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## Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying (2001)

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Venue: | Journal of Political Economy |

Citations: | 246 - 10 self |

### Citations

2592 | Large sample properties of generalized method of moments estimators - Hansen - 1982 |

2113 | Capital asset prices: A theory of market equilibrium under conditions of risk - Sharpe - 1964 |

1539 | Risk, return and equilibrium: empirical tests - Fama, MacBeth - 1973 |

1452 | By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior." - Campbell, Cochrane - 1995 |

889 |
Martingales and arbitrage in multiperiod securities markets
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Citation Context ...inear Factor Models with Time-Varying Coefficients We begin by imposing virtually no theoretical structure, appealing instead to a well-known existence theorem to motivate our empirical approach (see =-=Harrison and Kreps 1979-=-). This theorem states that, in the absence of arbitrage, there exists a stochastic discount factor, or pricing kernel, of R i,t�1, M t�1, such that, for any traded asset with a net return at time t t... |

790 | The relationship between return and the market value of common stocks
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Citation Context ...Friend 1973; Fama and MacBeth 1973). But recently, evidence has mounted that the CAPM is inconsistent with numerous empirical regularities of cross-sectional asset pricing data (see, e.g., Basu 1977; =-=Banz 1981-=-; Shanken 1985; Fama and French 1992, 1993). Perhaps most damning, the CAPM has demonstrated virtually no power to explain the cross section of average returns on assets sorted by size and book-to-mar... |

777 |
Dividend yields and expected stock returns.
- Fama, French
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Citation Context ...of empirical work finds that expected excess returns on aggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; Campbell and Shiller 1988; =-=Fama and French 1988-=-, 1989; Campbell 1991; Hodrick 1992; Lamont 1998; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on investor expectations of ... |

725 |
The dividend-price ratio and expectations of future dividends and discount factors,
- Shiller
- 1988
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Citation Context .... A large and growing body of empirical work finds that expected excess returns on aggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; =-=Campbell and Shiller 1988-=-; Fama and French 1988, 1989; Campbell 1991; Hodrick 1992; Lamont 1998; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on inv... |

713 |
Generalized instrumental variables estimation in nonlinear rational expectations models,
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Citation Context ...tunately, these models have also proved disappointing empirically. The consumption-based model has been rejected on U.S. data in its representative agent formulation with timeseparable power utility (=-=Hansen and Singleton 1982-=-, 1983); it has performed no better and often worse than the simple static CAPM in 1 Liew and Vassalou (2000) provide a first step in establishing an empirical link between the size and book-to-market... |

677 |
Habit Formation: A Resolution of the Equity Premium Puzzle, "
- Constantinides
- 1990
(Show Context)
Citation Context ...it stock; and X(s,) is the sensitivity function specified in Campbell and Cochrane. Similar but more complicated expressions can be derived for internal habit formation models (e.g., Sundaresan 1989; =-=Constantinides 1990-=-) by taking a local linear approximation of the respective stochastic discount factors. To our knowledge, almost all the cross-sectional tests of the CCAPM to date have pertained to models that assume... |

621 | An intertemporal asset pricing model with stochastic consumption and investment opportunities - Breeden - 1979 |

568 | Stock returns and the term structure, - Campbell - 1987 |

542 |
The conditional CAPM and the cross-section of expected returns
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- 1996
(Show Context)
Citation Context ...uch as l(s t) in (8), their fluctuations should be well captured by suitable proxies for time-varying risk premia. In contrast to traditional, discrete-time derivations of the conditional CAPM (e.g., =-=Jagannathan and Wang 1996-=-), which produces just two betas (one for the fundamental factor and one for the risk premium), habit models imply the existence of at least one beta for the multiplicative “cross term” of the factor ... |

532 | Prices of State-Contingent Claims Implicit in Options Prices - Breeden, Litzenberger - 1978 |

