The Leading Premium

Abstract

Different macroeconomic aggregates go through economic cycles with different timings (see, among others, Stock and Watson 1989, 2002; Estrella and Mishkin 1998). Variables that respond promptly to exogenous shocks are denoted as “leading,” whereas those that adjust with delay are called “lagging.”¹ Thus far, the empirical macroeconomic literature has focused mainly on leads and lags of aggregate indicators. Little is yet known about leads and lags across firms operating in different segments of the economy.

In this paper, we document the existence of a significant lead-lag structure in fundamental cash flows across industries. This structure is relevant to the explanation of the cross section of stock returns, as leading industries pay a higher average stock return than lagging industries, on the order of about 3.6|$\%$| per year. After controlling for heterogeneous exposure to a large number of aggregate risk factors, we obtain an estimate of the pure timing premium, that is, the premium on advance information (see Ai and Bansal 2018; Binsbergen, Brandt, and Koijen 2012; Binsbergen and Koijen 2017), ranging from 1.2|$\%$| to 1.7|$\%$| per year.² We control for heterogeneous exposure by considering several cycle-related risk factors and refer to the residual difference in the cost of equity of the two stocks, or sectors, as the (pure) timing premium.

Specifically, we propose a novel model in which industries are ex-ante identical, but can ex-post either lead or lag the cycle. We postulate that industry cash flows are affected by infrequent industry-specific growth shocks that propagate slowly across all of the other industries. The industry that receives the shock “first” ends up leading an aggregate cycle, and, since its shock slowly propagates to all the other industries, it eventually generates an aggregate fluctuation. In our empirical investigation, for example, we show that the IT sector was leading the cycle in the late 1990s, whereas real estate and banks were leading in the mid-2000s.

Under the aforementioned conditions, leading industries provide valuable anticipated resolution of uncertainty for industries that go through aggregate economic fluctuations with a delay. As a result, lagging firms bear less conditional cash flow uncertainty and, by no-arbitrage, have a higher price (or, equivalently, a lower yield) ceteris paribus. Leading firms, in contrast, play the role of early indicators, like canaries in a coal mine and pay a higher equity yield. According to our model, the leading premium is (i) a conditional phenomenon, as our industries are all ex-ante identical, and (ii) as high as 2|$\%$| per year under a reasonable calibration of both industry cash flows and preferences for early resolution of uncertainty (Epstein and Zin 1989).

In addition, our model suggests that we can identify leading and lagging firms just by computing conditional cross-correlations with leads and lags of an indicator of economic activity. Equivalently, the leading premium can be measured even without full information on the entire cross section of industry-level shocks. This insight is relevant because it reduces estimation complexity. Inspired by our model, we compute conditional leading/lagging indices for industry-level cash flows with respect to U.S. aggregate economic activity. We find substantial conditional variation in leads and lags across industries, but none over the long run. Hence, in the U.S. data, no industry is systematically leading/lagging the cycle, as in our model.

More specifically, we compute rolling-window correlations between U.S. aggregate growth and leads and lags of operating income growth at an industry level. Data are quarterly and span the period 1972--2017. We consider 17,000 firms, which we aggregate to industries using the industry classification scheme obtained from Kenneth French’s website.³ In each quarter, we compute cross-correlograms and aggregate leads and lags in three different ways, as described below in Section 2.1. We then assign the corresponding lead/lag indicator to the industry of interest. Note that this approach only uses past data to compute the cross-correlograms, and hence it can be used to construct an implementable investment strategy in real time.

Leading industries exhibit an average return that is approximately 3.6|$\%$| higher than that of lagging industries. Even though leading industries are very similar to lagging industries across many dimensions, their cash flow helps in predicting the cash flows of lagging industries. Leading firms also lead in terms of employment and both equity and debt issuance policies. Furthermore, their price-dividends ratio has forecasting power on future industrial production and unemployment above and beyond that of other common forecasting factors. In addition, we show that our findings are statistically significant after double-sorting on the lead/lag (LL) exposure and either the book-to-market ratio or size, implying that the LL premium is a broad phenomenon in the cross section.

