Equity Capital: A Puzzle? Ravi Bansal Ed Fang Amir Yaron This Version: June 25 Preliminary and Incomplete! Comments are welcome. Please do not cite without authors permission. Fuqua School of Business, Duke University, ravi.bansal@duke.edu. Department of Economics, Duke University, fang@duke.edu. The Wharton School, University of Pennsylvania and NBER, yarona@wharton.upenn.edu.
Equity Capital A Puzzle Abstract In almost any equilibrium model shifts in sectoral wealth have direct implications for asset returns, so as to induce investors to hold more or less of their wealth in the sector. In this paper we show that shifts in sectoral financial wealth have no bearing on the subsequent mean and volatility of sectoral returns. In the data, sectoral wealth, and asset returns show no relation this leads to the equity capital puzzle. Why then do investors hold more (less wealth share of an expanding (contracting sector?
1 Introduction Sectoral wealth (industry portfolios changes across time in 195 the equity capital of the health sector was 9% of total market capitalization, while in 24 it stands at 2%. This is clearly shown in Figure 1 which displays the variation in sectoral shares over time for 12 different industries. Relative wealth shifts are due to differential changes in expected returns or due to changes in shares of sectoral outputs of cash flows. The latter can happen due to expansions or contractions of different sectors. In equilibrium, agents have to hold all equity wealth, hence the shifts in sectoral equity wealth must contain information about shifts in expected returns and or-about return volatility. That is, sectors in which the wealth is expanding, either the sector s mean equity return should be rising or its volatility falling to provide investors with better trade-offs to hold the expanded sector. More generally sectoral shifts in wealth, in a market equilibrium, should have implications for the distribution of asset returns. Our empirical evidence indicates that sectoral shift in wealth have almost no information about subsequent asset returns leading to an equity wealth reallocation puzzle. That is, what inducements does the market offer for investors to hold more wealth in an expanding sector and less in a contracting one? To provide some intuition, consider the standard mean variance portfolio choice problem. The allocation of wealth is pinned by the conditional mean of returns and their joint second moment properties. Equilibrium holdings of the wealth, that is the share in market capitalization, should reflect the mean and variance of returns. Sectors, e.g., telecommunications in the 9 s see their market capitalization rise from 3 to 1% of market capitalization. For investors to be willing to hold more and more of their financial wealth in this sector, the market has to provide additional inducements; for example, the Sharpe Ratio must be rising. That is, as per the market clearing conditions in the CAPM, the sectoral wealth share shifts must predict the mean and variance (or covariances of returns. Further, as the wealth shares move, so should the distribution of asset returns. While the focus on the mean and variance is motivated by the implications of the CAPM these dimensions (i.e., the mean and variance continue in theory to be the first order effects that drive the portfolio choice even in more general settings. Additional dimensions, such as hedging demands may also play a role in driving portfolio choice but in this paper we concentrate on these first order effects. The equilibrium implications of the CAPM and sectoral models considered in Rosen-
berg and Ohlson (1979, Santos and Veronesi (23, Cochrane, Longstaff, and-santa-clara (24. Bansal, Dittmar, and Lundblad (22, and Hansen, Heaton and Li (24 look at properties of sectoral dividend shares to explain differences in mean returns. As in the CAPM, Cochrane, Longstaff, and Santa-Clara (24 theoretically show that the asset beta s and hence the mean and Sharpe Ratios for sectors that have expansions, typically, tend to rise; this is the inducement that the market provides for the agents to hold more current wealth in a given sector. In dynamic economies with Epstein and Zin (1989 preferences wealth share allocation across assets will reflect the usual myopic Sharpe Ratio, and the hedging demands. The first order effects are driven by the variation in mean and variance. The current equity wealth of a given sector is determined by the market value of existing equity shares plus the dollar value of new equity capital created in a given sector. The relation between current wealth shares, sectoral net flows (net payouts, and expected returns is provided. 1 In section 2.2 we show that discounting the net outflow equals the payouts from a sector minus the inflow of resources for each sector, via entry of new firms or expansion of existing ones, and thus provides the link to wealth shares. During periods of large inflows, the net outflow can be negative and otherwise positive. The result implies that variation in wealth shares reflects variation in the future sectoral net flow growth and the variation in expected returns over the market. This present value relation for wealth shares provides a sharp decomposition for the sources of variation in wealth shares between net outflow growth and expected returns. Given the wealth share decomposition, one should expect that variation in the wealth shares is significantly explained by variation in the expected excess return. However, wealth shares have no predictive power for future returns and almost all of wealth share fluctuations are due to variation in expected net outflow growth and close to zero due to variation in expected return. In fact, our results indicate that expanding sectors offer lower Sharpe Ratios and poor expected returns in the future. Sectors that have a positive share shock experience lower subsequent expected returns and a lower Sharpe Ratio. The projection coefficient of future returns on current shares (or share changes yield negative to zero slope coefficients. Hence mean returns adjustments, while there, are quite the opposite to what one might 1 The traditional approach is to discount the dividends that an investor holding one share would receive. This is fine for asking questions about the risk premia and returns. This approach assumes, that the sectoral scale is exogenous and the traditional dividend-per-dollar invested discounting specification does not provide the evolution of sectoral wealth across time.
