Intertemporal Market Risk and Cross-section of Greek Average Returns

Intertemporal Market Risks and the Cross-Section of Greek Average Returns Michail Koubouros1 University of Peloponnese Ekaterini Panopoulou2 National University of Ireland & University of Piraeus This draft: September 18, 2005 1Corresponding author: University of Peloponnese, Department of Economics, Terma Karaiskaki, 221 00 Tripolis, Greece. Phone: (+30) 2710 230129, fax: (+30) 2710 230139, e-mail: m.koub[email protected]. We are grateful to Gikas Hardouvelis, Dimitrios Malliaropulos, Jack Meyer and participants at various seminars at the University of Peloponnese, the University of Piraeus and the National University of Ireland for helpful comments and suggestions. We acknowledge …nancial support from the Greek Ministry of Education and the European Union under “Pythagoras”grant. The usual disclaimer applies. 2Department 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. Following Campbell and Vuolteenaho (American Economic Review, 2004) we check whether these two types of risk provide an empirical improvement over the static CAPM and if cash-‡ow risk is more important than discount-rate risk, as a rational I-CAPM risk story would predict. Our results suggest that the two-beta intertemporal model performs at least as well as the Fama-French (Journal of Financial Economics, 1993) three factor model since it explains half of the cross-sectional variation in average returns and delivers an economically and statistically acceptable estimate of the coe¢ cient of relative risk aversion. More importantly, despite the relative importance of market discount-rate risk, it is market dividend-growth risk that turns out to be far more important 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 di¤erent 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 su¢ 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 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 1For a recent review on the CAPM literature see, among others, Fama and French (2004). 1 cash-‡ow and discount-rate 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 o¤ers 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). The lifetime utility function of the investor is given by the recursive utility function Ut;de…ned over current real consumption, Ct, and future expected utility of real consumption, Et(Ut+1): Ut[Ct; Et(Ut+1)] = h(1 )C 1  t+EtU1 t+1 1 i 1(1) where 0<  < 1is the subjective discount factor,  > 0is the constant, under this speci…cation, coe¢ cient of relative risk aversion (CRRA), is a parameter de…ned as = (1 )=(1 1 );and  > 0is 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 (=1 ), 2 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: Wt+1 = (1 + RW;t+1)(WtCt)(2) where RW;t+1 is 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: EthG R1 W;t+1Ri;t+1i= 1; for i= 1; :::; N (3) where Gt+1 def =Ct+1 Ctis the optimally chosen gross growth rate of real consumption between tand t+1. 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 restrictions on assets’risk premia that places no role in consumption as a priced risk factor: EtRe i;t+1=Covt(ri;t+1; rW;t+1 Et[rW;t+1]) + (1 )Covt(ri;t+1;NDR W;t+1);(4) where EtRe i;t+1=Et[Ri;t+1]Rf;t+1, and Rf;t+1 is the simple return on the risk-free asset. The above equation can be viewed as a discrete-time version of Merton’s (1973) I-CAPM where changes in the future investment opportunity sets (captured by news about future total wealth portfolio returns, NDR W;t+1) 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 innovation) into news about future dividend (cash-‡ows) growth rates and returns (discount-rates). Formally, Campbell (1991) has derived the following approximate log linear decomposition of returns into time t+ 1 revision in expectations (news) about the present value of all future totalwealth dividend growth rates (cash-‡ow news, NCF W) and the time t+ 1 revision in expectations about the present value of all future total-wealth returns (discount-rate 3 news, NDR W): rW;t+1 Et+1 [rW;t+1] = NCF W;t+1 NDR W;t+1;(5) where NCF W;t+1 =Et+1 hP1 j=0 jdW;t+1+jiEthP1 j=0 jdW;t+1+jiand NDR m;t+1 =Et+1 hP1 j=1 jrW;t+1+jiEthP1 j=1 jrW;t+1+ji,PW t+1 is the real aggregate (market) stock price measured at the end of period t+ 1 (ex-dividend), dW;t+1 = log(DW;t+1)is the log of the real dividend payment to total wealth during this period, rW;t+1 = log(PW;t+1+DW;t+1 PW;t )is the one-period holding log real gross return on the total wealth portfolio, W= 1=[1 + exp(W)] and W=E[log(dW;t pW;t)] is the unconditional mean of the log aggregate dividend-price ratio. The …rst term in (5) is the time t+ 1 revision in dividend growth expectations and represents a permanent positive e¤ect on total wealth since it is never reversed subsequently, whereas the second one is the time t+ 1 revision in expectations about 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;t+1 Et+1 [rW;t+1]>0) is at a cost of lower future investment opportunities, i.e. Et+1 hP1 j=1 jrW;t+1+jiEthP1 j=1 jrW;t+1+ji<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 di¤erent roles for aggregate dividend growth rates’news and returns’news in determining asset risk premia: EtRe i;t+1=Covt(ri;t+1; NCF W;t+1) + Covt(ri;t+1;NDR W;t+1);(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, V art(rW;t+1 Et[rW;t+1]), we get: EtRe i;t+1=CF;ti;CF;t +DR;ti;DR;t (7) with CF;t =V art(rW;t+1 Et[rW;t+1]) ,DR;t =V art(rW;t+1 Et[rW;t+1]) and: i;W;t =Covt(ri;t+1; NCF W;t+1) V art(rW;t+1 Et[rW;t+1]) +Covt(ri;t+1;NDR W;t+1) V art(rW;t+1 Et[rW;t+1]) =i;CF;t +i;DR;t (8) 4 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;CF ) rather than for risks linked to shocks to total wealth portfolio returns ( i;DR;t), since any positive (negative) shock to wealth discount rates is at a bene…t (cost) of worse future investment opportunities, whereas the investor is never compensated later for every positive (negative) shock to dividends. Hence, the beta price of market cash-‡ow risk CF is a multiple of the beta risk prices of market discount-rate risk DR. Thus, for a conservative investor it must be CF > 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 di¤erent sets of common stock portfolios sorted on various …rm speci…c characteristics and risk measures and a set of economy-wide variables that serve as instruments. Following the common practice, these variables have been selected under the assumption that they forecast future returns. Lastly, we assume that the market (value-weighted) portfolio is a good proxy for the total-wealth portfolio in the Greek economy, so that RW=RM. We employ a variant of the Fama and French (1993) methodology to construct value-weighted returns on 25 …rm-characteristic single-sorted portfolios on book-tomarket, dividend-yield, size, price-earnings and 3-month momentum, and the two size and book-to-market factor mimicking portfolios, Small-Minus-Big (SMB) and High-Minus-Low (HML), respectively. The latter factor mimicking portfolios will be used as a benchmark in our asset pricing tests. In June, every year, we …rst break the full menu of A.S.E. common stocks available into 5 groups (based on accounting 5 information) each containing an equal number of stocks and second, we compute the simple market capitalization weighted-average monthly holding period return for each of the 5 portfolios for the following year using monthly closing prices. The annual dividend paid on each stock is divided by 12 and added to the monthly closing price, so that our returns include dividends. The procedure is repeated every year and we end up with time-series data of simple returns on each characteristics-sorted portfolio. 