International Market Risk and Cross-section of Greek Average Returns

Intertemporal Market Risks and the Cross-Section of Greek Average Returns1 Michail Koubouros2 University of Peloponnese & University of Piraeus Ekaterini Panopoulou3 National University of Ireland, Maynooth & University of Piraeus This draft: February 20, 2006 1We are intebted to Gikas Hardouvelis, Dimitrios Malliaropulos, Jack Meyer and an anonymous referee for their suggestions. We would also like to thank the seminar participants at the University of Peloponnese, the University of Piraeus, the National University of Ireland and the 4th HFAA Conference (Piraeus, 2005) for their helpful comments. We acknowledge nancial support from the Greek Ministry of National Education and Religious Affairs and the European Union under the “PYTHAGORAS: Funding of reasearch groups in the University of Piraeus” grant. The usual disclaimer applies. 2Corresponding author: University of Peloponnese, Department of Economics, Terma Karaiskaki, 221 00 Tripolis, Greece. Phone: (+30) 2710 230129, fax: (+30) 2710 230139, e-mail: [email protected]. 3Department of Banking and Financial Management, University of Piraeus, Greece and Department of Economics, National University of Ireland Maynooth, email: [email protected]. Abstract This paper examines whether the overall market risk along with risks reecting uncertainty related to the long run dynamics of market cash ows (dividends) and discount rates (returns) price average returns on single-sorted portfolios of the Greek stock market. Our results suggest that a two-beta intertemporal pricing model explains half of the cross-sectional variation in average returns and delivers an economically and statistically acceptable estimate of the coefcient of relative risk aversion. Despite the relative importance of market discount-rate risk, it is market dividend-growth risk that turns out to be far more signicant in determining average returns on Greek portfolios. JEL: G11, G12, G14 Keywords: CAPM, beta, cash ow risk, discount rate risk, risk aversion. 1 Introduction Numerous studies have shown that the single beta CAPM, at least in its unconditional form, performs poorly since the cross-sectional variation in unconditional market betas cannot match the observed spread in average excess returns.1Recently, Campbell and Vuolteenaho (2004) and Campbell, Polk and Vuolteenaho (2005) show that the market beta can be decomposed into a relatively bad cash-ow beta, reecting news about the market's future cash ows (dividend growth rates), and a relatively good discount-rate beta, reecting news about the market's future discount rates (returns). According to their model the two parts of total market risk have different implications in asset pricing. Specically, since market cash-ow shocks and discount-rate shocks represent permanent and temporary shocks to overall wealth respectively, rational conservative investors are particularly averse to the former and require a higher premium. More importantly, this cash-ow risk premium should be a multiple of their attitude toward risk. Empirically, Campbell and Vuolteenaho (2004) nd that their decomposition could solve the small-value puzzle found in US data. In this paper we study the cross-sectional behavior of cash-ow and discount-rate risks along with their ability to price returns for a set of 25 single sorted portfolios of the Greek stock market (Athens Stock Exchange, A.S.E.) for the period from 1991 to 2003. Using the empirical methodology of Campbell (1991), Campbell and Mei (1993), Campbell and Vuolteenaho (2004) and Campbell, Polk and Vuolteenaho (2005), we rst estimate market cash-ow and discount-rate news and betas and then check whether the sensitivities of portfolio returns to these total market risk components can serve as sufcient risk measures which are priced in A.S.E. returns. Although some recent studies examine the properties of the two components of aggregate market return in several emerging markets (e.g. Phylaktis and Ravazzolo, 2002), there is no other study, to the best of our knowledge, which examines the asset pricing implications of this decomposition using A.S.E. data. In this respect, our study comes as a direct complement to these empirical ndings since it provides some 1For a recent review on the CAPM literature see, among others, Fama and French (2004). 