expect based of model predictions. Bansal (24 argues that even if expected returns are constant for all assets, then the margin of adjustment for sectoral reallocation will be in the volatility of returns that is expanding sectors should have lower return variance and via that a higher Sharpe ratio. While expanding sectors do have a lower variance, it is not the case that they have higher Sharpe ratios. One possibility that we entertain and find is that when wealth shares are defined relative to aggregate wealth that includes human capital, these shares move very little. This is robust for different plausible scenarios for aggregate wealth measures. In this case, again, movements in the first two moments of returns cannot account for wealth shifts. This lead to the puzzle: If sectoral wealth is moving about what induces agents, in a competitive market, to hold these in their equity portfolios? The remainder of the paper is as follows: Section 2 describes the relationship between wealth shares, net payouts that account for investments into and out of a sector, and returns. In Section 3 we provide a simple example that demonstrates the general equilibrium link between shares and the first two moments of returns. Section 4 describes out data, while Section 5 provides our empirical analysis. Section 6 provides concluding remarks. 2 Wealth Shares, Growth, and Expected Return In this section we develop a decomposition that links wealth shares to sectoral growth, and expected returns. Consider the return per share, R t+1 = (n td t+1 + n t p t+1 n t+1 p t+1 + n t+1 p t+1 n t p t (1 The market value of existing shares is n t p t V t, which is the market capitalization or equity wealth in a given firm/sector. Price per share is p t, dividends per share is d t, and the number of outstanding shares at t, is n t. The above equation implies that R t+1 = D o,t+1 I t+1 + V t+1 V t (2 where D o,t+1 = n t d t+1 + (n t n t+1 p t+1, D o,t+1 (3
are the repurchase adjusted cash-dividends paid out by the equity markets. The minus reflects reduction in shares the second term lights up when n t+1 is less than or equal to n t, and I t+1 = (n t+1 n t + p t+1, I t+1 (4 is the inflow of resources at date t + 1 into the corporate sector, reflecting new investments in equity n t+1 is greater than n t. We refer to D o,t V t 1 as the payout yield; this includes outflows from firms to investors I (cash+repurchases relative to market capitalization. Similarly we name t V t 1 as the investment yield, and it corresponds to inflows from investors into firms. These two yields, measure the actual quantities on aggregate inflows and outflows, into and from the corporate sector. The equation above implies two equivalent expressions V t+1 = R t+1 D o,t+1 + I t+1 V t V t V t That is equity capital growth in a sector rises with equity returns and greater investment, and falls with larger payouts. A present value representation of the returns implies that V t = exp ( P j k=1 ln R t+k (D o,t+j I t+j That is, the current market capitalization reflects the discounted sum of the aggregate payouts less aggregate inflows (investments into the sector. The aggregate dividend yield is D o,t+1 I t+1 V t. It is important to note that D o is expected to rise, due to the current investments I these expectations are reflected in the current market value of the sector. 2 2.1 Wealth Shares and Payout Shares As the previous discussion suggests the appropriate measurement of wealth shares is crucial for trying to link them to the return distribution. It is important to acknowledge that wealth 2 The price per share that follows the equity capital is p t = P V [g n,t+1 (d t+1 i t+1 + g n,t+1 g n,t+2 (d t+2 i t+2 +..]
shares are determined by the shares of net payouts. One has to recognize that these can be fundamentally different than the standard dividend share models (e.g. Cochrane, Longstaff, and Santa-Clara (24, Santos and Veronesi (23. In these models the dividends of sectors cannot become negative, however, as we show below even for the aggregate market the total payouts can become negative. That is, equilibrium models for aggregate dividends ought to allow for negative payouts (or net dividends. The dividend shares in Bansal, Dittmar, and Lundblad (24 and Hansen, Heaton, and Li (24 can become negative however, these papers do not deal with the issue of aggregate payouts. To the best of our knowledge no other papers provide these measurements. Our measures indicate that any theory about wealth shares should also incorporate the possibility of negative dividend shares. The time-periods of negative net payouts are time periods when investors send more resources into the various sectors relative to what they receive from these sectors. In the next section we provide the present value based decomposition that links dividend shares to future asset returns and expected net payout growth. This decomposition helps interpret the sources of variation in wealth shares. 2.2 The Return-Shares Decomposition The return equation, in logs, can be stated as r t+1 = g o,t+1 vd t + ln[exp(vd t+1 + 1 exp(i t+1 ] (5 with g o,t+1 ln(d o,t+1 /D o,t, vd t ln(v t /D o,t, and i t+1 = ln(i t+1 /D o,t+1. A first order Taylor series expansion implies that r t+1 = κ + g o,t+1 vd t + κ 1 vd t+1 κ 2 i t+1 (6 where the κ s are constants based on the steady state values of v and i. 3 The above expression implies that, vd t = κ 1 κ 1 + κ j 1[(g o,t+j κ 2 i t+j r t+j ] (7 That is the sectoral wealth minus current outflow of aggregate dividends, reflects the aggregate dividend growth of the sector less investment. A rise in sectoral growth net of 3 In particular, κ 1 = the z and i. exp( vd 1+exp( vd exp(ī, and κ 2 = exp(ī 1+exp( vd exp(ī where bars refer to the average values of
investment, and/or a fall in expected returns raises the sectoral wealth. Consequently, vd t should predict the future returns or the future aggregate dividend growth net of investments. An expression for wealth shares is also easy to derive. Relative to the market equity capital (assuming, as in the data, that all κ s are about the same ln V t V m,t = ln D o,t D o,m,t + κ j 1[(g o,t+j κ 2 i t+j (g o,m,t+j κ 2 i m,t+j (r t+j r m,t+1 ](8 Clearly sectors that are expected to grow (dividend growth net of investments more rapidly see a rise in the relative wealth share. The above equation implies that for relative wealth share, s t, V ar(ln s t = cov(ln D o,t D o,m,t + κ j 1[(g o,t+j κ 2 i t+j (g o,m,t+j κ 2 i m,t+j ], ln s t cov( κ j 1(r t+j r m,t+1, ln s t (9 The above equation implies that variation in wealth shares are due to variation in outflow growth or due to variation is expected excess returns. That is fluctuations in wealth shares should predict relative (to the market outflow growth or excess returns. The above equation, provides a basis for thinking about what data dimensions explains the variation in wealth share fluctuations. Is the dominant influence, variation in net outflows or is it expected excess returns. In equilibrium models, such as the CAPM, imply that wealth shares and Sharpe Ratios are very tightly related intuitively, and as in Cochrane, Longstaff, and Santa-Clara (24 an increase the wealth share should increase the Sharpe Ratio. We recognize that there are pathological situations, such as when one sector starts to dominate the market (shares close to one, where the implications for the Sharpe Ratio may change. However, given the large number of sectors that we entertain in our empirical work, we do not think that these extreme share outcomes are important. Throughout the paper we will assume that wealth shares and payoff shares are stationary. That is we assume that that they have unit cointegration with the aggregate payoffs and with aggregate wealth.
