Long-run Consumption Risks in Assets Returns: Evidence from Economic Divisions

Long-run Consumption Risks in Assets Returns: Evidence from Economic Divisions Abdulrahman Alharbi 1 Abdullah Noman 2 Abstract: Bansal et al (2009) paper focus on measuring risk in consumption especially in the long-run. They proposed cointegrating dividends and consumption growth and using VAR that utilizes the deviation between the two series as an error correction. I used two datasets with monthly and annual frequency to test the power and predictability of the suggested model in comparison with other wellknown models. The data include S&P500 and all firms covered by CRSP database divided according to their economic division (2-Digit Standard Industrial Classification Codes) from the period 1958 to 2013. However, in these samples, we did not find support for the proposed benefits of using error correction VAR model that suggested by Bansal et al (2009) over consumption growth-based VAR. In general, we did not find evidence for long-run stock returns predictability in all tested assets pricing models (C-CAPM, consumption growth-based VAR, Error Correction VAR). Keywords: Assets Pricing, Long-run Risk, Consumption-based model, Vector autoregression (VAR), Error correction model (ECM). 1 Abdulrahman Alharbi, College of Business Administration,Nicholls State University abdulrahman.alharbi@nicholls.edu 2 Abdullah Noman, College of Business Administration, Nicholls State University, abdullah.noman@nicholls.edu 1

Long-run Consumption Risks in Assets Returns: Evidence from Economic Divisions Epstein & Zin (1989) propose that systematic risk of an asset is determined by covariance with both returns to the market portfolio and consumption growth. The risk is the changes in consumption and the representative agent is sensitive to that variation over time periods. However, the empirical findings confirmed that the assets pricing models do not explain much of assets pricing anomalies in short-run and perform even worse in longer horizons. The short-run anomalies resulted in well-known puzzles as they represent unexplained deviations from theoretical values. The poor performance of assets pricing models in the long-run triggered a debate about agents determinants of risk in long-run and ways to model them. French & Fama (1988) test the predictability of stock returns in multiple investment horizons and reported increased R 2 with increases in horizons and concluded that past returns might predict the future ones. Cambell & Shiller (1988) find that dividends-price ratio Granger causes the real consumption growth but the relation has the wrong sign. Cochrane (1999, p245) believe that the aggregate dividends are predictable by consumption/dividends ratio and in the long-run where the only source of risk would be the changes in the average consumption growth. Poterba & Summers (1988) tested the long-run of stock returns variances and found it to be less than one suggesting the stocks has less risk in the long-run. However, other researchers disagree with returns predictability. For example, Boudoukh et al (2006) suggested that the long-run predictability of stock is a myth and outlined several reasons for believing so. They show that the regression correlation between 1-year and 2-year estimators are about 99% percent. Therefore, the low predictability in short-run adds up with longer horizons and result in higher beta and R 2 because of regressions correlation. Bansal & Yaron (2004) paper attempts to resolve many assets market by using and consumption and dividends growth rates. They utilize Epstein and Zin s (1989) preference and 2

choose price-dividends ratio as it predicts long-horizon equity returns as documented by Campbell and Shiller (1988). The standard consumption-based asset pricing model with power utility with i.i.d consumption growth has problems in explaining equity premium puzzle, risk-free rate puzzle, excess volatility puzzle and a cross-section of stock returns. Bansal & Yaron propose a model that solves these puzzles by changing the two assumptions. Expected consumption and dividend growth contain a small persistent component. Shocks to the expected consumption growth alter the expectations about the assets pricing for long horizons (long-run risk). The conditional volatility of consumption and dividend growth is time-varying, implying time-varying risk premia. Agents fear adverse shocks to long-run growth and require a high-risk premium for holding risky assets. Risk-premia has three sources: short-run risk, long-run risk, consumption volatility risk. The paper supports the assumption that aggregate consumption and dividend growth processes are both has a small but persistent expected growth rate component and a conditional volatility component. Based on the ideas that assets different level sensitivity to various sources of systematic risk justify differences in risk premia, Bansal et al (2005) show that cash flow beta as a measure of economic risks can significantly explain assets risk premia. Asset prices reflect the discounted value of cash flows; return news, consequently, reflects revisions in expectations about the entire path of future cash flows and discount rates. Systematic risks of assets that their cash flows are subject to higher aggregate consumption risks should have larger cash flow beta and thus a higher risk premium. When portfolios have a greater covariance with consumption, they have higher risk premia. Bansal et al (2009) paper focused on measuring risk in consumption especially in the longrun. The paper utilizes the connection of changes in dividends and consumption to model cointegration-based VAR with error correction. The deviations of dividends from consumption contain a unit root causing the two series to drift apart. These deviations contain information about 3