1 new insights, in terms of a small and emerging market, on the independent role of economic fundamentals in pricing the cross-section of average stock returns. Our results indicate that the two-beta decomposition of the total market risk increases the ability of the static, single factor, CAPM to price Greek stock returns. More in detail, all portfolios exhibit considerable spread in risk exposure to market cash-ow and discountrate risk and both types of risk are cross-sectionally priced. Furthermore, by employing a discrete-time intertemporal asset pricing model, we nd that cash-ow risk is more important for the cross-section of average A.S.E. returns since it embodies a beta-risk premium that is much higher than the one embodied in discount-rate risk. Specically, the two-beta model captures almost half of the variation in portfolio mean returns, performs slightly better than the popular Fama-French (1993) model and delivers meaningful and highly signicant values of risk aversion. Overall, and in line with the US ndings of Campbell and Vuolteenaho (2004) and Campbell, Polk and Vuolteenaho (2005), the two-beta model explains the spread in returns found across value and size portfolios and thus provides valuable insights for the small-over-large and value-over-growth puzzles. The remainder of the paper is organized as follows: Section 2 provides the theoretical decomposition of total market risk into two parts; return risks associated with market's cash- ow and discount-rate dynamics. It also develops the intertemporal asset pricing framework that will be used for the asset pricing estimation. The dataset and the econometric methodology employed to extract the news components of market unexpected returns are given in Section 3. Section 4 presents the empirical results and, nally, Section 5 offers some concluding remarks. 2 The Model Agents are assumed to choose their optimal consumption and portfolio positions using the recursive utility framework provided by Epstein and Zin (1989, 1991) and Weil (1989). 2 The lifetime utility function of the investor is given by the recursive utility function Ut; dened over current real consumption, Ct, and expected utility of future real consumption, Et[UtC1]: Ut.Ct;Et[UtC1]/D.1/C 1  tCEt[U1 tC1]1  1 (1) where 0 <  < 1 is the subjective discount factor,  > 0 is the constant, under this specication, coefcient of relative risk aversion (CRRA), is a parameter dened as D .1 /=.11/; and  > 0 is the elasticity of intertemporal substitution (EIS) between current and expected future consumption. Equation (1) has the advantage of breaking the tight link between CRRA and EIS given by power utility (D1 ), thus, disconnecting investors' risk attitude across states of nature (described by ) and across time (described by ). The consumer is assumed to nance all her consumption plan entirely from her total real wealth Wt;given the following dynamic budget constraint: WtC1D.1CRW;tC1/.WtCt/(2) where RW;tC1is the net real return on total wealth. Epstein and Zin (1989) solve for the optimal portfolio and consumption policies and show that the following set of conditional moment restrictions hold for each asset iand the total-wealth portfolio W: Et[G R1 W;tC1Ri;tC1]D1Ifor iD1; :::; N(3) where GtC1 def DCtC1 Ctis the optimally chosen gross growth rate of real consumption between tand tC1. The above set of non-linear moment restrictions can be linearized using the assumption of joint conditional log-normality of asset returns and consumption in the spirit of Hansen and Singleton (1983). Using these strong assumptions along with the dynamic budget constraint in (2), Campbell (1993, 1996) derives the following cross-sectional linear 3 restrictions on assets' risk premia that places no role in consumption as a priced risk factor: Et[Re i;tC1]Dcovt.ri;tC1;rW;tC1Et[rW;tC1]/C.1/covt.ri;tC1;NDR W;tC1/; (4) where Et[Re i;tC1]def DEt[Ri;tC1]Rf;tC1, and Rf;tC1is the simple return on the risk-free asset. The above equation can be viewed as a discrete-time version of Merton's (1973) ICAPM where changes in the future investment opportunity sets (captured by news about future total wealth portfolio returns, NDR W;tC1) are also priced in addition to the contemporaneous market risk (the rst covariance term). Campbell and Vuolteenaho (2004) go one step further and, using the unexpected return decomposition developed by Campbell and Shiller (1988a) and further extended by Campbell (1991), break the rst factor (market return innovation) into news about future dividend (cash-ows) growth rates and news about future total returns (discount-rates). Formally, Campbell (1991) has derived the following approximate log linear decomposition of returns into time tC1 revision in expectations (news) about the present value of all future total-wealth dividend growth rates (cash-ow news, NC F W) and the time tC1 revision in expectations about the present value of all future total-wealth returns (discount-rate news, NDR W): rW;tC1EtC1[rW;tC1]DNC F W;tC1NDR W;tC1;(5) where NC F W;tC1DEtC1[P1 jD0j1dW;tC1Cj]Et[P1 jD0j1dW;tC1Cj] and NDR m;tC1D EtC1[P1 jD1jrW;tC1Cj]Et[P1 jD1jrW;tC1Cj], PW;tC1is the real aggregate (market) stock price measured at the end of period tC1 (ex-dividend), dW;tC1Dlog.DW;tC1/is the log of the real dividend payment to total wealth during this period, rW;tC1Dlog.PW;tC1CDW;tC1 PW;t/ is the one-period holding log real gross return on the total wealth portfolio, WD1=[1 C exp.W/] and WDE[log.dW;tpW;t/] is the unconditional mean of the log aggregate dividend-price ratio. The rst term in (5) is the time tC1 revision in dividend growth expectations and represents a permanent positive effect on total wealth since it is never reversed subsequently, whereas the second one is the time tC1 revision in expectations about 4 future returns on total wealth and thus can be viewed as a temporary shock to the total wealth since the unexpected capital gain today rW;tC1EtC1[rW;tC1]>0is at a cost of lower future investment opportunities, i.e. EtC1[P1 jD1jrW;tC1Cj]Et[P1 jD1jrW;tC1Cj]<0. Using the above decomposition of the total wealth unexpected return and the two factor asset pricing restriction in (4) we get the following asset pricing model that assigns different roles for aggregate dividend growth rates' news and returns' news in determining asset risk premia: Et[Re i;tC1]Dcovt.ri;tC1;NC F W;tC1/Ccovt.ri;tC1;NDR W;tC1/; (6) The covariance risk premium representation in (6) can have an equivalent beta-like premium representation (Cochrane, 2001). Multiplying and dividing by the variance of total-wealth return innovations, vart.rW;tC1EtrW;tC1/, we get: Et[Re i;tC1]DC F;ti;C F;tCDR;ti;DR;t(7) with C F;tDvart.rW;tC1Et[rW;tC1]/,DR;tDvart.rW;tC1Et[rW;tC1]/and: i;W;tDcovt.ri;tC1;NC F W;tC1/ vart.rW;tC1Et[rW;tC1]/Ccovt.ri;tC1;NDR W;tC1/ vart.rW;tC1Et[rW;tC1]/ Di;C F;tCi;DR;t(8) Equation (8) states that the required risk premium on asset iis jointly determined by the betas of its return with the corresponding decomposed components of the total market risk; cash-ow and discount-rate beta that add to the full total wealth, CAPM, beta. A conservative risk-averse investor ( > 1) demands a higher risk price for risks associated with total-wealth cash-ow (dividend growth) uncertainty (i;C F ) rather than for risks linked to shocks to total wealth portfolio returns (i;DR), since any positive (negative) shock to wealth discount rates is at a benet (cost) of worse future investment opportunities, whereas 5 the investor is never compensated later for every positive (negative) shock to dividends. Hence, the beta price of market cash-ow risk C F is a multiple of the beta risk prices of market discount-rate risk DR. Thus, for a conservative investor it must be C F > DR >0. In order to get comparable results to the empirical literature of the unconditional CAPM and, more importantly, to the empirical ndings of the two-beta model of Campbell and Vuolteenaho (2004) that places a relatively more important role in cash-ow risk, we condition down equation (7) and proceed with its unconditional version. 3 Data and Empirical Methodology Our study is based on monthly Greek asset and macroeconomic data for the period from June 1991 to May 2003 (133 monthly observations) obtained from the Datastream International database. Specically, our data consist of (a) different sets of common stock test portfolios sorted on various rm specic characteristics such as book-to-market, dividend yield, market capitalization, price-earnings ratio and 3-month momentum, and (b) a set of economy-wide variables that serve as instruments. The sorting characteristics where chosen in order to generate clear spreads in average returns that will challenge the empirical validity of the two-beta asset pricing model. On the other hand, and following the common practice, the state variables have been selected under the assumption that