3 Economic Implications for Wealth Shares Generalized Preferences For notational brevity, let the dividend share plus the (discounted anticipated aggregate payout variable be denoted by d t where d t = E t {ln D o,t D o,m,t + κ j 1[(g o,t+j κ 2 i t+j (g o,m,t+j κ 2 i m,t+j ]} and the discounted excess return on the market be Hence ln s t = d t q t q t = E t κ j 1[(r t+j r m,t+1 ] We can subtract the risk free rates from the return and the market return; this does not change the expression for q. We further assume that the expected excess returns (risk premia on the asset and the market are time varying AR(1 processes, then, it follows that r t q t = κ 1 [ 1 κ 1 ρ r m,t ]. 1 κ 1 ρ m For simplicity we also assume that all the ρ s are the same, in which case where τ = κ 1 1 κ 1 ρ. q t = τ[ r t r m,t ], We now derive the CAPM implications for wealth shares. With the CAPM assumptions, s t = 1 α Σ 1 t r t where r t is the vector of expected excess returns, and Σ t is the variance-covariance matrix of returns. For small shares, we have, ln(1 + s 1 s 1, hence, the vector of wealth shares, s t is s t = 1 + d t τ( r t r m,t where d t is dividend share plus expected relative growth vector for the different sectors and the vector of ex-ante expected excess returns is r t. We assume that the risk-free rate is
constant. Setting the left hand side equal to the CAPM portfolio implications, in equilibrium, it follows that and it follows that 1 α Σ 1 t r t = 1 + d t τ( r t r m,t r t = [1 + d t + τ r m,t ][ 1 α Σ 1 t + τi] 1 That is under CAPM assumptions, the ex-ante mean return is increasing in the dividend share. Further, if one assumes the CAPM is with a constant market risk premia, this implies that the asset beta must be increasing in expected relative dividend growth. In an attempt to use a model that captures sizeable risk premia, we follow Bansal and Yaron (24 and use more general preferences and cashflow processes. Specifically, we assume consumption and the optimal portfolio, r c are jointly log-normal and the representative agent has Epstein-Zin (1989 preferences. In this case, and using the standard log-approximation, the solution to the portfolio choice problem can be shown to be, s t = 1 γ Σ 1 t (E t r t+1 r f,t 1 + σ 2 t /2 + (1 1 γ Σ 1 where σ t is the main diagonal of Σ t, σ ht Cov t (r t+1 (E t+1 E t κj r c,t+j, and γ denotes risk aversion. The first term in the portfolio formula above is usually referred to as the myopic term, while the second reflects intertemporal hedging motives. Thus with more general preferences of the type presented here, portfolio choice will also include additional terms capturing hedging demands. t σ ht However, as can be seen from the above formula, the basic message that expected returns are increasing in dividend share is unaltered. This implication motivates our empirical work, that dividend shares and wealth shares should predict future returns in equilibrium. 4 Data Here we describe the construction of the various measures of interest. Our quarterly data is on industries and covers the time period from 1948.1 to 23.4. The return can always be stated as, R t+1 = h t+1 + y c,t+1 (1
where h t+1 is the price per-share capital gain and y c,t+1 is the conventional cash-dividend yield. To construct D o,t+1 the total outflows from a sector, the approach presented in Bansal, Dittmar and Lundblad (24 is pursued. First, the re-purchase adjusted capital gain is defined for each stock in the portfolio, h t+1 = [ p t+1 p t ] min[( n t+1 n t, 1]. (11 Then the payout (cash dividends plus repurchases yield is y o,t+1 = R t+1 h t+1, which implies that total payout is, D o,t+1 = y o,t+1 V t (12 where V t is the market value of all stocks in the portfolio. Further, the yield that reflects both inflows and outflows, y t+1 is constructed via, y t+1 D o,t+1 I t+1 V t = R t+1 V t+1 V t (13 Given y t+1, the inflow yield is y n,t+1 = I t+1 V t, where the inflows can be measured via the relation I t+1 = (y o,t+1 y t+1 V t (14 Table 1 has the data for the various objects of interest. As all the data is quarterly and have seasonals. The deseasonalized levels of D o,t, I t are constructed, by using a the trailing four quarter sum. The reported yields are based on this deseasonalized quantities. 4 5 Empirical Results Figure 2, shows the payout yields of the various sectors. It is important to note that the payout yields for various sectors fall during expansions. Even the aggregate payouts from the market, which correspond, to the equilibrium flows from the market to the households can be negative. This is displayed in Figure 3. During periods of expansion, labor and other income of households is used to inject money into the equity markets. The sectoral payouts also become negative, and vary considerably across time. The payout yield is quite stationary, unlike the cash-dividend yield that is traditionally used. While the traditional dividend yield 4 In practice, we construct D o, and measure the quantity D o,t+1 I t+1, these are summed for four quarters, and then I t+1 is extracted from these de-seasonalized measures
is very persistent and arguably predicts future returns, the well behaved payout yield mostly predicts future growth rates as we document below. Table 1 present the basic information about the wealth shares and returns. Clearly the variation in wealth shares is large it ranges from 2.2% to 7.8% for industry health and from 9.3% to 18.3% for industry manufacturing. Manufacturing s share has fallen across time and that of health care and financial services has increased considerably over time. The mean returns for these 12 industries range from 8% to 12%. These variations imply that returns distributions have to potentially be changing sizeably. To explore if share fluctuations contain information about subsequent mean returns, we present in Table 2 the projection coefficient from the regression, k κ j 1(r i,t+j r m,t+j = a i + b i log(s i,t + ɛ i,t+k (15 where r i,t+j and r m,t+j are the one-period log real returns for industry i and the market portfolio at time t + j, respectively. This projection is motivated by the second covariance term in equation (9. The slope coefficients of this equation provide the percentage of the share variation attributable to fluctuations in expected equity returns. Table 2 