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. The aggregate value mimicking factor portfolio HML was created using the 40-2040 rule employed by Fama and French (1993). However, for the SMB portfolio, we adjust the formation mechanism to account for peculiarities of the Greek data. We use the 70th quantile of the market value instead of the median that was used by Fama and French. Using a larger breakpoint we can create a distribution of the market value similar to that of Fama and French, while the small capitalization portfolio represents on average the 8% of the total A.S.E. market. At the end of June of each year, we create the size and book-to-market double-sorted portfolios of Fama and French (1993) (SL; SM; SH; BL; BM and BH) and calculate the value-weighted monthly returns for the next 6 months. Then, the aggregate book-to-market and size portfolios are de…ned as HML = (SH +BH)=2(SL +BL)=2and SMB = (SL +SM +SH)=3(BL +BM +BH)=3respectively. The second set used in our analysis consists of variables that have proven successful in predicting the future state of the economy and asset returns. The innovations of these variables are used to generate cash-‡ow and discount-rate news through a VAR(1) speci…cation. More in detail, we use: (a) the monthly log di¤erence of the OECD leading indicator,  log (LI), (b) the market log price-earnings ratio, pe; and (c) the small-stock value spread, V S; de…ned as the di¤erence between the log(B/M) of the small high-B/M portfolio and the log(B/M) of the small low-BE/ME portfolio.2 The asset pricing model in (7) uses cash-‡ow and discount-rate news as priced factors. We follow Campbell (1991) and we estimate them using a …rst-order vector autoregressive, VAR(1), model. We …rst estimate expected returns and the revisions 2Recently, the value spread V S variable has been found to be a good forecaster of US returns. See, among others, Campbell and Vuolteenaho (2004), Campbell, Polk and Vuolteenaho (2005) and Koubouros, Malliaropulos and Panopoulou (2005). Following this evidence we use the value spread as a predictor of A.S.E. returns. 6 in expectations about future returns (Et[rM;t+1]and (Et+1Et)P1 j=1 j MrM;t+1+j, respectively) and then we use rM;t+1 and equation (5) to back out the market cash- ‡ow news. This practice has an important advantage as it relies only on the dynamics of expected returns and there is no need for modelling the dynamics of dividends since the latter are derived by the VAR estimates and the realizations of returns and state variables. We assume that the data are generated by the following VAR(1) model: yt+1 =  + Ayt+ut+1;(9) where yt+1 = (rm;t+1; y1;t+1; :::; ym;t+1)is a m1vector of variables containing returns as its …rst element and (m1) variables which have predictive power for returns, is am1vector of constants and Ais a mmmatrix of constants. We estimate (9) for the market return and then compute cash-‡ow and discount-rate news as linear functions of the t+ 1 vector of innovations, ut+1: NDR M;t+1 =e10ut+1 NCF M;t+1 = (e10+e10)ut+1;(10) where e1is a m1vector with the …rst element equal to unity and the remaining elements equal to zero. The mapping of the shock vector to the news vectors is given by A(ImA)1.e10captures the long-run signi…cance of each individual VAR(1) shock to discount-rate expectations. The greater the absolute value of a variables coe¢ cient in the return prediction equation (the top row of A), the greater the weight the variable receives in the discount-rate-news formula (10). Also, more persistent variables should also receive more weight, which is captured by the term (ImA)1. 