the future returns. The suggested model predictability of dividends growth is better than traditional ones in the short and long horizons. That is an indication that the error correction term captures transitory variation in dividend growth rates. The suggested model explains 11.5% of return variation in the short horizon and 44.0% in the long run. The cointegrating residual, included in the error-correction specification, contains distinct information about future returns and is a significant predictor of both future growth rates and future returns at short and intermediate horizons. R 2 of EC-VAR specification explain more 75% at all horizons while other models results deteriorate with time. This proofs that the cointegration relation between dividends and consumption in determining assets risk premia is important in the short as well as the long horizons. Based on the preceding literature review, the long-run risk is usually linked to aggregate consumption. Since different sectors of an economy respond differently to changes in consumption growth, risk premia should be different in each division. I will use S&P500 and all firms covered by CRSP on the basis of their economic division (2-Digit Standard Industrial Classification Codes). I will follow a similar method that was developed by Bansal, Kiku, Yaron (2009) which is a cointegrating relation between dividends and consumption as a measure of long-run consumption risks. They used annual returns data all firms in CRSP from 1929 to 2002 and created twenty weighted-value portfolios. Ten size-sorted deciles portfolios and the other ten are sorted according to Book-tomarket decile portfolio. This attempt will be evidence for or possibly against the long-run consumption risks as being a key determinant of risk premia in all investment horizons. Data Two datasets are used in this paper. Data used are tested at different monthly and annually frequencies. The data includes S&P500 and CRSP monthly data. I am following Bansal et al (2009) methodology. First, I utilize aggregate data, S&P500, to check if the relation dividends and 4

consumption growth are maintained at the aggregate level and whether cointegration of this relationship explains something on short and long horizons. Second, I use monthly CRSP data to establish a basis of comparison between our results and that of Bansal et al (2009). Third, I use economic division (2-digit SIC) as a measurement of the strength of the relationship between dividends and consumption growth its cointegration. The reason for using economic division is the firm s in the same division are likely to be affected similarly by market conditions including changes in consumption growth. Moreover, systematic risks of assets that their cash flows are subject to higher aggregate consumption risks should have larger cash flow beta and thus a higher risk premium according to Bansal et al (2005). Table 1A: Summary Statistics: S&P 500 Cash Flow growth Returns Portfolio Frequency mean SD mean SD S&P500 m1 One-month forecast 0.0014 0.0063 0.0299 0.0372 S&P500 m3 3-month forecast 0.0041 0.0173 0.3229 0.0369 S&P500 m6 Six-month forecast 0.0081 0.0318 0.6457 0.0669 S&P500 m12 12-month forecast 0.0169 0.0631 1.3986 0.1344 S&P500 y1 One-year forecast 0.0117 0.0900 0.0526 0.1618 S&P500 y5 Five-year forecast 0.0540 0.2012 0.2855 0.3643 S&P500 y10 Ten-year forecast 0.1431 0.2508 0.6542 0.5811 Table 1B: Summary Statistics: 2-Digit SIC Cash Flow growth Returns 2-Digit SIC mean SD mean SD A. Agriculture, Forestry, & Fishing 0.0000 0.0000 0.0000 0.0000 B. Mining -0.0366 0.4532-0.0205 0.1525 C. Construction -0.0589 0.5296-0.0007 0.1965 D. Manufacturing -0.0643 0.2205-0.0059 0.1344 E. Transportation & Public Utilities -0.0602 0.2108-0.0059 0.1139 F. Wholesale Trade -0.0385 0.3145-0.0016 0.1343 G. Retail Trade 0.1431-0.0555-0.0014 0.1380 H. Finance, Insurance, & Real Estate 0.0107 0.2443 0.0256 0.1187 I. Services -0.0300 0.3965-0.0004 0.1452 J. Public Administration -0.4072 0.8590 0.0066 0.2246 K. Nonclassifiable Establishments -0.0056 1.8338 0.0029 0.2359 5