shows that almost all the slope coefficients are both economically and statistically are close to being insignificant. This apparent lack of fit is confirmed by the scatter-plots of expected returns and log shares by industry as displayed in Figure 4. Further, what is surprising is that almost all of the slope coefficients in Table 2 are negative. This implies that increases in shares are associated with a decline in long run mean excess returns. This result is robust to considering excess returns with respect to the risk free rate. The R 2 s of these projections of both short and long horizons are quite small. The average slope coefficient indicates that only about 1% of the variation in shares is due to fluctuations in expected excess returns. As the variation in shares must be due to either variations in expected returns or cash flows, Table 3 reports the projection coefficient from the regression, k d i,t + κ j 1( g o,i,t+j g o,m,t+j = a i + b i log(s i,t + ɛ i,t+k (16 where d i,t = log(d o,i,t log(d o,m,t and D o,i,t is the total payout of sector i during time period t, and g o,i,t+j = (g o,m,t+j κ 2 i i,t+j (g o,m,t+j κ 2 i m,t+j is the investment-adjusted
payout growth of sector i relative to the market. This projection is motivated by the first covariance term of equation (9. Table 3 shows that most the variation in shares is due to expectation about future netpayoffs (cashflows. On average the slope coefficients are positive and significant and the R 2 s are sizeable for most industries. The average coefficient across industries is about.75, that is about 75% of the variation in shares is due to net payoff variation. This pronounced relationship is also confirmed by the industry scatter-plots relating log-shares and cashflows displayed in Figure 5. Table 4 explores if current shares predict future return volatility. Specifically we consider the projection, σ i,t+k = a i + b i log(s i,t + ɛ i,t+k (17 where volatility is measured as the sum of the absolute value of unconditional residuals, that is σ i,t+k = k j= r i,t+j r i, and r i is the unconditional mean of quarterly returns for asset i. The main result from Table 4 is that the share do not predict in any measurable manner future volatility of returns. The slope coefficients and the adjusted R 2 are virtually zero. We also measured the volatility by fitting EGARCH volatility model, and as the results are similar we do not report them. An argument can be made that the influence of shifts in shares on returns and volatility are hard to measure in short time series. To address this point Table 5 reports a pooled cross sectional time series approach to measure the effects of shares levels and share changes on expected returns and volatility. The message from the pool regression is virtually identical to the univariate time series evidence discussed above. A rise in shares significantly predicts a reduction in future mean returns, and in terms of volatility predictability the slope coefficients are negative but are not statistically significant. An additional robustness check that accounts for correlations across returns is to solve for the portfolio weights using the CAPM to solve for equilibrium shares. In executing this we compute conditional mean of the returns by regressing 3-year cumulative future returns onto the market shares of 11 industries. We rely on the unconditional variance-covariance matrix of the residuals. We solve the mean variance portfolio choice problem where the target mean equals the average return on the market portfolio. Table 6 reports the projection of the implied CAPM shares on observed wealth shares, that is the regression s i = α + b i s CAP i M. Table 6 shows that the implied CAPM shares have close to zero predictive power. The
adjusted R 2 are zero except for industries Durables and Money. Finally, as an additional check that our results are not driven by level effects we repeat the analysis in Tables 2 and 3 but use as the regressor the variation in relative shares. Table 7 and 8 provide the corresponding results for these projections. The results in Table 2 and 3 are clearly robust to the use of relative shares; that is variations in relative shares virtually do not predict future expected returns but have quite substantial predictability of future net payouts. As a final experiment, we sort portfolios by growth of market share and analyze whether such growth characteristics are associated with subsequent mean expected returns and volatility. Table 9 provide the results. The columns are for low, middle, high (LG/MG/HG and where the growth rate is computed over the preceding horizon of 4,8, and 12 quarters. The rows provide information about the mean and variance of the subsequent returns of the three sorted portfolios up to 12 quarters in the future. The results clearly indicate that the high growth sector has the lowest subsequent returns on average, in fact mostly negative in excess of the market, while the low growth sector has the highest return. In terms of Sharpe ratios the evidence indicates the Sharpe ratio of the high-growth sector is the lowest. This evidence is consistent with our earlier evidence and highlights equity allocations. 6 Conclusion In this paper we inquire about the market forces that motivate economic agents to hold more (or less of their wealth in an expanding (or contracting sector. Traditional theory suggests that the markets provide agents a better deal in the form of higher mean returns or lower volatility, and potentially a higher Sharpe Ratio, to induce greater investments in expanding sectors. We find that this is not the case in the data. Indeed expanding sectors seems to typically offer a bad Sharpe Ratio deal relative to contracting sectors. One possibility is that these sectors hedge other risks for agents. However, based on our empirical evidence, these hedging demands would have to account for almost all of the rationale for agent s willingness to hold more wealth in an expanding sector we find the magnitudes of this to be quite implausible. Traditional economic motivations have difficultly in accounting for the sectoral wealth shifts, this leads to equity capital puzzle: What are the market forces that induce agents to hold more aggregate wealth in expanding sectors and less in shrinking
sectors?