In the last part of our analysis, we run standard time-series and cross-sectional asset pricing tests. Our goal is not “adding another factor to the zoo” (Feng, Giglio, and Xiu 2020). Rather, we gather empirical guidance on the deeper economic concept highlighted in our model, that is, the size and relevance of the timing premium. After controlling for heterogeneous exposure to risk for several other risk factors—for example, investment minus consumption (Kogan and Papanikolaou 2014), durability (Gomes, Kogan, and Yogo 2009), industry-momentum (Moskowitz and Grinblatt 1999), industry betting-against-beta (Asness, Frazzini, and Pedersen 2014a), the five factors suggested by Fama and French (2015), the q-factors (Hou, Xue, and Zhang 2015b,a), and momentum (Carhart 1997)—we find a pure annual timing premium of about 1.5|$\%$|⁠. This result conforms to our model well, and it provides additional and independent empirical evidence in favor of the relevance of advance information in the spirit of Ai and Bansal (2018). Equivalently, leads and lags in the diffusion of fundamental shocks across industries are an important dimension of equity pricing.

Related literature. As mentioned above, prior papers have already documented that heterogeneous exposure to contemporaneous news shocks can explain many cross sections of equity returns (see, among others, Bansal, Dittmar, and Lundblad 2005). We differ from prior studies by showing that heterogeneous timing of exposure to news shocks explains a substantial share of the leading premium.

Kadan and Manela (2018) estimate the value of information using options. We empirically quantify the relevance of heterogeneity in the timing of exposure of cash flows to aggregate shocks for the cross section of equity returns. Our results are significant beyond announcement events (Patton and Verado 2012; Savor and Wilson 2013, 2016).

Koijen, Lustig, and Van Nieuwerburgh (2017) show that the Cochrane and Piazzesi (2005) factor is a strong predictor of economic activity, with a lead of up to 10 quarters relative to GDP growth. They provide evidence suggesting that this factor relates to a value-minus-growth stocks strategy. Like them, we show that both the cash flows and the price-dividend ratio of leading firms forecasts economic activity, even after controlling for other common predictors. In addition, we show that the cash flow of lagging firms is more predictable than that of leading firms. The same applies to employment and both equity and debt issuance.

Hong, Torous, and Valkanov (2007) investigate whether high-frequency industry returns can forecast excess returns on the CRSP market index. They find evidence of predictability, but only on very short horizons of 1 or 2 months. In contrast to previous studies, our empirical investigation is based on cash flow fundamentals and focuses on longer time horizons. As a result, we are silent about the speed at which prices fully embody available information (Hou 2007; Cohen and Frazzini 2008). In our model, the endogenous cross section of returns features no lead-lag structure, that is, all returns move simultaneously, but with different endogenous sensitivities.

On the other side, our attention on leads and lags across industry-level cash flows is broad and does not hinge on specific network links, like for example customer-to-supplier (Cohen and Frazzini 2008) or intermediate-to-final-producer (Gofman, Segal, and Wu 2020). In addition, our leading and lagging portfolios have similar exposures to the concentration and the sparsity network factors proposed by Herskovic (2018), as well as similar markups (Gofman, Segal, and Wu 2020). Future research should enrich our cash flow models, taking into account the results in Herskovic et al. (2020) and Ahern (2013).

We acknowledge that lagging firms can learn from the fundamentals of leading firms and adjust their investment decisions to endogenously alter their payouts (see, among others, Albuquerque and Miao 2014). For the sake of tractability, however, we abstract away from investment decisions. By no-arbitrage, the portion of the leading premium driven by the timing premium depends on the spread between the equity and the risk-free bond yield curve. Richer settings like those suggested by Lettau and Wachter (2007, 2011), and Belo, Colin-Dufresne, and Goldstein (2014) are consistent with the empirical evidence in Binsbergen, Brandt, and Koijen (2012), Binsbergen et al. (2013), and Binsbergen and Koijen (2017), but they would produce similar insights about the nature of the leading premium.

1. Intuition Based on No-Arbitrage

Before presenting our equilibrium model, we provide basic intuition in a simplified setting. Consider two stocks, denoted as leading and lagging. For the sake of simplicity, assume that they both pay dividends only once, |$n$| periods from now. From a time-0 perspective, the dividend of the leading firm, |$D^{lead}_{n}$|⁠, is assumed to be unknown and random because the leading stock faces economic uncertainty. In order to abstract away from average growth, we assume |$E_0[D^{lead}_{n}]=D^{lead}_0$|⁠. Consistent with our empirical analysis, we assume that the leading stock provides information about the future cash flow of the lagging firm. To make the intuition as crisp as possible, assume that |$D^{lag}_n=D^{lead}_{0}$|⁠, that is, the future cash flow of the lagging stock is perfectly forecastable given the current cash flow of the leading firm.

If investors are adverse to dividend uncertainty, we have |$ v_0(n)>y_0(n)$|⁠, and lagging firms are more valuable than leading firms. Equivalently, an investment strategy long in the leading and short in the lagging stock should pay a leading premium equal to the forward equity premium.