Empirical Results In this section, I examine Bansal et al (2009) framework to assets risks in consumption. I first analyze the possibility of cointegrating assets dividends with consumption and what this cointegration effect on the predictability of assets growth rates and returns. I then calculate each portfolio s consumption beta and different investment horizons expected returns as implied by EC- VAR (Error Correction-Vector of Autoregression) framework. Table 2A: Cointegration Parameters and ACF: S&P 500 Portfolio Frequency δ ACF(1) ACF(5) ACF(10) Unit Root S&P500 m1 One-month forecast 0.2014 0.9914 0.8705 0.6735-2.545 S&P500 m3 3-month forecast 0.2019 0.9922 0.8734 0.6766-2.752* S&P500 m6 Six-month forecast 0.2060 0.9928 0.8807 0.6852-2.701* S&P500 m12 12-month forecast 0.2205 0.9937 0.8987 0.7123-2.846* S&P500 y1 One-year forecast 0.2291 0.7844 0.0924-0.1301-2.252 S&P500 y5 Five-year forecast 0.1581 0.8989 0.1500-0.2634-2.495* S&P500 y10 Ten-year forecast 0.1431 0.9394 0.2732-0.3009-3.252* * indicate existence of unit root Table 2B: Cointegration Parameters and ACF Portfolio Freq. δ ACF(1) ACF(5) ACF(10) Unit Root A. Agriculture, Forest& Fishing Annual 0.2138 0.5183 0.0235 0.0511-3.950 B. Mining Annual 0.2640 0.4955-0.1446-0.0452-4.199 C. Construction Annual 0.2664 0.6111 0.0875 0.0296-3.501 D. Manufacturing Annual 0.0398 0.4875-0.0102-0.0059-4.156 E. Transportation &Pub. Utilities Annual 0.0842 0.5451-0.0611 0.0525-3.624 F. Wholesale Trade Annual -0.1379 0.6429 0.0943 0.1405-3.238 G. Retail Trade Annual 0.2784 0.7530 0.3825 0.2646-2.449 H. Fin, Insurance, & Real Estate Annual -0.1378 0.4462-0.2152-0.0150-4.094* I. Services Annual -0.3588 0.6677 0.0402-0.0306-3.750 J. Public Administration Annual -0.1110 0.6240 0.2396-0.2336-2.538 K. Nonclassifiable Establishments Annual 0.2138 0.5183 0.0235 0.0511-3.950* * indicate existence of unit root 6

Table 2 shows the estimated cointegration parameters between portfolios cash flows and consumption, the sample autocorrelation functions (ACF) of the cointegrating residuals, and unit root test statistics and associated critical value. The estimated cointegration parameters are coefficient regressing the deterministically detrended dividends on detrended consumption using OLS. It can be seen that the majority of portfolios with monthly frequency autocorrelations function exhibit a relatively rapid decline. As proposed by Bansal 2009, the long-run dynamics of portfolios dividends and aggregate consumption are governed by the same permanent component that can be eliminated by the appropriate linear combination of the levels. However, monthly frequency does not strongly support this argument as most of them contain a unit root and hence dividends growth and consumption growth cannot be cointegrated. These series that will not be considered in further test and analysis. Moreover, the first column shows the estimated cointegration parameters which change with data frequency changes but it does not have a clear pattern. That is may be an indication that consumption risk is not clear in longer horizons regardless of data frequency. It is also possible that important information which affects dividends is lost when data frequency changed. For instance, the table shows one-year forecast using monthly data, S&P500 m12, and one-year annual data, S&P500 y1 which has a higher cointegration parameters and lower autocorrelation function that decays at a faster pace. Four of 2-digit SIC have a negative relation with growth in consumption. However, two of them has non-stationary and will not be considered in further test and analysis. Wholesale Trade and services sectors have a negative relation with consumption growth. The unit-root tests suggest cointegration of three monthly S&P500 portfolios and one S&P500 portfolios with annual frequency. There are 2 out of 11 sectors has a unit root. The 7