References [1] Bansal Ravi, and Amir Yaron, 24, Risks For the Long Run: A Potential Resolution of Asset Pricing Puzzles, Journal of Finance, 8, 21-4. [2] Bansal Ravi, Robert Dittmar, and Christian Lundblad, 25, Forthcoming, Journal of Finance. [3] Cochrane, John H., Francis Longstaff and Pedro Santa Clara 24, Two Trees: Asset Price Dynamics Induced by Market Clearing, Working Paper, University of Chicago. [4] Epstein Larry., and Stanley Zin, 1989, Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework, Econometrica, 57, 937-969. [5] Fama, Eugene F., and Kenneth R. French, 1996, Multifactor Explanations of Asset Pricing Anomalies, Journal of Finance, 51, 55 84. [6] Hansen, Lars Peter, John Heaton and Nang Li, 24, Consumption Strikes Back?, Working Paper, University of Chicago. [7] Rosenberg, B. and J.A. Ohlson, 1976, The stationary distribution of returns and portfolio separation in capital markets:a fundamental contradiction, Journal of Finance and Quantitative Analysis,11 393-41. [8] Santos Tano and Pietro Versonesi, 24, Labor Income and Predictable Stock Returns, Forthcoming, Review of Financial Studies.
Table 1: Summary Statistics Industry R i Std(R i y bdl Std(y bdl y mvg Std(y mvg s i Std(s i Markt.23.81.35.13.16.21 1.. BusEq.28.122.21.14 -.1.29.95.43 Chemi.23.85.33.1.26.24.67.26 Durbles.27.14.43.2.36.31.64.16 Energy.25.85.4.11.28.34.127.46 Hlth.3.96.24.1.9.25.5.28 Manuf.22.94.34.15.22.3.138.45 Money.26.89.36.11.15.33.112.8 NoDur.25.84.35.14.28.18.74.18 Other.21.11.31.17.8.46.75.19 Shops.24.1.28.16.2.27.63.15 Telcm.2.85.44.2.14.14.61.17 Utils.2.72.58.2.18.25.73.23 Means and standard deviations for the market and 12 industries. The data is quarterly observation from 1947.2 to 23.4. R i is the simple real return of asset i. y bdl is the dividend yield calculated by Bansal, Dittmar and Lundblad (25 approach see the text. y mvg is the dividend-yield calculated by market value growth approach see text. s i is the market share for industry i. All dividends are deseasonalized by 4-quarter moving sum. The quantities are at annual rate.
Table 2: Return Predictability by Market Share Industry q4 R2 q8 R2 q12 R2 q2 R2 BusEq -.128.12 -.274.221 -.386.32 -.536.299.51.83.19.178 Chems -.28.15 -.58.35 -.74.44 -.83.45.26.46.53.63 Durbl -.64.24 -.143.69 -.196.113 -.225.17.37.61.65.65 Enrgy -.37.11 -.73.29 -.75.26 -.2 -.3.31.59.77.93 Hlth -.15.2 -.38.13 -.53.2 -.89.45.29.58.83.113 Manuf -.5 -.4 -.13 -.2.5 -.5.13.6.27.52.67.83 Money.2 -.4.8 -.1.16.8.23.27.9.16.2.22 NoDur -.173.134 -.333.247 -.443.325 -.538.36.69.16.115.124 Other -.2 -.5 -.3 -.1 -.58.4 -.78.5.41.72.18.178 Shops -.75.33 -.16.8 -.237.141 -.397.285.34.59.76.97 Telcm -.212.153 -.424.272 -.532.331 -.566.339.84.155.169.86 Utils -.56.28 -.96.57 -.131.87 -.17.32.37.6.78.15 The entries are from regressing future returns in excess of the market return onto current log market share. Specifically we regress kx κ j 1 (r i,t+j r m,t+j = a i + b i log(s i,t + ɛ i,t+k where r i,t+j and r m,t+j are the one-period log real return for industry i and the market portfolio at time t + j, respectively, and s i,t is the market share at time t for industry i. The market share, s i,t is the fraction of industry s i market value of total financial wealth. Formally, it is s i,t = ME i,t P N i=1 ME i,t where N = 12 is the number of industries. The regression uses quarterly observations from 1948.1 to 23.4. The standard errors under the estimated coefficients are Newey-West adjusted standard errors with 4 lags.
Table 3: Predicting Future Cashflows by Market Share Industry q4 R2 q8 R2 q12 R2 q2 R2 BusEq.622.326.519.24.442.126.38.33.218.21.228.354 Chems.787.58.727.488.77.55.656.482.115.117.123.127 Durbl 1.393.564 1.33.55 1.25.55 1.97.538.28.194.19.164 Enrgy.715.588.697.575.694.578.812.749.93.95.94.7 Hlth.933.87.917.774.91.737.866.681.88.11.133.161 Manuf 1.115.743 1.54.695 1.87.716 1.126.694.89.85.99.19 Money.922.875.911.888.9.894.872.896.42.42.43.49 NoDur.735.448.676.384.679.364.851.428.145.189.216.24 Other 1.18.31 1.42.321.89.237.475.64.197.18.191.22 Shops.688.28.717.312.694.34.518.179.213.246.234.178 Telcm.515.87.4.46.21.8.139 -.1.214.21.162.32 Utils.634.56.623.455.668.469.832.445.11.96.98.161 The entries are from regressing future cashflows onto current log market share. regression is d i,t + kx κ j 1 ( g o,i,t+j g o,m,t+j = a i + b i log(s i,t + ɛ i,t+k Specifically the where d i,t = log(d o,i,t log(d o,m,t and D o,i,t is the total payout of sector i during period t; g o,i,t+j = (g o,i,t+j κ 2 i i,t+j (g o,m,t+j κ 2 i m,t+j is the investment-adjusted payout growth of sector i relative to the market. The market share, s i,t is the fraction of industry s i market value of total financial wealth. Formally, it is s i,t = ME i,t P N i=1 ME i,t where N = 12 is the number of industries. The regression uses quarterly observations from 1948.1 to 23.4. The standard errors under the estimated coefficients are Newey-West adjusted standard errors with 4 lags.