This result is important for two reasons. First, in this setting the leading premium features no time-discounting, as it is determined by the difference between the expected dividend at time |$n$| and the certain payoff |$F_{0,n}$| paid at time |$n$|⁠, that is, it can be regarded as the price of a static lottery. Hence, this premium is a pure measure of the value of advance information on |$n$|-period-ahead cash flows.

Second, the leading premium equals the difference between equity and bond yields of the same maturity. Thus, to obtain a positive leading premium, we need a model that produces a significant positive gap between the yield curve of zero-coupon equities and that of bonds over the horizon for which leading industry cash flows predict lagging industry cash flows.

It is important to highlight that the existence of a leading premium depends on the spread between the equity and the bond yield curve, not on the slope of the equity curve. In the main text, we adopt an equilibrium model that delivers an upward-sloping aggregate equity yield curve for the sole sake of analytical tractability. Richer settings like those of Lettau and Wachter (2007), Lettau and Wachter (2011), Croce, Lettau, and Ludvigson (2014), and Ai et al. (2018), which are consistent with the empirical evidence in Binsbergen, Brandt, and Koijen (2012), Binsbergen et al. (2013), and Binsbergen and Koijen (2017), would produce similar insights about the nature of the leading premium. In Section IA-C of the Internet Appendix, we provide additional empirical support for this intuition.

2. An Equilibrium Model for the Leading Premium

In this section, we present a model that is instructive for our empirical investigation. The model clarifies under which conditions we should expect to observe a leading premium, and it enables us to obtain a list of testable hypotheses. In what follows, we (i) define our measures of leads and lags, (ii) describe our industry-level cash flow model, and (iii) look at asset pricing results. In the spirit of the literature, we use aggregate output to “set the clock”, that is, aggregate output is used as a common reference to identify leading and lagging industries.

2.1 Measuring leads and lags

In this section, we discuss the measures that we adopt to identify leading and lagging industries. Since these measures are quite common in the macroeconomic literature, the readers familiar with cross-correlograms may want to go directly to the next section.

2.2 The cash flow model

We introduce a simple diffusion model to provide intuition about our way of identifying conditionally leading and lagging industries. This model is stylized in many dimensions and is not meant to perfectly describe the data. Rather, our goal is to show that our cross-correlations have the potential to identify leading and lagging sectors when shocks diffuse across stocks with connected cash flows. Sorting on lead and lag indicators enables us to capture a sizable conditional risk premium that we denote as the leading premium without running an industry-level structural estimation that would be subject to excessive estimation uncertainty.

For the sake of computational simplicity, we focus on an economy with three industries evenly spread out over a circle. Since we assume that it takes one period for an industry-specific shock to reach the next industry, |$N=3$| is equivalent to studying an economy in which there is at most a delay of one period in the transmission of a shock. We also look at the case |$N=4$|⁠, where it takes at most two periods before all locations (industries) are affected by a specific shock. Since we solve the model with an approximation of the fourth order, choosing |$N>4$| exposes us to the curse of dimensionality. As a result, in our equilibrium model we have at most two periods of leads/lags.

In what follows, we explain the role of each variable in detail. We choose the autoregressive parameter |$\rho\approx 1$|⁠, so that our infrequent shocks have long-lasting implications for growth, that is, they produce relevant medium-term cycles. The second term on the right-hand side of Equation (5) captures the spillover of the shocks that propagate from all industries |$j\neq i$| towards industry |$i$|⁠. These spillovers propagate forever along the circle with intensity |$\lambda$| and decay rate |$\rho$|⁠.

In order to have well-defined industry-prompted cycles, we interact the shock |$J^i_t$| with the process |$p_{t-1}^i$|⁠. We note that |$p_t^i$| is close to zero when other industries have already received shocks and hence their expected growth is far from their unconditional mean (i.e., |$\phi_2 \sum_{j\neq i} (x^j_t)^2$| is a sizable negative number). This is a parsimonious way to represent the fact that different aggregate cycles are often driven by booms or busts in specific industries. In our empirical investigation, for example, we show that the IT sector was leading the cycle in the late 1990s, whereas real estate and banks were leading in the mid-2000s. Thanks to this assumption, a leading industry conveys relevant information about the cycle that other industries may experience (for additional details, see Appendix A).

Finally, we note that all of our industries are ex-ante identical and hence none of them are unconditionally leading or lagging. Equivalently, in this setting, the leading premium is solely a conditional phenomenon, consistent with our empirical findings. In addition, in our model all industries have the same network characteristics, such as upstreamness, again consistent with what we document in Section 3.