469 |
Dividend yields and expected stock returns: Alternative procedures for inference and measurement,
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Citation Context ...s returns on aggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; Campbell and Shiller 1988; Fama and French 1988, 1989; Campbell 1991; =-=Hodrick 1992-=-; Lamont 1998; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on investor expectations of future excess returns. For example,... |

458 | Understanding Risk and Return - Campbell - 1996 |

445 | Stochastic consumption, risk aversion, and the temporal behavior of asset returns, - Singleton - 1983 |

435 | Asset pricing with heterogeneous consumers. - Constantinides, Duffie - 1996 |

418 |
Capital market equilibrium with restricted borrowing,
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Citation Context ...tion for asset i with constant betas given by ′ E[R i,t�1] p E[R 0,t] � bl, (4) where E[R 0,t] is the average return on a zero-beta portfolio that is uncorrelated with the stochastic discount factor (=-=Black 1972-=-), and b { ′ �1 Cov (f, ¯ ¯f ) Cov (f, ¯ R i,t�1) is a vector of regression coefficients from a multiple regression of returns on the variable factors. In the empirical analysis that follows, we focus... |

382 | Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence,’ - Campbell, Mankiw - 1989 |

360 |
A Variance Decomposition for Stock Returns,
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(Show Context)
Citation Context ... expected excess returns on aggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; Campbell and Shiller 1988; Fama and French 1988, 1989; =-=Campbell 1991-=-; Hodrick 1992; Lamont 1998; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on investor expectations of future excess returns... |

354 | The capital asset pricing model: Some empirical tests,
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- 1972
(Show Context)
Citation Context ...o table 1. Dc denotes consumption growth. models with only financial factors. Such arguments for large zero-beta estimates have a long tradition in the cross-sectional asset pricing literature (e.g., =-=Black et al. 1972-=-; Miller and Scholes 1972). However, if the sampling error is not independently and identically distributed and if multiple factors are poorly measured, there is little that can be said about the dire... |

322 |
Investment performance of common stocks in relation to their price-earnings ratios: a test of the efficient market hypothesis
- Basu
- 1977
(Show Context)
Citation Context ... Blume and Friend 1973; Fama and MacBeth 1973). But recently, evidence has mounted that the CAPM is inconsistent with numerous empirical regularities of cross-sectional asset pricing data (see, e.g., =-=Basu 1977-=-; Banz 1981; Shanken 1985; Fama and French 1992, 1993). Perhaps most damning, the CAPM has demonstrated virtually no power to explain the cross section of average returns on assets sorted by size and ... |

321 | Consumption, aggregate wealth, and expected stock returns.
- Lettau, Ludvigson
- 2001
(Show Context)
Citation Context ...k market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; Campbell and Shiller 1988; Fama and French 1988, 1989; Campbell 1991; Hodrick 1992; Lamont 1998; =-=Lettau and Ludvigson 2001-=-). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on investor expectations of future excess returns. For example, in models with habit formation, in whic... |

320 | The valuation of uncertain income streams and the pricing of options, - Rubinstein - 1976 |

319 | Portfolio choice and asset prices; the importance of entrepreneurial risk. - Heaton, Lucas - 1997 |

300 | A critique of the asset pricing theory's tests: part I: on past and potential testability of the theory - Roll - 1977 |

286 |
Small-sample bias in GMM estimation of covariance structures,
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- 1996
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Citation Context ... this argument for two reasons. First, second-stage GMM estimation is unsuitable in studies that have a small time-series sample relative to the cross-sectional sample size (Ferson and Foerster 1994; =-=Altonji and Segal 1996-=-; Christiano and Den Haan 1996; Hansen et al. 1996; Ahn and Gadarowski 1999). Our quarterly data yield far fewer time-series observations than in many previous 31 We use the term “second-stage” loosel... |

259 | Evidence on the characteristics of cross sectional variation in stock returns - Daniel, Titman - 1997 |

258 | Time-varying conditional covariances in tests of asset pricing models, - Harvey - 1989 |