they exhibit some forecasting ability over future portfolio returns. Lastly, we assume that the total market value-weighted portfolio is a good proxy for the total-wealth portfolio in the Greek economy, so that RWDRM. We employ a variant of the Fama and French (1993) methodology to construct valueweighted returns on 25 rm-characteristic portfolios sorted on the above characteristics, and returns on the two Fama and French (1993) aggregate size and book-to-market factor mimicking portfolios, Small-Minus-Big (SM B) and High-Minus-Low (H M L), respectively. The latter factor-mimicking portfolios will be used as benchmarks in our asset pricing 6 tests. The portfolio construction procedure has as follows. In June, every year, we break the full menu of A.S.E. common stocks available into 5 groups based (once at a time) on lastmonth book-to-market, dividend yield, market capitalization, price-earnings ratio and 3month momentum, so that each group contains an equal number of stocks. We rst collect monthly closing prices for each stock and since the theoretical decomposition in (5) requires continuous data on dividends we divide the annual dividend payment by 12 and add it to the monthly closing price.2Then, we compute the value-weighted monthly holding period simple portfolio return by weighting each stock by its relative contribution to the portfolio's total capitalization. The procedure is repeated every year and we end up with time-series data of simple returns on each characteristics-sorted portfolio. Finally, and although the model in (7) is written in real log returns, we assume that for the monthly test interval we employ, ination rates are almost fully forecastable, and thus we proxy real log returns with nominal log returns. For the construction of the returns on the aggregate value factor-mimicking zero-cost portfolio (High Minus Low, H M L) we used the 30-40-30 rule employed by Fama and French (1993). However, for the aggregate size factor-mimicking zero-cost portfolio (Small Minus Big, SM B) we adjust the formation procedure to account for the characteristics of the Greek data. We use the 70th quantile of the total market value instead of the median that was used by Fama and French. Given, that few large stocks dominate the Greek stock market, a 50% sorting would generate a small-cap portfolio that would represent only a very small proportion of the total market value. In this respect, using a larger breakpoint we can create a distribution of aggregate market value across portfolios that is relatively similar to the distribution in Fama and French(1993), while the small capitalization portfolio represents on average the 8% of the total A.S.E. market capitalization.3At the end of June 2Although this technique of spreading the dividends over the year on the closing price assumes strong form efciency of the market, it is common practice when constructing total market indexes that assume reinvestment of dividends over the next period. We thank an anonymous referee for pointing this out. 3For a similar construction procedure using data from the UK market, see Dimson, Nagel and Quigley (2003). 7 the unconditional version of the asset pricing model in (7). However, and given the low quality of risk-free rate data for our sample period we proceed with the zero-beta versions of our asset pricing tests. So, the constant term 0in the linear specications below is no longer the average pricing error as it would be in (4), (6) and (7), and thus, it can (or better should, under the hypothesis of the existence of a zero-beta asset in A.S.E.) be different from zero. The model is tested against the static CAPM and the Fama-French (1993) three-factor. More specically, we consider the following cross-sectional specication of the two beta (cash-ow and discount-rate) model: ET[Ri]D0CC Fb i;C F CDRb i;DR;(13) and we test this two-beta specication against the popular static single-beta CAPM that imposes the same risk prices in cash-ow and discount-rate risk and thus prices aggregate market risk, i;M: ET[Ri]D0CMb i;M;(14) and the popular three-factor Fama-French (1993) model that adds aggregate value (H M L) and size (SM B) factor mimicking portfolios as competing factors to the aggregate market return: ET[Ri]D0CMb i;MCH M Lb i;H M L CSM Bb i;SM B;(15) In all equations ET[Ri] denotes average (sample mean) portfolio returns and b i;kdenote the estimated betas on the kth factor