2.3 Pricing kernel

By no-arbitrage, our leading premium is connected to the spread between the equity yield curve and the bond yield curve. See Section 1 for an example in which these two concepts perfectly coincide. Equivalently, the leading premium is partially a reflection of the timing premium. Hence, any equilibrium asset pricing model able to deliver a substantial timing premium can produce a sizable leading premium. In what follows, we focus on an equilibrium model featuring preferences sensitive to the timing of information about future growth.

Since we focus on an endowment economy in which consumption equals output, consumption growth equals aggregate output growth and is determined according to Equation (3).

2.4 Model calibration and results

In Table 1, we report our benchmark calibration as well as our targeted annualized moments. Our calibration of the preference parameters is consistent with that of Bansal and Yaron (2004). On the cash flow side, our calibration strategy differs in several dimensions. First, our industry-level expected quarterly growth process has a persistence |$\rho$| of 79|$\%$|⁠, a value lower than in a typical long-run risk model. After accounting for the diffusion of spillovers determined by |$\lambda$|⁠, the overall persistence is consistent with the literature.

Second, we model the infrequent arrival of sizable shocks, as opposed to having a Gaussian diffusion. Because of these shocks, the distribution of growth rates features fatter tails than that of aggregate output. We calibrate the parameters |$\phi_0$| and |$\phi_1$| so that both the kurtosis and the volatility of each industry cash flow growth relative to that of aggregate output conforms to the data. Specifically, we use Compustat data to measure operating income for the Fama-French 30 industries. Since in our model we only have three industries, we group our 30 industries in three portfolios comprising an equal number of industries. In Table 1, we report both the volatility and the kurtosis of operating income growth aggregated at the portfolio level relative to the same moments computed on the growth of operating income aggregated across all firms in our data set.⁴ Additional details on the role of |$\phi_0$| and |$\phi_1$| are reported in Section IA-A of the Internet Appendix. We set |$\tau$| to be small so that (i) the model features balanced growth, and (ii) the cointegration of cash flows across industries is not detectable in a small sample, as in the data.

We set the volatility of the common short-run shock, |$\sigma$|⁠, to a value that makes aggregate output growth volatility very moderate compared to the data. We choose this strategy because we are aware that aggregate consumption growth has been half of that of output over the same long sample. An alternative way to keep the volatility of output on the low side would be to increase the number of industries at the cost of greatly increasing our computational time.

We solve our model using high-order perturbation methods and depict the impulse response function upon the realization of a positive growth shock to industry |$i=1$| in Figure 1. We start by discussing the case |$N=3$| (see panel (a)). The growth increase in industry 1 is a leading indicator of the boom that the other industries will exhibit. In this specific calibration, industries 2 and 3 share the same growth path as industry 1 after approximately 12 quarters. The middle panel of this figure proves that our cross-correlograms are able to correctly sort leading and lagging industries. The difference in the weighted averages of leads and lags starts to mean-revert after 16 periods, whereas the difference based on the maximum cross-correlation requires a longer time to mean-revert given that it takes discrete (i.e., integer) values.

Figure 1

The leading premium in the model 

This figure depicts impulse response functions upon the arrival of a positive shock to expected growth in industry |$i=1$|⁠. The shock arrives at |$t=1$| and affects cash flows at |$t=2$|⁠. The left plot shows industry-level cash flow growth rates (⁠|$\Delta d^{(i)}$|⁠) as well as the growth rate of the aggregate cash flow (⁠|$\Delta c$|⁠). The middle plot shows the difference in our lead/lag indicators across industries. In panel (a), |$N=3$| and industry 3 behaves as industry 2. In panel (b), |$N=4$| and industries 2 and 4 behave similarly. In panel (a), we plot both the indicator based on the maximum cross-correlation (“max”) and that computed as a weighted average of leads and lags (“vw”). The rightmost plot presents annualized conditional risk premia with either recursive preferences (benchmark) or time-additive preferences (CRRA). “Managed” refers to an investment strategy that goes long (short) industries with a higher (lower) LL indicator. When |$\phi_2=0$|⁠, we have |$p_t^i\equiv1$|⁠.

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We acknowledge that in very long samples a vector autoregression with time-varying coefficients may convey all of the relevant information dynamics about cash flows. In relatively short samples with a large cross section, however, estimating such a high-dimensional VAR with sufficient precision appears extremely challenging. Our simulation results suggest that cross-correlograms may be a useful non parametric alternative tool to identify leading industries that have just received an infrequent growth shock.