remaining portfolios test statistics are close to the MacKinnon critical value of 10% with exception to 5-year forecast. Table 3A : Predictability Evidence: S&P 500 Dividends Growth Portfolio Frequency EC-VAR VAR S&P500 m3 3-month forecast 0.51 0.68 S&P500 m6 Six-month forecast 0.76 0.75 S&P500 m12 12-month forecast 0.96 0.91 S&P500 y10 Ten-year forecast 0.54 0.26 Table 3A above shows the R 2 for projecting dividends in different forecasting horizons using monthly or annual data. The R 2 of dividend projection implied EC-VAR, third column, and VAR, last column, are obtained by running VAR of change in demeaned consumption, dividends, pricedividends ratio and the level of price-dividends ratio. In case of EC-VAR, I add to the previous VAR variables the residual of regressing detrended dividends on detrended consumption as in Bansal et al (2001) to show that dividend growth rates are predicted by the cointegrating residuals. That is the current deviations of an asset s cash flows from their long-run relation with consumption should forecast the dynamics of dividend growth rates while dividends are moving back toward the equilibrium. R 2 increases with increasing forecasting periods for the two models both in monthly series. However, the differences in R 2 of two models are not constant. For example, the R 2 difference increases in the three-month forecast from one month forecast and then decrease in the six-month forecast and again it increases with the 12-month forecast. Annual frequency data shows EC-VAR superior performance in dividends projection compared to VAR model. Although adding error term surely improved the predictability of dividends growth in longer horizons, EC-VAR did not capture the transitory variation in dividend growth rates as argued by Bansal et al (2009). Table 3B: Predictability Evidence: 2-Digit SIC Dividends Growth 8

Portfolio Freq. EC-VAR VAR EC-VAR VAR EC-VAR VAR 1-yr 1-yr 5-yr 5-yr 10-yr 10-yr A. Agriculture, Forest& Fishing Annual 0.0277 0.0879 0.2031 0.1152 0.2111 0.197 B. Mining Annual 0.2859 0.0558 0.3943 0.3011 0.2982 0.2812 C. Construction Annual 0.1583 0.1748 0.6273 0.552 0.4596 0.4508 D. Manufacturing Annual 0.2644 0.2542 0.4648 0.4232 0.2643 0.2541 E. Transportatio &Pub. Utilities Annual 0.1883 0.0992 0.5815 0.4959 0.3742 0.3578 F. Wholesale Trade Annual 0.3093 0.0772 0.4418 0.4409 0.6289 0.5032 G. Retail Trade Annual 0.1212 0.093 0.6197 0.4797 0.587 0.5563 I. Services Annual 0.0277 0.0879 0.2031 0.1152 0.2111 0.197 J. Public Administration Annual 0.2859 0.0558 0.3943 0.3011 0.2982 0.2812 For the 2-SIC code sectors, the result is mixed. For 1-year horizons, R 2 implied by EC-VAR is relatively better than the other model s R 2 in six sectors. This pattern continues as R 2 implied by ER- VAR in eight sectors for both 5-years and 10-year investment horizons is higher that of consumptionbased VAR model. Although adding error term surely improved the predictability of dividends growth in longer horizons, EC-VAR does not capture the transitory variation in dividend growth rates as argued by Bansal et al (2009). Table 4A : Predictability Evidence: S&P 500 Returns EC-VAR VAR Portfolio Frequency R 2 R 2 TR R 2 R 2 TR S&P500 m3 3-month forecast 0.00 0.00 0.66 0.25 S&P500 m6 Six-month forecast 0.00 0.00 0.63 0.33 S&P500 m12 12-month forecast 0.00 0.00 0.63 0.46 S&P500 y10 Ten-year forecast 0.06 0.05 0.48 0.26 In table 4A, asset return predictability provides evidence against EC-VAR model. The table shows return and total return projections adjusted R 2 values for horizons 3,6,12 months and 10 years implied by the EC-VAR and VAR model. The EC-VAR specification almost explains nothing about of returns variation. Its best performance is 5% in 10-year forecasting. In contrary to Banasal et al (2009) finding, VAR, the model that does not cointegrate dividends growth and consumption, 9