as dened in (11) and (12). We estimate the unconditional unrestricted prices of beta risks (b s) for the aforementioned models as well as the following restricted version of the two-beta model in (16): ET[Ri]D0C b i;C F Cb i;C F (16) This last version enables to estimate the coefcient of relative risk aversion and the risk premium on the discount-rate factor . The model predicts that the premium associated 14 with market cash-ow risk must be a multiple of the premium associated with discountrate risk. For a conservative risk-averse investor ( > 1 in (1)); C F must be greater than DR;i.e. C F > DR. Table 6 presents the empirical ndings of the cross-sectional asset pricing tests. The table reports the mean and standard error for each estimate, as well as the average adj.-R2of the regression. Figure 1 gives a visual illustration of the empirical ability of the alternative models by plotting the realized and tted average returns. The better the model performs the closest to the 45-degree line the points fall. A perfect match (R2D100%) is achieved when all points fall on the 45-degree line. Contrary to many US studies (e.g. Fama and French, 1992, Campbell, Polk and Vuolteenaho, 2004), the traditional static CAPM performs quite well and explains almost half of the crosssectional variation in average returns. However, it fails to produce a signicant estimate for the zero-beta coefcient (b 0D 0:005 with s:e:D0:0048). Next, we check whether the two-beta decomposition in (13) with unrestricted prices of beta risk can improve the empirical validity of the standard static CAPM and whether there are different roles in market cash-ow and discount-rate risks. The model performs quite well and generates statistically signicant premia and explains 46.6% of the observed crosssectional variation in A.S.E. portfolio returns. More importantly, it generates signicant risk premia for both types of risk with the premium associated with market cash-ow risk being much higher than that associated with market's discount-rate risk (b C F D0:0274 and b DR D0:0096). These results are in line with Campbell and Vuolteenaho (2004) and in favor of the total market risk decomposition in (7) and (8). Further, when we estimate the restricted version of the model in (16) the factor of proportionality, which is restricted to be equal to the coefcient of relative risk aversion,  ; is both economically and statistically signicant. Specically, the estimate of bD2:8572 (s:e:D0:1612) is in the range hypothesized by Mehra and Prescott (1985) that could solve the well known equity premium puzzle. We also tested for unconstrained risk premia using cash-ow and discount-rate risk once at a 15 time (see, columns labelled CF and DR). Again, our results indicate that, although both types of intertemporal market risks are needed to describe the cross-section of returns, cash-ow risk is much more important with a risk premium three times higher than the one of discountrate risk. The respective estimates are b C F D0:0320 and b DR D0:0107. The two FamaFrench (1993) factors, H M L and SM B;perform relatively well by explaining the same proportion of cross-sectional volatility as the two-beta model, but fail to deliver positive and statistically signicant premium for the overall market risk (b MD 0:0015;s:e:D0:0064). What is more, none of the aggregate value and size premia (H M L and SM B) are signi- cant at the 1% level. Lastly, and for experimental purposes we use all factors in an extended model. Our results suggest that the relative importance of cash-ow risk is clear but we are inconclusive on the one of the discount-rate risk, especially when the signicant size risk is included. 5 Conclusions This paper builds on the decomposition of the overall market, or CAPM, risk into parts reecting time variation related to the dynamics of aggregate market cash ows and discount rates using data from the small and emerging Greek stock market (Athens Stock Exchange). Employing the methodology of Campbell (1991), Campbell and Mei (1993) and Campbell and Vuolteenaho (2004) we decompose market betas into two sub-betas, associated with revisions in expectations about future market dividend growth rates and future returns. Using a VAR(1) approach and a discrete time version of Merton's I-CAPM, we test whether these components of overall market risk are rationally priced and thus explain the value, size and momentum premia