In addition, in the rightmost panel we depict the expected return of a zero-dollar strategy long in leading and short in lagging industries. We consider both our benchmark calibration and two alternative calibrations in which |$\gamma=1/\psi$|⁠, that is, the agent has time-additive preferences with either high or low risk aversion. This panel shows three important results. First, as soon as an industry-cycle starts, the leading industry can feature a further conditional risk premium as large as 2|$\%$|⁠. An investment strategy based on our backward-looking LL indicator would capture the variation in risk premia with delay and deliver a leading premium of about 0.9|$\%$|⁠. When |$N=4$| (see panel (b)), the cross section of leads and lags becomes wider and the leading premium becomes as large as 2|$\%$| (dashed line, “Managed”). As time goes by, our LL indicator correctly identifies the most leading and lagging industries, that is, industry 1 and 3, respectively. As a result, the leading premium remains high and persistent.

Second, the leading premium is a relevant conditional phenomenon. On the one hand, as the cycle fully diffuses across industries, the implied leading premium declines to zero, that is, it does not persist unconditionally. On the other hand, the premium is still sizable after one whole year, meaning that its half-life is quite long.

Third, when |$\gamma=1/\Psi$|⁠, only short-run shocks are priced. Since our model features no leads/lags of short-run shocks, with time-additive preferences, there is no leading premium. Consistent with what we presented above in Section 1, when |$\gamma>1/\Psi$| growth news shocks are priced, and hence anticipated information about them generates a leading premium.

We conclude by noting two additional important aspects. Both the middle and the rightmost panels of Figure 1 remain unchanged if we explore the response to a negative shock to the expected growth of the cash flow in industry 1. On the one hand, this is consistent with the idea that in the model the leading premium is a pure reflection of the premium on the timing of information. On the other hand, this result proves that our study is not isomorphic to timing industries.

Second, if we were to set |$\phi_2=0$|⁠, we would observe no leading premium. When |$\phi_2=0$|⁠, we have |$p^i_t=1$| for all |$i$| and |$t$|⁠, and hence it is no longer true that an industry-specific cycle provides useful information about the cycle of the other industries. This is because industry-driven cycles become equally likely across industries and over time. Equivalently, without heterogeneity in |$p^i_t$| across industries, there is no well-defined endogenous lead/lag structure. For additional details, see Appendix A.

2.5 Model-inspired empirical tests

Inspired by our model, in the next section, we ask the following questions. First, is there a relevant conditional variation in cash flow leads and lags across industries? What about unconditionally?

Second, assuming that we can identify leading and lagging industries, is there a sizable leading or lagging premium? Through the lens of our model, this exercise can inform us about the implied preference of investors for early resolution of uncertainty.

Finally, how large is the share of the leading premium that is solely driven by the timing premium? In order to address these questions, we use standard asset pricing techniques to control for heterogeneous exposure to risk to empirically identify the timing premium embedded in the industry cross section.

In what follows, we also report several robustness tests that link our empirical investigation to the narrative of our illustrative model.

3. Empirical Investigation

Data sources. In our empirical analysis, we use monthly stock returns from CRSP as well as the corresponding quarterly data from Compustat for the period from from 1967:Q1 to 2017:Q4. The quarterly data coverage in Compustat prior to 1967 is too limited for our investigation. We group firms into 30 industries following the classification scheme available on Kenneth French’s website. We assign firms to industries using SIC codes from CRSP. We compute industry-level output by aggregating firms’ operating income before depreciation and net of interest expenses, income taxes, and dividends as in Acharya et al. (2014).⁵ We also employ alternative measures in our robustness exercises, which we will describe in detail in the next sections. We use dummy variables to remove seasonality. We gather aggregate U.S. consumption and output data from the National Income and Product Accounts (NIPA). All variables are seasonally adjusted and in real units. Inflation is computed using the Consumer Price Index (CPI).

LL indicators. For each industry, in each quarter, we compute the |$\pm 4$|-quarter cross-correlation between industry-level output growth and the domestic output growth using 20-quarter rolling windows. According to the methods described in the previous section, we then compute conditional quarterly lead-lag measures for each industry. This procedure generates a panel of industry-level lead-lag indicators spanning 51 years.

To provide economic guidance about our measure, in Figure 2, we report our industry-level weighted average LL indicators for the IT, the finance, and the real estate industries using observations starting from 1975. We focus on these industries because they have been important drivers of the last two main economic cycles in the United States and hence represent a natural reference point for our methodology.

Figure 2

Lead-lag indicator for selected industries 

This figure depicts the lead-lag (LL) indicator for three major industries. The LL indicator is computed in two steps. First, for each industry, in each quarter we compute the |$\pm 4$|-quarter cross-correlation between industry-level output growth and the domestic output growth using 20-quarter rolling windows. Second, we compute the industry-level weighted average of leads and lags and assign it to the corresponding industry as its LL indicator. A positive (negative) LL indicator denotes an industry whose output growth leads (lags) GDP growth. Quarterly growth rates are adjusted for inflation and seasonality. Gray bars denote NBER recession periods.