explains between 48% in ten-year forecasting period to 66% of returns variation. Therefore, including the cointegrating residual did not improve the predictability of asset returns. Table 4B: Predictability Evidence: 2-Digit SIC Returns Portfolio Freq. EC-VAR VAR EC-VAR VAR EC-VAR VAR 1-yr 1-yr 5-yr 5-yr 10-yr 10-yr A. Agriculture, Forest& Fishing Annual 0.16 0.04 0.29 0.23 0.52 0.50 B. Mining Annual 0.04 0.02 0.51 0.50 0.66 0.59 C. Construction Annual 0.12 0.08 0.40 0.38 0.33 0.30 D. Manufacturing Annual 0.14 0.05 0.46 0.41 0.65 0.64 E. Transportat. &Pub. Utilities Annual 0.05 0.02 0.48 0.47 0.65 0.63 F. Wholesale Trade Annual 0.06 0.10 0.12 0.12 0.42 0.39 G. Retail Trade Annual 0.05 0.11 0.25 0.25 0.15 0.15 I. Services Annual 0.16 0.04 0.29 0.23 0.52 0.50 J. Public Administration Annual 0.04 0.02 0.51 0.50 0.66 0.59 R 2 implied by EC-VAR specification is always better than that of VAR in all economic sectors for all investment horizons. That indicates that the economics division may be an important factor in explaining dividends and consumption growth cointegration. It also supports the finding that consumption growth affects economic sectors differently and consistent with Bansal et al (2005) viewpoint that systematic risks of assets that their cash flows are subject to higher aggregate consumption risks should have larger cash flow beta and thus a higher risk premium. Table 5A : Conditional Means Returns: S&P 500 Returns Portfolio Frequency EC-VAR VAR S&P500 m3 3-month forecast -0.1614-0.1617 S&P500 m6 Six-month forecast 3.0460 3.0453 S&P500 m12 12-month forecast 2.6709 2.6694 S&P500 y10 Ten-year forecast 2.6299 2.6558 Table 5B : Conditional Means Returns: 2-Digit SIC Returns Portfolio Freq. EC-VAR VAR EC-VAR VAR EC-VAR VAR 1-yr 1-yr 5-yr 5-yr 10-yr 10-yr A. Agriculture, Forest& Fishing Annual 0.0229 0.0229 0.0429 0.0429 0.0562 0.0562 B. Mining Annual 0.0231 0.0231 0.0426 0.0426 0.0562 0.0562 10

C. Construction Annual 0.0228 0.0228 0.0425 0.0425 0.0562 0.0562 D. Manufacturing Annual 0.0227 0.0227 0.0424 0.0424 0.0561 0.0561 E. Transportatio &Pub. Utilities Annual 0.0234 0.0234 0.0428 0.0428 0.0568 0.0568 F. Wholesale Trade Annual 0.0228 0.0228 0.0425 0.0425 0.0561 0.0561 G. Retail Trade Annual 0.0227 0.0227 0.0425 0.0425 0.0561 0.0561 I. Services Annual 0.0229 0.0229 0.0429 0.0429 0.0562 0.0562 J. Public Administration Annual 0.0231 0.0231 0.0426 0.0426 0.0562 0.0562 Table 5A above shows mean returns for the portfolios at the 3, 6, 12 months and 10-year horizons as implied by the EC-VAR and VAR models. Table 5B also shows 2-digit SIC base portfolio for both in 1-year, 5-year, 10-year investment horizons. Following Bansal et al (2009), VAR model uses only its beta and the demeaned consumption growth to estimate dividends growth and hence the estimated returns as in Campbell & Sheller (1988). However, EC-VAR adds to dividends growth the correction term before estimating the returns. The conditional returns of the two models are similar and differences between the returns are not affected either by horizon nor by changing the data frequency. This finding is not supportive of the idea that error correction improves the predictability of the returns and cointegrating the dividends growth and consumption growth maintain the long-term relationship of the two series. Table 6A: Consumption Betas by Horizons: S&P 500 Returns UCOND. VAR EC-VAR Portfolio Β S.E. P.vl. β S.E. P.vl. β S.E. P.vl. S&P500 m3 0.3360 0.0618 0.0000 0.2750 0.0218 0.0000-0.4690 0.3290 0.0650 S&P500 m6 0.3010 0.0413 0.0000 0.2590 0.0227 0.0000-0.6240 0.3680 0.0300 S&P500 m12 0.2920 0.0361 0.0000 0.2500 0.0262 0.0000-0.9040 0.4186 0.0080 S&P500 y10 1.2137 0.1589 0.0000 1.0703 0.2377 0.0000 0.1299 0.3612 0.7200 Table 6 presents the consumption beta by horizon to assess the implications of cointegration as a determinant of assets consumption risks. The betas as implied by the EC-VAR are insignificant and reveal considerable variation with an unexpected negative sign which contradicts the literature. VAR betas are significant throughout the investment horizons but they are much smaller than C-CAPM 11