observed in our monthly 1991-2003 sample. The theoretical model predicts that although both types of risk are important for the cross-section, market cash- ow risk (captured by the sensitivity of returns to market cash-ow news) should earn a higher beta-risk premium than market discount-rate risk. 16 The two-beta model performs quite well in pricing average returns on single-sorted portfolios according to book-to-market, dividend-yield, market capitalization, price-earnings and 3-month momentum. Consistent with theory, the model delivers an economically and statistically signicant estimate of the coefcient of relative risk aversion (close to 3), explains almost half of the cross-sectional variation in A.S.E. portfolio returns and generally performs at least as good as the popular three-factor Fama-French (1993) model. We nd that the exposure of Greek stock portfolios to risks associated with permanent shocks to aggregate market value (captured by market cash-ow risk) is compensated with higher unconditional risk prices than the exposure to risks associated with future market returns. Our results are in favor of a rational risk I-CAPM-type story where economic agents have a long-term optimizing behavior, do not behave myopically and value stocks according to their long-run riskiness. 17 References Brennan, M., A. Wang and Y. Xia, 2004, “Estimation and Test of a Simple Model of Intertemporal Asset Pricing,” Journal of Finance, 59, 1743-1775. Campbell, J. Y., 1991, “A Variance Decomposition of Stock Returns,” Economic Journal,101, 157-159. Campbell, J. Y., 1993, “Intertemporal Asset Pricing without Consumption Data,” American Economic Review, 83, 487-512. Campbell, J. Y., 1996, “Understanding Risk and Return,” Journal of Political Economy, 104, 298-345. Campbell, J. Y. and J. Mei, 1993, “Where Do Betas Come From? Asset Pricing Dynamics and the Sources of Systematic Risk,” Review of Financial Studies, 6, 567-592. Campbell, J. Y., C. Polk and T. Vuolteenaho, 2005, “Growth or Glamour? Fundamentals and Systematic Risk in Stock Returns,” NBER Working Paper No. 11389. Campbell, J. Y. and R. Shiller, 1988a, “The Dividend-Price Ratio and Expectations About Future Dividends and Discount factors,” Review of Financial Studies, 1, 195-228 Campbell, J. Y. and R. Shiller, 1988b, “Stock Prices, Earnings and Expected Dividends,” Journal of Finance, 43, 661-676. Campbell, J. Y. and R. Shiller, 1998, “Valuation Ratios and the Long-Run Stock Market Outlook,” Journal of Portfolio Management, 24, 11-26. Campbell, J. Y. and T. Vuolteenaho, 2004, “Bad Beta, Good Beta,” American Economic Review, 94, 1249-1275. Chow, G. C., 1960. “Tests of Equality Between Sets of Coefcients in Two Linear Regressions,” Econometrica, 28, 591 605. Cochrane, J. H., 2001, Asset Pricing, Princeton University Press, Princeton NJ. 18 Dickey, D. A. and W. A. Fuller, 1979, “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, 74, 427– 431. Dimson, E., 1979, “Risk Measurement When Shares are Subject to Infrequent Trading, Journal of Financial Economics, 7, 197-226. Dimson, E., S. Nagel and G. Quigley, 2003, “Capturing the Value Premium in the U.K. 1955-2001,” Financial Analysts Journal, 59, 35-45. Eleswarapu, V. and M. Reinganum, 2004, “The Predictability of Aggregate Stock Market Returns: Evidence Based on Glamour Stocks,” Journal of Business, 77(2), 275-294. Elliott, G., T. J. Rothenberg and J. H. Stock, 1996, “Efcient Tests for an Autoregressive Unit Root,” Econometrica, 64, 813-836. Epstein, L. and S. Zin, 1989, “Substitution, Risk Aversion and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework,” Econometrica, 57, 937-969. Epstein, L. and S. Zin, 1991, “Substitution, Risk Aversion and the Temporal Behavior of Consumption and Asset Returns: An Empirical Investigation,” Journal of Political Economy, 99, 263-286. Fama, E. F. and K. R. French, 1988, “Dividend Yields and Expected Stock Returns”, Journal of Financial Economics, 22, 3-27. Fama, E. F. and K. R. French, 1989, “Business Conditions and Expected Returns on Stocks and Bonds,” Journal of Financial Economics, 25, 23-49. Fama, E. F. and K. R. French, 1992, “The Cross-Section of Expected Stock Returns,” Journal of Finance, 47, 427-465. Fama, E. F. and K. R. French, 1993, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, 33, 3-56. Fama, E. F. and K. R. French, 2004, “The Capital Asset Pricing Model: Theory and Evi19 dence,” Journal of Economic