251 |
Asymptotic Properties of Least Squares Estimators of Co integrating Vectors", manuscript,
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Citation Context ...ates of the parameters in ̂t cay are “superconsistent,” converging to the true parameter values at a rate proportional to the sample size T rather than proportional to �T as in ordinary applications (=-=Stock 1987-=-).1256 journal of political economy TABLE 1 Fama-MacBeth Regressions Using 25 Fama-French Portfolios: l j Coefficient Estimates on Betas in Cross-Sectional Regression Row Constant cay ̂t Factors t�1 ... |

240 | Data-snooping biases in tests of financial asset pricing models, The Review of Financial Studies - Lo, MacKinlay - 1990 |

239 |
A cross-sectional test of an investment-based asset pricing model.
- Cochrane
- 1996
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Citation Context ...ow. The scaling variable is ̂cay.sresurrecting the (c)capm 1241 explaining the cross section of average asset returns (Mankiw and Shapiro 1986; Breeden, Gibbons, and Litzenberger 1989; Campbell 1996; =-=Cochrane 1996-=-); and it has been generally replaced as an explanation for systematic risk by a variety of portfolio-based models (e.g., Elton, Gruber, and Blake 1995; Fama and French 1996). Moreover, the CCAPM perf... |

212 |
Finite-sample properties of some alternative GMM estimators',
- Hansen
- 1996
(Show Context)
Citation Context ...M estimation is unsuitable in studies that have a small time-series sample relative to the cross-sectional sample size (Ferson and Foerster 1994; Altonji and Segal 1996; Christiano and Den Haan 1996; =-=Hansen et al. 1996-=-; Ahn and Gadarowski 1999). Our quarterly data yield far fewer time-series observations than in many previous 31 We use the term “second-stage” loosely here to refer to any GMM estimation in which the... |

211 | Security Prices, Risk, and Maximal Gains from Diversification - Lintner - 1965 |

210 | Characteristics, covariances, and average returns: 1929-1997, - Davis, Fama, et al. - 2000 |

208 |
The Dividend-Price Ratio and
- Campbell, Shiller
- 1988
(Show Context)
Citation Context .... A large and growing body of empirical work finds that expected excess returns on aggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; =-=Campbell and Shiller 1988-=-; Fama and French 1988, 1989; Campbell 1991; Hodrick 1992; Lamont 1998; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on inv... |

190 |
Earnings and Expected Returns.
- Lamont
- 1998
(Show Context)
Citation Context ...ggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; Campbell and Shiller 1988; Fama and French 1988, 1989; Campbell 1991; Hodrick 1992; =-=Lamont 1998-=-; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on investor expectations of future excess returns. For example, in models wi... |

171 |
Assessing specification errors in stochastic discount factor model.
- Hansen, Jagannathan
- 1997
(Show Context)
Citation Context ...one “stage.”resurrecting the (c)capm 1277 empirical applications for which monthly data were available. Both the optimal GMM weighting matrix of Hansen (1982) and the secondmoment matrix of returns (=-=Hansen and Jagannathan 1997-=-) are likely to be poorly estimated in samples of the size encountered here. Indeed, for this reason, it is often argued that first-stage GMM should serve as a robustness check on the results of any s... |

161 | Stock Return Predictability and Model Uncertainty,” - Avramov - 2002 |

161 | Another look at the cross-section of expected stock returns - Kothari, Shanken, et al. - 1995 |

161 |
Stock prices and social dynamics.
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- 1984
(Show Context)
Citation Context ...nts of returns. A large and growing body of empirical work finds that expected excess returns on aggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., =-=Shiller 1984-=-; Campbell and Shiller 1988; Fama and French 1988, 1989; Campbell 1991; Hodrick 1992; Lamont 1998; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discoun... |

147 | Can book-to-market, size and momentum be risk factors that predict economic growth - Liew, Vassalou - 2000 |