betas. It is noted that as the horizon increases the precision of the estimates suffers since the standard error increases. The tables B and C show 2-digit SIC base portfolio for both in 1-year, 5-year investment horizons. The table uses three assets pricing model: unconditional C-CAPM, EC-VAR, and VAR. Table 6B: One-year Consumption Betas by Horizons: 2-Digit SIC Returns UCOND. VAR EC-VAR Portfolio Β S.E. β S.E. β S.E. A. Agri, Forest& Fish 0.0172 0.0188 0.0172 0.0188 0.0172 0.0188 B. Mining -0.0046 0.0178-0.0046 0.0178-0.0046 0.0178 C. Construction 0.0052 0.0146 0.0052 0.0146 0.0052 0.0146 D. Manufacturing 0.0077 0.0125 0.0077 0.0125 0.0077 0.0125 E. Trans &Pub. Utili -0.0023 0.0157-0.0023 0.0157-0.0023 0.0157 F. Wholesale Trade -0.0091 0.0168-0.0091 0.0168-0.0091 0.0168 G. Retail Trade 0.0033 0.0184 0.0033 0.0184 0.0033 0.0184 I. Services 0.0172 0.0188 0.0172 0.0188 0.0172 0.0188 J. Public Administ. 0.0033 0.0184 0.0033 0.0184 0.0033 0.0184 Table 6C: Five-year Consumption Betas by Horizons: 2-Digit SIC Returns UCOND. EC-VAR VAR Portfolio Β S.E. β S.E. β S.E. A. Agri, Forest& Fish 0.0172 0.0188 0.0032 0.0329 0.0032 0.0329 B. Mining -0.0046 0.0178-0.0108 0.0334-0.0108 0.0334 C. Construction 0.0052 0.0146 0.0059 0.0261 0.0059 0.0261 D. Manufacturing 0.0077 0.0125-0.0071 0.0239-0.0071 0.0239 E. Trans &Pub. Utili -0.0023 0.0157-0.0049 0.0244-0.0049 0.0244 F. Wholesale Trade -0.0091 0.0168-0.0288 0.0294-0.0288 0.0294 G. Retail Trade 0.0033 0.0184-0.0198 0.0388-0.0198 0.0388 I. Services 0.0172 0.0188 0.0032 0.0329 0.0032 0.0329 J. Public Administ. 0.0033 0.0184-0.0108 0.0334-0.0108 0.0334 The C-CAPM coefficient is significant in all horizon and almost the same for the monthly frequency and very large for the 10-year investment horizons. Some Betas of economic division are negative in all models which reflect the nature of that division rather than a misspecification of data. 12