Table 4: Predicting Volatility by Market Share Industry q4 R2 q8 R2 q12 R2 q2 R2 BusEq.313.338.617.455.864.499 1.85.338.94.191.27.49 Chems -.29.9 -.62.24 -.88.36 -.126.49.24.42.59.93 Durbl -.69.11 -.57..42 -.3.252.5.66.12.164.221 Enrgy.69.63.121.92.17.141.264.222.28.49.58.75 Hlth.32.27.59.47.79.61.94.65.19.38.56.85 Manuf -.22 -.1 -.21 -.3.16 -.4.135.2.6.118.165.242 Money.19.2.32.27.43.36.61.51.11.22.31.47 NoDur.26 -.2.4 -.2.24 -.4 -.71 -.2.57.96.136.215 Other.55.7.74.5.89.5.22.32.79.14.166.135 Shops.5.2.81.2.93.1.41 -.4.71.146.221.319 Telcm -.16 -.4 -.4 -.3 -.63 -.2 -.373.4.64.13.189.129 Utils -.114.177 -.218.261 -.33.298 -.421.236.27.45.53.89 The entries are from regressing future volatility onto current log market share. Specifically the regression is σ i,t+k = a i + b i log(s i,t + ɛ i,t+k where the volatility is measured as the sum of absolute unconditional residuals. i.e., σ i,t+k = kx r i,t+j r i, j= and r i is the unconditional mean of the returns for asset i. The market share, s i,t is the fraction of industry s i market value of total financial wealth. Formally, it is s i,t = ME i,t P N i=1 ME i,t where N = 12 is the number of industries. The regression uses quarterly observations from 1948.1 to 23.4. The standard errors under the estimated coefficients are Newey-West adjusted standard errors with 4 lags.
Table 5: Panel Regression with Fixed Effects K (r i,t+j r m,t+j K ɛ i,t+j ɛ m,t+j K log(s i,t s i log(s i,t s i 1 -.7 -.12 -.2 -.6 (.3 (.5 (.3 (.6 4 -.33 -.67 -.5 -.24 (.11 (.22 (.13 (.24 8 -.69 -.146 -.7 -.31 (.21 (.39 (.25 (.47 12 -.9 -.195 -.7 -.23 (.28 (.47 (.33 (.6 The table reports slope coefficients in panel regressions with portfolio-specific fixed effects. The four columns correspond to the following 2 sets of regressions respectively. KX KX (r i,t+j r m,t+j = α i + βlog(s i,t + ɛ i,t+k (r i,t+j r m,t+j = α i + β s i,t + ɛ i,t+k and KX KX ɛ i,t+j ɛ m,t+j = α i + βlog(s i,t + ɛ i,t+k ɛ i,t+j ɛ m,t+j = α i + β s i,t + ɛ i,t+k where s i = log(s i,t log(s i,t 12 and K is the future holding horizon in number of quarters. ɛ i,t+j and ɛ m,t+j are the demeaned log returns of industry i and the market portfolio, respectively, in period t + j. The Newey-West adjusted standard errors are in the parentheses under the slope coefficients. The number of lags in the Newey-West adjustment is equal to the number of the holding periods K.
Table 6: Implied Shares Under CAPM Restrictions Industry Intercept t-stat Slope t-stat Rcapm 2 BusEq.95 15.557 -.46-1.289.13 Chems.62 9.93.16 1.231.1 Durbl.51 7.335 -.25-1.959.52 Enrgy.131 15.54 -.5 -.178 -.19 Hlth.48 12.597 -.38 -.97 -.1 Manuf.143 22.684 -.17-1.12.4 Money.17 1.9.51.851 -.5 NoDur.73 18.71 -.3 -.273 -.18 Other.75 24.39.12.79 -.7 Shops.61 3.121 -.8 -.778 -.8 Telcm.64 27.319 -.43-2.44.84 Utils.78 5.631 -.2 -.145 -.19 This table examines CAPM restrictions. Based on estimated conditional expected returns and the covariance matrix the table provide the CAPM based implied industry shares. Long-term conditional expected returns of each sector are derived by regressing the 3-year cumulative future returns on market shares of 11 sectors. Based on the estimated expected returns, the market shares for each sector are derived based on mean-variance optimization restrictions. shares are compared to the observed shares. The implied The observed value share s i,t is the fraction of industry market value in the financial wealth, i.e. ME s i,t = P i,t Ni=1, where N = 12 is the number of industries. For the implied shares, we solve the ME i,t problem min s 1 2 s t Σ ts t s.t s t ˆµ t = r m and s t ι = 1 The optimal market shares are where ŝ t = g t + h tr m,t g t = h t = 1 [B t(σ 1 t ι A t(σ 1 t ˆµ t] D t 1 [C t(σ 1 t ˆµ t A t(σ 1 t ι] D t and A t = ι Σ 1 t ˆµ t B t = ˆµ tσ 1 t ˆµ t C t = ι Σ 1 t ι D t = B tc t A 2 t ˆµ t is the vector of expected return for all sectors at time t. Σ t is estimated by the unconditional variance-covariance matrix of the 12 industry returns (assumed constant here. R 2 capm is the R 2 in the regression of actual shares on a constant and the implied shares for each industry.