138 | Conditioning variables and the cross section of stock returns - Ferson, Harvey |

122 | A critique of size-related anomalies. - Berk - 1995 |

115 | Empirical Test of the Consumption-Oriented CAPM - Breeden, Gibbons, et al. - 1989 |

106 |
Finite sample properties of generalized method of moments in tests of conditional asset pricing model,
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Citation Context ...atrix is employed. We make this argument for two reasons. First, second-stage GMM estimation is unsuitable in studies that have a small time-series sample relative to the cross-sectional sample size (=-=Ferson and Foerster 1994-=-; Altonji and Segal 1996; Christiano and Den Haan 1996; Hansen et al. 1996; Ahn and Gadarowski 1999). Our quarterly data yield far fewer time-series observations than in many previous 31 We use the te... |

95 | Explaining the Poor Performance of Consumption-Based Asset Pricing Models.” - Campbell, Cochrane - 2000 |

93 | A Variance Decomposition for - Campbell - 1991 |

91 | On the Cross-sectional Relation between Expected Returns and Betas,” - Roll, Ross - 1994 |

87 | How Relevant is Volatility Forecasting for Financial Risk Management?”,
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Citation Context ...tic discount factor will in general not be constant. Although predictable movements in volatility may be a source of variation in b,, they appear to be more concentrated in high-frequency data (e.g., =-=Christoffersen and Diebold 2000-=-). Since risk-free interest rates are also not highly variable, the denominator of b, is not likely to vary much in monthly or quarterly data. On the other hand, a large empirical literature (cited in... |

83 |
A new look at the capital asset pricing model,
- Blume, Friend
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(Show Context)
Citation Context ...5) has long been a pillar of academic finance, and early evidence seemed to favor the theory’s central tenet that the market portfolio be mean-variance efficient (see Black, Jensen, and Scholes 1972; =-=Blume and Friend 1973-=-; Fama and MacBeth 1973). But recently, evidence has mounted that the CAPM is inconsistent with numerous empirical regularities of cross-sectional asset pricing data (see, e.g., Basu 1977; Banz 1981; ... |

78 | Multivariate tests of the zero beta CAPM",
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Citation Context ...; Fama and MacBeth 1973). But recently, evidence has mounted that the CAPM is inconsistent with numerous empirical regularities of cross-sectional asset pricing data (see, e.g., Basu 1977; Banz 1981; =-=Shanken 1985-=-; Fama and French 1992, 1993). Perhaps most damning, the CAPM has demonstrated virtually no power to explain the cross section of average returns on assets sorted by size and book-to-market equity rat... |

69 | Portfolio Inefficiency and the Cross-Section of Expected Returns,” - Kandel, Stambaugh - 1995 |

64 | Evaluating the Specification Errors of Asset Pricing Models.” - Hodrick, Zhang - 2001 |

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60 |
Rate of Return in Relation to Risk: A Re-Examination of Some Recent Findings. In
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Citation Context ...es consumption growth. models with only financial factors. Such arguments for large zero-beta estimates have a long tradition in the cross-sectional asset pricing literature (e.g., Black et al. 1972; =-=Miller and Scholes 1972-=-). However, if the sampling error is not independently and identically distributed and if multiple factors are poorly measured, there is little that can be said about the direction of bias. Procedures... |

52 |
Risk and return: Consumption beta versus market beta,
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Citation Context ...he pricing errors are generated using the Fama-MacBeth regressions in table 3 below. The scaling variable is ̂cay.sresurrecting the (c)capm 1241 explaining the cross section of average asset returns (=-=Mankiw and Shapiro 1986-=-; Breeden, Gibbons, and Litzenberger 1989; Campbell 1996; Cochrane 1996); and it has been generally replaced as an explanation for systematic risk by a variety of portfolio-based models (e.g., Elton, ... |

52 | Human Capital and Capital Market Equilibrium." - Fama, Schwert - 1977 |

47 | Tests of Asset Pricing with Time-Varying Expected Risk Premiums and Market Betas”, - Ferson, Kandel, et al. - 1987 |

