividend-price ratio (dp): log of a 12-month moving sum of dividends paid on the S&P 500 index minus the log of prices on the S&P 500 index. 2. Log dividend yield (dy): log of a 12-month moving sum of dividends paid on the S&P 500 index minus the log of lagged prices on the S&P 500 index. 18 The source of these data is the online library of Amit Goyal. 25