Table 7: Predicting Future Returns by Relative Market Shares Industry q4 R2 q8 R2 q12 R2 q2 R2 BusEq -.85.78 -.177.159 -.222.172 -.167.48.36.55.68.112 Chems -.13.1 -.24.6 -.32.1 -.54.36.17.29.36.41 Durbl -.29.1 -.7.42 -.81.51 -.71.47.25.43.46.46 Enrgy -.8 -.4 -.18 -.2 -.12 -.4.37.5.28.5.64.68 Hlth -.7 -.3 -.19. -.26.1 -.6.17.25.52.78.117 Manuf.6 -.3.1 -.3.28.6.71.59.21.39.51.63 Money.2 -.4.6 -.3.12.1.14.5.11.19.24.25 NoDur -.18.86 -.27.16 -.271.213 -.348.312.35.54.62.72 Shops -.47.22 -.99.53 -.145.88 -.27.214.35.64.81.79 Telcm -.91.85 -.172.138 -.219.169 -.235.178.51.88.1.76 Utils -.38.18 -.59.35 -.78.54 -.74.41.32.51.64.66 The table entries are based on regressing future returns in excess of the market return on relative log share. The regression is kx κ j 1 (r i,t+j r m,t+j = a i + b i log( s i,t + ɛ i,t+k where r i,t+j and r m,t+j are the one-period log real returns for industry i and the market portfolio at time t + j, respectively, and s i,t is the relative market share. The relative market share s i,t is the ratio of market equity value of industry i relative to a benchmark industry: s i,t = ME i,t ME bench,t. The benchmark industry is other. The regression is based on quarterly observations from 1948.1 to 23.4. The standard errors under the estimated coefficients are Newey-West adjusted standard errors with 4 lags.
Table 8: Predicting Future Cashflow by Relative Market Shares Industry q4 R2 q8 R2 q12 R2 q2 R2 BusEq.82.455.836.447.796.368.568.119.12.144.177.35 Chems.867.372.776.331.683.292.42.134.222.236.232.25 Durbl 1.296.595 1.226.599 1.15.552.824.42.181.186.181.165 Enrgy.82.326.77.279.599.229.595.273.187.173.169.163 Hlth 1.121.73 1.175.77 1.25.682 1.173.562.96.124.152.224 Manuf 1.31.514.922.471.872.479.596.296.133.114.13.122 Money 1.15.722 1.45.768 1.36.754 1.36.736.64.7.73.16 NoDur 1.141.387 1.61.352.99.269.531.89.218.268.283.316 Shops 1.7.345 1.121.392 1.4.329.327.35.238.243.232.287 Telcm.733.27.641.145.59.81.32.18.159.179.166.217 Utils.724.328.734.31.729.281.683.198.128.15.151.193 The table entries are based on regressing future cashflows on relative log share. The regression is The regression is d i,t + kx κ j 1 ( g o,i,t+j g o,m,t+j = a i + b i log( s i,t + ɛ i,t+k where d i,t = log(d o,i,t log(d o,m,t and D o,i,t are the total payout of sector i during time period t. g o,i,t+j = (g o,m,t+j κ 2 i i,t+j (g o,m,t+j κ 2 i m,t+j is the investment-adjusted payout growth of sector i relative to the market. The relative market share, s i,t, is the ratio of market equity value of industry i relative to a benchmark industry: s i,t = ME i,t ME bench,t. The benchmark industry is other. The regression is based on quarterly observations from 1948.1 to 23.4. The standard errors under the estimated coefficients are Newey-West adjusted standard errors with 4 lags.
Table 9: Event Study: Value Share Changes and Future Returns L = 4 L = 8 L = 12 LG MG HG LG MG HG LG MG HG ω i -8.86 2.94 16.3-11.63 6.22 26.96-13.8 9.46 36.7 s.e. 1.61 1.5 1.48 2.87 2.75 2.73 4.3 4.5 3.87 K = 1 r 1 -.27.7.55.11.2.47.8.28 -.6 s.e..57.56.6.59.58.61.57.56.65 r 2 -.38 -.3.51 -.1 -.18.34 -.3.18 -.9 s.e..24.17.16.26.17.18.25.2.19 σ 2 1.72.87.88 1.93.84.98 1.7 1.6.96 s.e..32.15.9.45.17.13.33.24.13 K = 4 r 1.24.56.87.88.26.25.57 1.3-1.1 s.e. 1.81 1.8 2.2 1.8 1.81 2.14 1.77 1.9 2.16 r 2 -.33.6.58.33 -.2.5.34.87 -.9 s.e..81.5.51.86.59.62.9.67.64 σ 2 7.55 3.59 3.72 7.78 3.58 3.75 7.44 4.8 3.73 s.e. 2.16.71.48 2.6.77.46 1.72.9.42 K = 8 r 1 1.45 1.1 -.85 1.98.54-1.9 1.38 1.4-3.4 s.e. 3.15 3.24 3.81 3.5 3.3 4.3 3.2 3.5 3.99 r 2.82.61 -.93 1.65.38-1.53 1.55 1.72-2.55 s.e. 1.7.97 1.4 1.28 1.7 1.26 1.34 1.22 1.15 σ 2 14.1 7.6 7.67 14.44 7.74 7.78 13.85 8.33 7.76 s.e. 4.16 1.71 1. 