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We find it reassuring that our methodology detects several well-known economic patterns. For example, the IT industry became progressively more leading in the 1995–2000 subsample, that is, during the IT boom. The boom of the early 2000s, instead, was led by real estate, with finance becoming progressively more leading after 2005 and during the Great Recession. In Appendix B, we show that our correlograms are very distinct across lagging and leading industries (Figure B.2). Furthermore, we list leading and lagging industries across 5-year subsamples (Table B.1) and report the persistence of leading and lagging industries both in our data and from simulated data (Table B.2). In the data, industries stay in the leading/lagging portfolio for 1.5 consecutive years on average. In the model, this figure is equal to about 1.8 years. In addition, we acknowledge that the data show a strongly time-varying composition of the leading industries that cannot be matched by our simple circle-shaped network.

3.1 Portfolio sorting, risk premia, and characteristics

Portfolio sorting. We start with the Fama-French 30-industry cross section. In each quarter, we sort firms grouped in our 30 industries according to their maximum correlation LL indicator value and divide them into three portfolios. Our lead (lag) portfolio contains on average the top six leading (lagging) industries and represents in each quarter at least 15|$\%$| of total market capitalization, implying that our results are not driven by a fraction of small and potentially illiquid firms. Our results also hold when we form portfolios comprising either a fixed number of industries or different levels of capitalization (see Internet Appendix, Tables IA-B1 and IA-B2, respectively).

For each portfolio, we compute value-weighted monthly returns and highlight the following relevant facts. First, we construct a lead-lag factor by considering the returns of a zero-dollar investment strategy long in the leading and short in the lagging portfolio. This strategy pays an average annualized excess return of 3.6|$\%$|⁠, as shown in Table 2.

Second, within each portfolio we identify the industries whose absolute value of correlation with output is above the median. We group the above-median industries in subportfolios denoted as “Strong,” given that they feature a stronger and less noisy lead/lag connection with aggregate output. We then study the return of a zero-dollar investment strategy long in Lead-Strong and short in Lag-Strong. We obtain even stronger results (see panel A of Table 2, rightmost column).⁶

The different versions of the LL factor generate Sharpe ratios ranging from 0.28 to 0.35, and their CAPM unconditional alphas range from 4|$\%$| to 4.36|$\%$|⁠, a sizable number. The average quarterly turnover is stable and very moderate at about 12|$\%$|⁠.⁷ According to our methodology, industries move across portfolios at most once a year.

The next three rows in Table 2 confirm that the moderate migration of industries across portfolios is due to the persistence of our LL measures. In addition, across all possible indicators, the gap between the LL indicator of the leading industries and that of the lagging industries is very stable also at the end of the quarter in which the portfolio has been formed (ex-post measure).

We regress our LL return on a constant and on a dummy variable that takes a value of one during recession periods. In the last row of the table, we report our estimates and conclude that our returns are not significantly different during recessions. In addition, in Figure 3, we depict the cumulative log excess returns obtained investing in the leading and the lagging portfolio as well as the those from the lead-lag strategy. A visual inspection of the time path of our factor shows that it is acyclical, that is, not synchronized with either industrial production or recession periods.

Figure 3

Lead-lag cumulative excess return 

This figure depicts cumulative log excess returns for our leading and lagging portfolios, as well for the lead-lag factor. The solid line depicts the log of the industrial production series for the United States. Shaded areas denote recession periods. Leads and lags are identified by maximum absolute value of cross correlations.

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Given the similarity of our results across different measures of leads and lags, in what follows we keep the maximum cross-correlation as our benchmark.

Conditional and unconditional sorting. In Table 3, we report both annualized average value-weighted returns and CAPM alphas for a zero-dollar strategy long in leading industries and short in lagging industries. The rightmost column reports the difference in the LL indicator across the leading and the lagging portfolios. In panel A, we update our portfolios at either the quarterly or annual frequency. Our results do not hinge on high-frequency rebalancing and resorting. The leading premium can be captured even when we form our portfolios only once a year.

In panel B, the portfolios are static, as they are formed only once and their weights are rebalanced quarterly. Initial Sorting refers to a portfolio constructed using our standard procedure over the first observations of our sample. Hence, this portfolio refers to an implementable strategy. Unconditional LL refers to an investment strategy based on a full-sample computation of the unconditional leads and lags. Regardless of whether we use a static initial sorting or an unconditional one, the implied premium is statistically not different from zero. Hence, the gap in the lead-lag indicators vanishes in these cases. In other words, our industries do not feature systematic differences in their leads/lags, and our leading premium is a conditional phenomenon.