Perspectives, 18, 25-46. Hansen, L. P. and K. J. Singleton, 1983, “Stochastic Consumption, Risk Aversion and the Temporal Behavior of Asset Returns,” Journal of Political Economy, 91, 249-268. Koubouros, M., D. Malliaropulos and E. Panopoulou, 2005, “Long-Run Cash-Flow and Discount-Rate Risks in the Cross-Section of US Returns,” National University of Ireland, Maynooth, working paper No. 1580505. Kwiatkowski, D., P. C. B. Phillips, P. Schmidt and Y. Shin, 1992, “Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We that Economic Time Series Have a Unit Root?” Journal of Econometrics, 54, 159-178. Liu, N. and L. Zhangy, 2005, “The Value Spread as a Predictor of Returns,” NBER working paper No. 11326. McQueen, G., M. Pinegar and St. Thorley, 1996, “Delayed Reaction to Good News and the Cross-Autocorrelation of Portfolio Returns,” Journal of Finance, 51, 889-919. Mehra, R. and E. Prescott ,1985, “The Equity Premium: A Puzzle,” Journal of Monetary Economics, 15, 145-161. Merton, R., 1973, “An intertemporal capital asset pricing model, Econometrica, 41, 867887. Peterson, J. and G. Sanger, 1995, “Cross-Autocorrelations, Systematic Risk and the Period of Listing,” unpublished paper, University of Notre Dame. Phillips, P. C. B. and P. Perron, 1988, “Testing for a Unit Root in Time Series Regression,” Biometrika, 75, 335–346. Phylaktis, K. and F. Ravazzolo, 2002, “Measuring Financial and Economic Integration with Equity Prices in Emerging Markets,” Journal of International Money and Finance, 21, 879903 . Rozeff, M., 1984, “Dividend Yields and Equity Risk Premiums,” Journal of Portfolio Man20 agement, 10, 68-75. Scholes, M. and J. Williams, 1977, “Estimating Betas from Nonsynchronous Data,” Journal of Financial Economics, 5, 309-327. Weil, P., 1989, “The Equity Premium Puzzle and the Riskfree Rate Puzzle,” Journal of Monetary Economics, 24, 401–421 21 Table 1. VAR estimates for market portfolio and diagnostic tests Panel A: VAR Estimates rM;tC11log .L ItC1/ptC1etC1V StC1 constant 0:033 .0:021/ 0:023 .0:009/0:055 .0:029/ 0:032 .0:041/ rM;t0:147 .0:086/ 0:056 .0:039/ 0:043 .0:119/ 0:185 .0:165/ 1log .L It/0:194 .0:160/0:528 .0:073/ 0:077 .0:223/ 0:405 .0:308/ ptet0:007 .0:001/ 0:011 .0:007/ 0:969 .0:021/0:044 .0:028/ V St0:036 .0:006/ 0:003 .0:006/ 0:034 .0:018/ 0:967 .0:025/ R29:5% 32:9% 94:7% 91:9% F-stat. 3:530 16:499 598:4 384:70 Panel B: Unit Root Tests rM1log .L I/pe V S ADF 10:199 6:391 1:722 1:746 ADF-GLS 10:200 6:088 1:7401:759 PP 10:259 6:388 1:944 2:046 KPSS 0:229 0:095 0:180 0:137 Panel C: LM Test for Heteroscedasticity (ARCH Test: lag D4/ OurMOu1log.L I /OupeOuV S F-stat. 0:327 1:081 2:134 0:709 p-value [0:859] [0:369] [0:080] [0:593] Note: Panel A. presents estimates of the VAR(1) system in (9). rM;is the value-weighted market return, 1log .L I/is the change in the logarithm of the OECD leading indicator, peis the market log price-earnings ratio and V S is the value-spread dened as the difference between the log(B/M) of the small high-B/M portfolio and the log(B/M) of the small low-BE/ME portfolio. Standard errors of the estimates are in parentheses. Panel B. presents the unit-root tests for the state variables used in the VAR(1). ADF, ADF-GLS, PP and KPSS stand for the values of the Dickey-Fuller, Dickey-Fuller with GLS detrending, Phillips-Perron and Kwiatkowski-Phillips-Schmidt-Shin tests, respectively. *, ** and *** denote signicance at 10%, 5% and 1%, respectively. Panel C. reports the values of ARCH heteroscedasticity tests on the estimated VAR(1) residuals. The sample period spans from June 1991 to May 2003. 22 Table 2. Market portfolio cash-ow and discount-rate news Covariance matrix of news News corr/std.dev. NC F MNDR MNC F MNDR M NC F M0:0081 0:0034 NC M0:091 0:563 NDR M0:0034 0:0046 ND M0:563 0:215 Correlations of innovations with news Functions Innovations/News NC F mNDR mNC F MNDR M rM0:679 0:225 rMshock 1:052 0:052 1log .L I/0:277 0:295 1log .L I /shock 0:683 0:683 pe0:224 0:398 peshock 0:273 0:273 V S 0:603 0:855 V S shock 0:399 0:399 Note: The table reports the estimated covariance matrix (upper-left) and the correlation matrix with standard deviations (upper-right) of the estimated market portfolio cash-ow and discount rate news using equations (9) to (10), the correlations of innovations of state variables with market news (lower-left) and the mapping functions dened in (10). The sample period spans from June 1991 to May 2003. 23