4 Empirical Evidence 4.1 Estimation of Cash-Flow and Discount-Rate News and Betas Table 1 reports parameter estimates for the market VAR(1) model. Our estimates suggest that the state variables have some predictive power for stock market excess returns (adj.-R2of 9:5%). Speci…cally, monthly market returns display some degree 7 References [1] Brennan Michael, Ashley Wang and Yihong Xia (2004), Estimation and test of a simple model of intertemporal asset pricing, Journal of Finance 59, 1743-1775. [2] Campbell, John (1991), A variance decomposition of stock returns, Economic Journal 101, 157-159. [3] Campbell, John (1993), Intertemporal asset pricing without consumption data, American Economic Review 83, 487-512. [4] Campbell, John (1996), Understanding risk and return, Journal of Political Economy 104, 298-345. [5] Campbell, John and Jiapping Mei (1993), Where do betas come from? Asset pricing dynamics and the sources of systematic risk, Review of Financial Studies, 6, 567-592. [6] Campbell, John, Christofer Polk and Tuomo Vuolteenaho (2005), Growth or glamour? 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[29] Scholes, Myron and Joseph Williams (1977), Estimating betas from nonsynchronous data, Journal of Financial Economics 5, 309-327. 15 [30] Weil, Philippe (1989), The equity premium puzzle and the riskfree rate puzzle, Journal of Monetary Economics 24, 401–421 16 Table 1. VAR estimates for market portfolio rm;t+1  log (LIt+1)pt+1 et+1 V St+1 constant 0:033 (0:021) 0:023 (0:009) 0:055 (0:029) 0:032 (0:041) rm;t 0:147 (0:086) 0:056 (0:039) 0:043 (0:119) 0:185 (0:165)  log (LIt) 0:194 (0:160) 0:528 (0:073) 0:077 (0:223) 0:405 (0:308) ptet0:007 (0:015) 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 LM Test for Heteroscedasticity (ARCH Test: lag = 4) ^urW^u log(LI)^upe^uV S F-stat. 0:327 1:081 2:134 0:709 p-value [0:859] [0:369] [0:080] [0:593] Table 2: Market portfolio cash-‡ow and discount-rate news Covariance matrix of news News corr/st.d. NCF MNDR MNCF MNDR M NCF 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 NCF mNDR mNCF MNDR M rM0:679 0:225 rMshock 1:052 0:052  log (LI) 0:277 0:295  log (LI)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 17 Table 3. Summary statistics Portfolio Mean St.Dev 1236912 Market portfolio 9.85 3.06 0.13 0.08 0.06 0.05 -0.11 -0.05 Panel A. Book-to-market Portfolios High 16.07 3.67 0.12 0.01 0.16 0.12 -0.10 0.02 2 8.16 3.42 0.19 0.09 0.07 0.03 -0.13 -0.06 3 9.99 3.44 0.16 0.14 -0.02 0.07 -0.15 0.00 4 5.63 3.30 0.13 0.16 0.09 0.00 -0.03 -0.07 Low 8.59 3.25 0.15 0.06 0.04 0.05 -0.01 -0.10 Panel B. Dividend-Yield Portfolios High 13.62 2.96 0.07 0.02 0.06 0.05 -0.17 -0.02 2 6.05 3.47 0.11 0.15 0.00 0.06 -0.13 0.06 3 9.40 3.39 0.18 0.11 0.01 0.00 -0.06 -0.09 4 8.25 3.44 0.15 0.09 0.15 0.05 -0.06 -0.08 Low 6.13 3.50 0.16 0.22 0.05 0.06 -0.11 -0.08 Panel C. Size Portfolios Large 9.08 2.97 0.10 0.02 0.02 0.04 -0.15 -0.02 2 9.05 3.69 0.19 0.19 0.16 0.09 0.03 -0.03 3 14.68 4.09 0.26 0.17 0.19 0.07 0.03 -0.07 4 16.28 4.33 0.25 0.23 0.25 0.13 0.05 -0.05 Small 34.27 5.02 0.27 0.26 0.27 0.15 0.08 -0.15 Panel D. Price-to-Earnings Portfolios High 5.53 