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38 | The Alpha Factor Asset Pricing Model: A Parable,” - Ferson, Sarkissian, et al. - 1999 |

34 |
Small-sample Properties of GMM-based Wald Tests,
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Citation Context ...re significantly, several investigations have found that these tests, which rely on a consistent estimate of the variance-covariance matrix of pricing errors, have poor small-sample properties (e.g., =-=Burnside and Eichenbaum 1996-=-; Hansen, Heaton, and Yaron 1996). The small sample size of the Wald tests exceeds the asymptotic size, and this is especially true when the number of moment restrictions is large relative to the time... |

28 | Habit-formation: A Resolution of the Equity Premium Puzzle,” - Constantinides - 1990 |

21 | By Force of Habit: A Consumption-based Explanation - Campbell, Cochrane - 1999 |

19 |
Small Sample Properties of the Model Specification Test Based on the Hansen-Jagannathan Distance.”
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Citation Context ...itable in studies that havesa small time-series sample relative to the cross-sectional sample sizes(Ferson and Foerster 1994; Altonji and Segal 1996; Christian0 and DensHaan 1996; Hansen et al. 1996; =-=Ahn and Gadarowski 1999-=-). Our quar-sterly data yield far fewer time-series observations than in many previouss'' We use the term "second-stage" loosely here to refer to any GMM estimation in whichsthe matrix used to weight ... |

18 | On selection biases in book-to-market based tests of asset pricing models, Northwestern Universi& Workingpaper 167 - Breen, Korajczyk |

17 | Asset Prices and Default-Free Term Structure in an Equilibrium Model of Default, - Chang, Sundaresan - 2001 |

16 | Risk Factors in the Returns on Stocks and Bonds - Common |

14 | Does Saving Anticipate Declining Future Labor Income? An Alternate Test of the Permanent Income Hypothesis. Econometrica 55 no - Campbell - 1987 |

14 | Asymptotic Theory for Estimating Beta Pricing Models Using Cross-Sectional Regressions - Jagannathan, Wang - 1998 |

12 | Small-sample Properties of GMM for Business-cycle Data - CHRISTIANO, HAAN - 1996 |

10 | Explanations of Asset Pricing Anomalies - ”Multifactor - 1996 |

9 | Asset Pricing with Heterogeneous Consumers.” J.P.E - Constantinides, Duffie - 1996 |

9 | The Cross-Section of Expected Returns.Journal of Finance 47 - Fama, French - 1992 |

6 |
Habit Formation: A Resolution of the Equity
- Constantinides
- 1990
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Citation Context ...t stock; and l(s t) is the sensitivity function specified in Campbell and Cochrane. Similar but more complicated expressions can be derived for internal habit formation models (e.g., Sundaresan 1989; =-=Constantinides 1990-=-) by taking a local linear approximation of the respective stochastic discount factors. To our knowledge, almost all the cross-sectional tests of the CCAPM to date have pertained to models that assume... |

5 | and Book-to-Market Factors in Earnings and Returns - ”Size - 1995 |

5 |
Multivariate Tests of the Zero-Beta
- Shanken
- 1985
(Show Context)
Citation Context ...; Fama and MacBeth 1973). But recently, evidence has mounted that the CAPM is inconsistent with numerous empirical regularities of cross-sectional asset pricing data (see, e.g., Basu 1977; Banz 1981; =-=Shanken 1985-=-; Fama and French 1992, 1993). Perhaps most damning, the CAPM has demonstrated virtually no power to explain the cross section of average returns on assets sorted by size and book-to-market equity rat... |