It is clear EC-VAR did not outperform consumption based VAR model. The error- correction model is not supported in our sample. Table 7A: Price of Risk: S&P 500 Monthly and Annual Data Frequency UCOND. EC-VAR VAR Portfolio ƛ S.E. R 2 ƛ S.E. R 2 ƛ S.E. R 2 S&P500 m3 0.1831 0.0427 0.09-0.5852 0.0293 0.10 1.0008 0.0413 0.10 S&P500 m6 0.0848 0.0244 0.16-0.2925 0.0106 0.16 0.7085 0.0220 0.16 S&P500 m12 0.0295 0.0122 0.02-0.1705 0.0049 0.30 3.7924 0.0945 0.30 S&P500 y10 0.0300 0.0212 0.00-0.0140 0.0015 0.00 0.0017 0.0002 0.00 Table 7B: Price of Risk: All Economic Sectors UCOND. EC-VAR VAR Portfolio ƛ S.E. R 2 ƛ S.E. R 2 ƛ S.E. R 2 1-year 0.1831 0.0002 0.20 0.1481 0.0388 0.20 2.7076 0.0158 0.20 5-year 0.1831 0.0002 0.20 0.0138 2.3477 0.02-0.2173 0.0001 0.60 Tables 7A and 7B explore the risk-return relation and with the preceding specifications, C- CAPM and EC-VAR and VAR. The tables present the market prices of risk using one-step GMM and along with that the robust standard errors and R 2 are reported. At the three-month horizon, betas implied EC-VAR model explain 10% of the cross-sectional variation in mean returns with a negative price of risk of 0.58 (SE = 0.02). This explanatory power is sustained with six-month horizons, with adjusted R2 of 0.16. However, EC-VAR explanatory power with ten-year investment horizons vanishes which also the case in other models. The table also shows 2-digit SIC base portfolio for both in 1-year, 5-year. At the one-year horizon, betas implied EC-VAR model explain 20% of the crosssectional variation in mean returns with a positive price of risk of 0.14 (SE = 0.03). This explanatory power is sustained only in a case of VAR which increases to 60% in five-year investment horizon. However, EC-VAR explanatory power with five-year investment declines tremendously to almost zero in five-year investment horizons. 13

Conclusion Bansal et al (2009) paper focused on measuring risk in consumption especially in the longrun. The paper links the changes in dividends and consumption with cointegration-based VAR with error correction to improve model predictability because the deviations of dividends from consumption contain information about the future returns. The possibility of cointegration helps in determining risk premia. Since Bansal et al (2009) concluded that the long-run risk is almost completely dominated by consumption growth, then it has to be true that risk premia of each division in the economy reflect its responses to changes in consumption growth. Because each economic division responds differently to consumption growth shocks, risk premia should be different for each division. Bansal used only annual data from 1929 to 2002 that have only 74 observations which might negatively affect the power of the tests. To avoid that, I used two datasets with monthly and annual frequencies. The data include S&P500 and all firms covered by CRSP on the basis of their economic division (2-Digit Standard Industrial Classification Codes). I first analyze the possibility of cointegrating assets dividends with consumption and what this cointegration effect on the predictability of assets growth rates and returns. I find that two monthly and annual S&P500, two economic divisions (out of 11) series cannot be cointegrated. The EC-VAR predictability power, measured by R 2 of dividend projection, is not superior to the VAR model in most economic sectors and investment horizons. The EC-VAR predictability power is tested by its implied returns. By regressing implied returns on the expected returns, the goodness of fit of EC-VAR is worse than that of VAR model in aggregate data and is not better when it comes to economic division returns predictability. The conditional returns of the two models are similar and differences between the returns are not affected by either the horizon or frequency changes. This finding is not supportive of the idea that error correction improves the predictability of the returns 14

and using the cointegration of the dividends growth and consumption growth maintain the long-term relationship of the two series. To assess the implications of cointegration as a determinant of assets consumption risks, the consumption beta by investment horizon were evaluated. Nevertheless, the betas as implied by the EC-VAR are insignificant and reveal considerable variation with an unexpected negative sign. It also noted that EC-VAR did not outperform consumption based VAR model over investment horizons or across divisions. Furthermore, EC-VAR ability to capture that differences in mean returns across various investment horizons evaluated using one-step GMM. EC-VAR was not better than VAR and give a negative price of risk. In our sample, the proposed benefits of EC-VAR over consumption growth-based VAR are noted. The findings of this paper cast doubt on the long-run stock returns predictability regardless of the assets pricing model being used. 15

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