Characteristics. In Table 4, we report key characteristics for our leading and lagging portfolios at both the industry and the firm level. Our leading premium is not driven by systematic differences in the upstreamness of our industries. Consistent with our model presented in Section 2, industries may be leading with respect to both upstream and downstream shocks (Cohen and Frazzini 2008; Herskovic et al. 2020).

This result holds whether we measure upstreamness as in Antràs et al. (2012) or look at other indicators such as (i) the dollar value of goods supplied to other industries over the dollar value of goods used by a specific industry and (ii) the value of intermediate goods used by an industry over its total added value. In addition, we see no significant link between leading firms and investment-goods producers. Taking an industrial organization view, we document that leading stocks tend to be in industries featuring slightly more concentrated sales, that is, industries where we have fewer but larger firms. After double-sorting on leads/lags and HHI, we see that the leading premium is concentrated among industries with a medium level of HHI (see Internet Appendix, Table IA-B4). Equivalently, our leading premium is not due to extremely competitive or monopolistic industries. Furthermore, we see no difference in markups (De Loecker, Eeckhout, and Unger 2020; Clara, Corhay, and Kung 2021) across leading and lagging industries.

Turning our attention to firm-level characteristics, we point out that only tangibility is statistically different across leading and lagging firms. In one of our next empirical steps, we show that the leading premium remains relevant even after controlling for the tangibility factor (see Internet Appendix, Table IA-B17). Looking at all the other variables, we find no systematic difference in financial leverage, growth opportunities, innovation intensity, and profitability.

We complete our analysis by comparing investment characteristics across leading and lagging portfolios. From a statistical point of view, firms in leading industries have an average investment intensity comparable to that of lagging firms. Lagging firms, however, adjust their investments more (as indicated by a higher standard deviation of the ratio of investment to total assets, |$StD(I/A)$|⁠). These results are broadly consistent with the idea that lagging firms have time to process information about future fluctuations and use information to revise their investment plans.⁸ In addition, our leading and lagging portfolios have similar exposures, |$\beta^p_{N_C}$| and |$\beta^p_{N_S}$|⁠, to the concentration and the sparsity network factor proposed by Herskovic (2018) (see Internet Appendix, Table IA-B3, for additional details).

Leads, lags, and firm activity. Our model suggests that leading firms should be riskier than lagging firms because leading firm cash flows are less predictable than those of lagging firms. We explore this dimension by running forecasting regressions on both operating income and sales and we report our main results in Table 5 (top portion). In each panel A, we use a set of common leading indicators (term spread, default spread, aggregate price-dividend ratio, inflation, and forward rate) in order to forecast the growth rate of the aggregated cash flows of both the leading and lagging portfolios. Consistent with the intuition of our model, the cash flows of the lagging industries are more predictable than those of the leading industries, as they feature higher adjusted |$R^2$| values across all forecasting horizons.

In panels B and C, we strengthen our results by documenting that over longer horizons the growth rate of the cash flows of leading industries forecasts the cash flow growth of lagging industries, whereas the opposite is not true. In addition, at all horizons, the cash flows of lagging industries can be predicted by the growth rate of the cash flow of the industries in our leading portfolio with a sizable adjusted |$R^2$|⁠. Furthermore, for a given predictive horizon, the |$R^2$| is always higher for the cash flows of the lagging portfolio.

We repeat the same steps with financing variables such as equity and debt issuance. We find very similar results, meaning that the financing activity of leading firms predicts that of lagging firms across different quarters. This regularity is also present when we look at a flexible input of production such as labor.⁹ For employment (bottom-right panel), we use annual data from Compustat, and hence run our forecasting regressions only one period ahead. Interestingly, investment (bottom-left panel) is synchronized across leading and lagging firms. In the spirit of what is shown in Table 4, lagging firms have time to process information about future fluctuations and use it to revise their investment plans more aggressively and without waiting. This is an equilibrium outcome when (i) firms pre commit to investment, and (ii) adjusting investment afterward is increasingly costly (see our Internet Appendix, Section IA-D).

Our estimation results are stable across subsamples. We discuss this point further in our Internet Appendix (see, e.g., Figure IA-B2).