4 | Risk Factors in the Returns on - Common - 1993 |

3 |
How Relevant is Volatility Forecasting for
- Christoffersen, Diebold
- 1997
(Show Context)
Citation Context ...tic discount factor will in general not be constant. Although predictable movements in volatility may be a source of variation in bt, they appear to be more concentrated in high-frequency data (e.g., =-=Christoffersen and Diebold 2000-=-). Since risk-free interest rates are also not highly variable, the denominator of bt is not likely to vary much in monthly or quarterly data. On the other hand, a large empirical literature (cited in... |

3 | Size and Book-to-Market Factors in Earings and Returns.Journal of Finance 50 - Fama, French - 1995 |

3 | An International Dynamic Asset Pricing Model. Unpublished paper - Hodrick, Ng, et al. - 1998 |

2 |
Small-Sample Properties of GMM-Based
- Burnside, Eichenbaum
- 1996
(Show Context)
Citation Context ... significantly,sseveral investigations have found that these tests, which rely on a con-ssistent estimate of the variance-covariance matrix of pricing errors, havespoor small-sample properties (e.g., =-=Burnside and Eichenbaum 1996-=-;sHansen, Heaton, and Yaron 1996). The small sample size of the Waldstests exceeds the asymptotic size, and this is especially true when thesnumber of moment restrictions is large relative to the time... |

2 | Characteristics or Covariances?Journal of Portfolio Management 24(4 - Daniel, Titman - 1998 |

1 | Asset Prices and Default-Free Term the (c)capm 1285 Structure in an Equilibrium Model of Default.” Working paper - Chang, Sundaresan - 1999 |

1 | Seasonality and Heteroscedasticity in Consumption-Based Asset Pricing: An Analysis of Linear Models - Ferson, Harvey - 1993 |

1 | Asymptotic Theory for Estimating Beta-Pricing Models Using CrossSectional Regression - “An - 1998 |

1 | 1972. the (c)capm 1287 - Praeger - 1973 |

1 | Asset Pricing: An Empirical Investigation - “Intertemporal - 1990 |

1 | the Estimation of Beta-Pricing Models - “On - 1992 |

1 | A Critique of Size-Related Anomalies." Rev - Berk - 1995 |

1 | Tests of Asset Pricing with Time-Varying Expected Risk Premiums and Market Betas - Finance - 1999 |

1 |
A New Look at the Capital Asset Pricing Model."J. Finance 28
- Blume, Friend
- 1973
(Show Context)
Citation Context ...5) has long been a pillar of academic finance, and early evidence seemed to favor the theory's central tenet that the market portfolio be mean-variance efficient (see Black, Jensen, and Scholes 1972; =-=Blume and Friend 1973-=-; Fama and MacBeth 1973). But recently, evidence has mounted that the CAPM is inconsistent with numerous empirical regularities of cross-sectional asset pricing data (see, e.g., Basu 1977; Banz 1981; ... |

1 | Asset Prices and Default-Free Term THE (C)CAPM Structure in an Equilibrium Model of Default." Working paper - Chang, Sundaresan - 1999 |

1 | Risk Factors - Common - 1993 |

1 |
Earnings and Expected Returns."J. Finance 53
- Lamont
- 1998
(Show Context)
Citation Context ...ggregate stock market indexes are predictable, suggesting that risk premia vary over time (see, e.g., Shiller 1984; Campbell and Shiller 1988; Fama and French 1988, 1989; Campbell 1991; Hodrick 1992; =-=Lamont 1998-=-; Lettau and Ludvigson 2001). Yet if risk premia are time-varying, parameters in the stochastic discount factor will depend on investor expectations of future excess returns. For example, in models wi... |

1 | THE (C)CAPM 1287 Merton, Robert C. "An Intertemporal Capital Asset Pricing Model." Econometrica 41 - Praeger - 1972 |

1 | Asset Prices and Default-Free Term RESURRECTING THE (C)CAPM 1285 Structure in an Equilibrium Model of Default." Working paper - Chang, Sundaresan - 1999 |

1 | c)CAPM 1287 Merton, Robert C. "An Intertemporal Capital Asset Pricing Model." Econometrica 41 - THE - 1973 |