3.89 0.24 0.14 0.08 -0.03 -0.02 -0.12 2 6.60 3.53 0.17 0.11 0.04 0.06 0.00 -0.06 3 10.19 3.37 0.18 0.24 0.08 0.11 -0.10 -0.04 4 9.32 2.99 0.13 0.10 -0.01 0.11 -0.11 0.02 Low 19.80 3.05 0.13 0.07 0.03 0.14 -0.10 0.03 Panel E. 3-Month Momentum Portfolios Winners 17.78 3.37 0.28 0.22 0.19 0.11 -0.11 -0.06 2 13.84 3.52 0.09 0.12 0.10 0.10 -0.15 -0.10 3 13.70 3.56 0.21 0.22 0.09 0.06 -0.01 -0.03 4 5.26 3.71 0.10 0.08 0.01 0.03 0.06 -0.09 Losers 3.01 4.03 0.04 0.04 0.01 0.08 -0.06 0.01 18 Table 4. CAPM, Cash-‡ow, discount-rates, HML and SMB betas Panel A. Book-to-market portfolios b i;m s.e. b i;CF s.e.:b i;DR s.e. b i;HML s.e. b i;SMB s.e. High 1.445 0.222 0.760 0.131 0.685 0.235 -0.185 0.246 0.364 0.243 2 1.300 0.216 0.714 0.149 0.586 0.253 -0.189 0.218 0.224 0.205 3 1.170 0.196 0.706 0.162 0.464 0.226 0.038 0.233 0.140 0.224 4 1.183 0.218 0.621 0.122 0.562 0.235 0.244 0.245 0.027 0.190 Low 0.893 0.212 0.479 0.124 0.414 0.232 0.374 0.210 0.077 0.195 Panel B. Dividend-yield portfolios b i;m s.e. b i;CF s.e.:b i;DR s.e. b i;HML s.e. b i;SMB s.e. High 1.025 0.156 0.684 0.132 0.341 0.186 -0.177 0.154 -0.030 0.163 2 1.046 0.217 0.633 0.185 0.412 0.240 -0.115 0.232 0.022 0.209 3 1.270 0.240 0.681 0.135 0.589 0.257 0.274 0.239 0.005 0.199 4 1.102 0.262 0.526 0.122 0.576 0.258 0.351 0.232 0.379 0.221 Low 1.170 0.272 0.577 0.151 0.593 0.241 0.346 0.228 0.251 0.227 Panel C. Size portfolios b i;m s.e. b i;CF s.e.:b i;DR s.e. b i;HML s.e. b i;SMB s.e. Large 0.850 0.141 0.608 0.107 0.242 0.190 0.037 0.155 -0.198 0.188 2 1.474 0.312 0.641 0.171 0.834 0.279 0.151 0.288 0.572 0.203 3 1.713 0.372 0.632 0.183 1.081 0.301 0.103 0.342 1.025 0.220 4 1.833 0.398 0.648 0.171 1.185 0.307 0.233 0.352 1.434 0.238 Small 2.275 0.517 0.714 0.234 1.561 0.363 0.154 0.430 1.764 0.308 Panel D. Price-to-earnings portfolios b i;m s.e. b i;CF s.e.:b i;DR s.e. b i;HML s.e. b i;SMB s.e. High 1.364 0.287 0.658 0.163 0.706 0.275 0.518 0.296 0.402 0.220 2 1.178 0.194 0.624 0.128 0.554 0.227 0.287 0.237 0.115 0.225 3 1.150 0.245 0.625 0.156 0.525 0.265 0.025 0.218 0.230 0.217 4 1.024 0.176 0.610 0.138 0.414 0.188 -0.062 0.177 -0.018 0.170 Low 1.025 0.194 0.730 0.173 0.296 0.215 -0.029 0.167 0.070 0.150 Panel E. 3-month momentum b i;m s.e. b i;CF s.e.:b i;DR s.e. b i;HML s.e. b i;SMB s.e. Winners 1.338 0.348 0.699 0.151 0.639 0.340 0.299 0.224 0.539 0.261 2 1.081 0.288 0.526 0.111 0.555 0.294 0.214 0.224 0.385 0.245 3 1.324 0.328 0.678 0.152 0.646 0.315 0.251 0.247 0.432 0.200 4 1.213 0.236 0.518 0.166 0.696 0.253 0.040 0.301 0.241 0.193 Losers 1.101 0.248 0.424 0.163 0.677 0.249 -0.159 0.341 0.077 0.176 19 Table 5. Cross-sectional Asset Pricing Tests CAPM Two-Beta CF DR Fama-French All 0 0:005 (0:0048) 0:0139 (0:0062) 0:0107 (0:0065) 0:0026 (0:0031) 0:0088 (0:0072) 0:0025 (0:0070) m 0:0115 (0:0038) 0:0015 (0:0064) CF 0:0274 (0:0093) 0:0320 (0:0113) 0:0166 (0:0076) DR 0:0096 (0:0043) 0:0107 (0:0051) 0:0132 (0:0082) HML 0:0066 (0:0036) 0:0051 (0:0032) SMB 0:0098 (0:0044) 0:0159 (0:0054) adj.-R242:2% 46:6% 21:5% 30:4% 48:5% 62:6% 2:8572 (0:1612) 0:0096 (0:0043) 20 0 0,005 0,01 0,015 0,02 0,025 0,03 0 0,005 0,01 0,015 0,02 0,025 0,03 Realized Average Returns Fitted Average Returns Figure 1. Fitted vs. Realized Average Returns: CAPM 0 0,005 0,01 0,015 0,02 0,025 0,03 0 0,005 0,01 0,015 0,02 0,025 0,03 Realized Average Returns Fitted Average Returns Figure 2. Fitted vs. Realized Average Returns: Unrestricted Two-Beta ICAPM 0 0,005 0,01 0,015 0,02 0,025 0,03 0 0,005 0,01 0,015 0,02 0,025 0,03 Realized Average Returns Fitted Average Returns Figure 3. Fitted vs. Realized Average Returns: Restricted Two-Beta ICAPM