Predictability of aggregate activity. Our model suggests that leading industries convey news that are priced because they concern the future growth of the overall economy. In order to test this aspect of the model, we assess whether (i) the cash flows growth and (ii) the aggregate valuation ratio of our leading firms have predictive power for industrial production and unemployment beyond that of classical predictors. Specifically, we construct the price-dividend ratio for both the aggregate stock market and our leading portfolio and use these two ratios in standard forecasting regressions.

We report our findings in Tables 6 and 7 for cash flows and valuation ratios, respectively. We note three relevant results. First, as indicated by the results shown in Table 6, the growth rate of the cash flows of leading industries predicts future economic performance even after controlling for total cash flow growth in addition to other classical forecasting variables.

Second, Table 7 shows that our leading price-dividend ratio exhibits significant predictive power for both industrial production and employment. This result obtains while controlling for other well-known predictive factors, such as the aggregate price-dividend ratio, a measure for the aggregate credit spread, inflation, and the federal funds rate.

Third, the predictive power of the leading price-dividend ratio is increasing in the horizon of our regressions in terms of both coefficient magnitude (⁠|$\gamma_h$|⁠) and contribution to the adjusted |$R^2$|⁠. This contribution is measured by the difference between the adjusted |$R^2$| values with and without the leading price-dividend ratio included in the regression. Similar results are featured in Table 6 for our cash flows–based regressions. We note that we do not focus on cumulative growth rates and hence are not exposed to the potential problems pointed out by Valkanov (2003). Our estimates are adjusted for the Stambaugh (1986) bias, and our inference is based on a bootstrap procedure that mitigates the issues pointed out by Torous, Valkanov, and Yan (2004).

|$X$| comprises the price-dividend ratio of the leading portfolio as well as the following additional controls: term spread, default spread, aggregate price-dividend ratio, inflation, and federal funds rate.

According to the model, the excess returns of our leading industries should have higher exposure to growth news shocks than those of lagging industries. We test this assumption by regressing our LL financial factor, |$r^{LL}:=r^{lead}-r^{lag}$|⁠, on the LINS factor, |$\hat{e}_t$|⁠,while controlling for the FF3 factors. The data support our model. This is also true when we include additional macroeconomic controls (see Table 8). We see this result as supportive of the mechanism implied by our equilibrium model. In Section 3.3, we perform additional tests regarding the market price of risk of these factors.

3.2 Additional Dimensions

Robustness. In the Internet Appendix IA-B, we show that our results are robust to many variations of our benchmark methodology. For example, we consider: alternative ways to predict economic fluctuations; using consumption as opposed to output when constructing the LL indicators; adopting a wider range of leads and lags when computing the LL indicators; using alternative cash flow measures; alternative granularities across industries, as well as double sorts on size and book-to-market.

Leading premium and cross section of risk factors. Given the way we form our LL factor, it is natural to ask whether it is connected to other well-known risk factors already explored in the literature. In this section, we run standard time-series tests in order to check whether: (i) other factors fully explain ours, and (ii) our factor explains other existing ones. We think it important to state that our goal is not “adding another factor to the zoo” (Feng, Giglio, and Xiu 2020). Rather, we gather empirical guidance regarding the deeper economic concept highlighted in our model, that is, the size and relevance of the timing premium.

In addition, we note that in an economy in which shocks diffuse immediately across sectors, our lead-lag factor should not provide additional information once we control for other aggregate factors. Equivalently, we should not expect to find a significant alpha. In many of our exercises, however, we find a strong disconnect between our leading premium and other well-known risk factors. We interpret these results as suggesting that existing risk factors are not enough to fully capture the role of the many shocks that affect our granular cross section of industries. We report our detailed results in the Internet Appendix, Section OL-B1.

3.3 The timing premium in the cross section

In this section, we perform a cross-sectional investigation in order to (i) test key predictions of our model, and (ii) better disentangle the portion of our leading premium that is associated exclusively with advance information and cannot be attributed to heterogeneous exposure to other factors connected to cyclical economic activity.

We estimate this model across many different cross sections of test assets using the FF3 model as baseline, and we augment it with either our LL financial factor or our news shocks–based LINS factor. We use many different cross sections of test assets both for robustness and to address the criticism of Lewellen, Nagel, and Shanken (2010) related to the strong factor structure of the size and book-to-market cross sections.

In Table 9, we report for each cross section both the spread in the portfolio exposures to our LL-based factors and a measure of the implied timing premium, given by the spread in exposures multiplied by the market price of risk. On average, the timing premium ranges from 1.20|$\%$| to 1.7|$\%$|⁠, depending on whether we adopt our LL or our LINS factor. The middle point in this range is about 1.45|$\%$| per year, that is, about 40|$\%$| of our leading premium of around 3.6|$\%$|⁠, as documented in Table 2.¹¹