3.89 1.95.97 3.47 1.9.86 K = 12 r 1 2.38 1.5-2.71 2.49.32-3.6 2.31.62-5.7 s.e. 4.59 4.95 5.61 4.5 5.2 5.83 4.43 5.29 5.88 r 2 2.4.92-2.22 2.58.68-2.45 2.97 1.52-3.41 s.e. 1.3 1.3 1.44 1.6 1.35 1.64 1.84 1.55 1.39 σ 2 19.48 11.42 11.72 19.5 11.4 11.86 19.5 12.9 11.49 s.e. 5.3 2.6 1.42 5.6 2.97 1.33 4.6 2.97 1.2 This table provides evidence on the relationship between value share changes and log future returns for aggregate industry portfolios. Portfolios of industries are formed in each quarter by sorting on growth of market share in the past L quarters which are held for K quarters. LG, MG and HG represent the low, medium,and high share growth portfolios respectively. In each portfolio there are 4 industries. K is the number of quarters over which the returns and volatilities are calculated. ω i,t is the ratio of the market capitalization of industry i with respect to the total economy. The total economy includes both financial wealth as well as human capital. That is, ω i,t = ME i,t / P N ME j,t + κ LI t, where N = 12 is the number of industries and LI is the quarterly labor income. κ = 129.9/4 represents the average ratio of labor to capital income. ω i = log(ω i,t log(ω i,t L. r 1 average demeaned cumulative holding period portfolio log returns. Unconditional means are removed from the log returns of each industry. Portfolio returns are the equal-weighted average of demeaned industry returns in the portfolio. r 1 equal to the time-series average of demeaned portfolio returns. r 2 is average holding-period portfolio returns in excess of the market return. Log market returns are subtracted from log returns from each industry. Portfolio returns are the equal-weighted average of excess industry returns in the portfolio. r 2 equal to the time-series average of portfolio excess returns. σt+k 2 integrated volatility of a given portfolio in the holding period. Calculation follows 3 steps: 1 calculate the squares of sums of demeaned industry excess log returns within a given portfolio for each quarter in the holding period; 2 Add up the squares of sums over the holding period for portfolios formed in each quarter; 3 average the quarterly time-series from step 2 for each portfolio. The sample covers quarterly data from 1948.1 to 23.4. Newey-West standard errors are reported underneath the means. The number of lags in the Newey-West adjustment is equal to the number of holding periods K.
Figure 1: : Sectoral Wealth Shares This figure presents the relative market shares of various industry portfolios over the time period 1948.1 24.3. BusEq Chems Durbl.3.2.1.2.15.1.5 196 Enrgy 198 2 196 Money 198 2.12.1.8.6.4.12.1.8.6.4.2 196 Hlth 198 2 196 NoDur 198 2.1.8.6.4.2.15.1 196 Manuf 198 2 196 Other 198 2.25.2.15.1.5 196 Shops 198 2.12.1.8.6.4 196 Telcm 198 2.15.1.5 196 Utils 198 2.8.6.4 196 198 2.1.8.6.4 196 198 2.12.1.8.6.4.2 196 198 2
Figure 2: : Payout Yields by Industry This figure presents the payout yields by industry. The red line depicts the standard dividend yield y o, while the blue line depicts the net payout yield reflecting net inflows and outflows, y..2 BusEq.2 Chems.2 Durbl.2.2 196 Enrgy 198 2.2.2 196 Hlth 198 2.2.2 196 Manuf 198 2.2.2 196 Money 198 2.2.2 196 NoDur 198 2.2.2 196 Other 198 2.2.2 196 Shops 198 2.2.2 196 Telcm 198 2.2.2 196 Utils 198 2.2 196 198 2.2 196 198 2.2 196 198 2
Figure 3: : Aggregate Market Payout Yields This figure presents the payouts corresponding to the aggregate market portfolio. The red line depicts the standard dividend yield y o, while the blue line depicts the net payout yield reflecting net inflows and outflows, y..1.8 MVG BDL.6.4.2.2.4.6.8.1 195 1955 196 1965 197 1975 198 1985 199 1995 2
Figure 4: : Scatter-plot of expected returns and log market shares Each scatter-plot provides the log market share and the 4-year cumulative expected return 2 BusEq 1 Chems 2 Durbl exret t+16 1 exret t+16.5 exret t+16 1 1 4 3 Enrgy 2 1 1 log(si t.5 5 4 Hlth 3 2 2 log(si t 1 4 3.5Manuf 3 2.5 2 log(si t exret t+16 exret t+16 1 exret t+16 1 1 4 Money 3 2 1 log(si t 1 6 NoDur 4 2 2 log(si t 1 4 Other 3 2 1 log(si t exret t+16 exret t+16 1 exret t+16 1 5 4 Shops 3 2 1 log(si t 1 4 3.5Telcm 3 2.5 2 log(si t 1 4 3.5 Utils 3 2.5 1 log(si t exret t+16 exret t+16 exret t+16 1 4.5 4 3.5 3 log(si t 2 5 4 3 2 log(si t 1 5 4 3 2 log(si t
Figure 5: : Scatter-plot of log d i and log market shares Each scatter-plot provides the log market share and 4 years of dividend growth BusEq Chems Durbl log(d i,t 2 4 log(d i,t 2 4 log(d i,t 2 4 6 4 3 Enrgy 2 1 1 log(s i,t 6 4 Hlth 3 2 2 log(s i,t 6 3.5 3 Manuf 2.5 2 1 log(s i,t log(d i,t 2 3 log(d i,t 3 4 log(d i,t 2 3 4 4 3 Money 2 1 log(s i,t 5 5 4 NoDur 3 2 2 log(s i,t 4 3 2.5Other 2 1.5 log(s i,t log(d i,t 2 log(d i,t 3 log(d i,t 2 4 4 3 Shops 2 1 1 log(s i,t 4 3.5 3 Telcm 2.5 2 1 log(s i,t 4 4 3 Utils 2 1 2 log(s i,t log(d i,t 2 3 log(d i,t 2 3 log(d i,t 2.5 3 4 3.5 3 2.5 2 log(s i,t 4 4 3 2 log(s i,t 3.5 4 3 2 log(s i,t