Pricing assets with stochastic cash-flow growth

We model the time series behavior of dividend growth rates, as well as the profitability rate, with a variety of autoregressive moving-average processes, and use the capital asset pricing model (CAPM) to derive the appropriate discount rate. One of the most important implications of this research is that the rate of return beta changes with the time to maturity of the expected cash flow, and the degree of mean reversion displayed by the growth rate. We explore the consequences of this observation for three different strands of the literature. The first is for the value premium anomaly, the second for stock valuation and learning about long-run profitability, and the third is for the St. Petersburg paradox. One of the most surprising results is that the CAPM implies a higher rate of return beta for value stocks than growth stocks. Therefore, value stocks must have higher expected returns, and this is what is required theoretically in order to explain the well-known value premium anomaly.     

Sensitivity of Multivariate Tests of the Capital Asset-Pricing Model to the Return Measurement Interval

The capital asset-pricing model's (CAPM) primary empirical implication is a positively sloped linear relation between a security's expected rate of return and its relative risk (beta). Recent research indicates that inferences about the risk-return relation are sensitive to the choice of the return measurement interval. We perform multivariate tests of the Sharpe-Lintner CAPM using monthly and annual returns on market-value-ranked portfolios. The CAPM is rejected using monthly returns, a result consistent with previous research. In contrast, we fail to reject the CAPM when annual holding period returns are used.     

Beta lives - some statistical perspectives on the capital asset pricing model

This note summarizes some technical issues relevant to the use of the idea of excess return in empirical modelling. We cover the case where the aim is to construct a measure of expected return on an asset and a model of the CAPM type is used. We review some of the problems and show examples where the basic CAPM may be used to develop other results which relate the expected returns on assets both to the expected return on the market and other factors.     

Systematic risk and timescales

Abstract

In this paper we propose a new approach to estimating the systematic risk (the beta of an asset) in a capital asset pricing model (CAPM). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. At each scale, the wavelet variance of the market return and the wavelet covariance between the market return and a portfolio are calculated to obtain an estimate of the portfolio's beta. The empirical results show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model are more relevant in the medium long run as compared to short time horizons.     

Federal Reserve Monetary Policy and Industry Stock Returns

Recent studies identify stock return patterns associated with changes in Federal Reserve monetary policy. We find that these return patterns prevail across sixteen industry stock indices. However, significant cross-industry variation exists as the apparel industry exhibits mean annual returns that are 50% higher under an expansive Fed policy than under a restrictive policy, while the same return difference for the oil industry is only 20%. This cross-industry variation suggests that monetary conditions may be used by investors to estimate different expected returns across industries. Furthermore, the findings support the view that monetary considerations should be considered in ex ante asset pricing models such as the CAPM.     

Pension benefits, wealth accumulation, and capital market equilibrium: a life cycle hypothesis-based dynamic model

This paper examines the impacts of pension benefits on capital asset pricing in conjunction with wealth accumulation and retirement, and derives and tests a dynamic capital asset pricing model (CAPM) within the framework of a life cycle hypothesis-based dynamic model. The life cycle hypothesis-based dynamic model maximizes the expected utility of the individual's lifetime wealth in a continuous time process. An optimal solution of the individual's wealth path, incorporating the ages of retirement and death, is obtained and, based on the optimal wealth path, an analysis of comparative dynamics is pursued. The dynamic CAPM is then derived from the optimal wealth path; simulation and nonparametric tests are undertaken to evaluate the performance of the dynamic CAPM as compared to the traditional model which does not consider the impacts of pension benefits and the static model that incorporates the effects of pension benefits. The test results suggest that the proposed dynamic CAPM closely states the expected rate of return for a capital asset; that the new dynamic CAPM is preferable over the static model that is preferable over the traditional model; and that the three models considered are statistically distinguishable from one another.     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

考虑流动性的三阶矩资本资产定价的理论模型与实证研究

本文把流动性风险、偏态风险引进传统CAPM模型中,推导出基于流动性的三阶矩资本资产定价的理论模型。本文的模型表明,证券(组合)的收益依赖于它的期望流动性成本、其流动性成本和市场流动性成本的协方差以及其收益和市场收益的协方差与协偏态。本文采用我国A股市场的股票收益数据对模型进行了实证检验.检验结果表明,我国A股市场的证券(组合)的风险溢价在大盘升降区间体现了不同的特征,无论是在全样本区间还是两个子样本区间,基于流动性的三阶矩资本资产定价模型都能更好的拟合资产收益,说明了流动性和偏态因素在我国A股市场的资产定价中有重要影响。     

The CAPM is Alive and Well: A Review and Synthesis

Mean-Variance (M-V) analysis and the CAPM are derived in the expected utility framework. Behavioural Economists and Psychologists (BE&P) advocate that expected utility is invalid, suggesting Prospect Theory as a substitute paradigm. Moreover, they show that the M-V rule, which is the foundation of the CAPM, is not always consistent with peoples' choices. Thus, BE&P cast doubt on the validity of expected utility paradigm and of the M-V rule, hence the CAPM is theoretically questionable. In addition, there is very little empirical support to the CAPM. We show in this study that the CAPM is theoretically valid even when one accepts the BE&P framework and even when expected utility is invalid. Moreover, within the BE&P framework there is a strong experimental support for the CAPM.     

The Determinants of REIT Institutional Ownership: Tests of the CAPM

This study examines the determinants of institutional investment demand for REIT common stock. We estimate the demand function for financial institutions using the mean return and CAPM risk measures (beta and standard error) for REIT stocks. The objective is to determine whether institutional investment decisions are influenced by CAPM model attributes. In addition, we examine the predicatability of REIT institutional ownership based on the factors in our model. We employ conventional OLS forecasting techniques, as well as two neural network models in order to deal with possible nonlinearities in the relationships.     

Information and capital asset pricing

Investors in a market frequently update their diverse perceptions of the values of risky assets, thus invalidating the classic capital asset pricing model's (CAPM) assumption of complete agreement among investors. To accommodate information asymmetry and belief updating, we have developed an empirically testable information-adjusted CAPM, which states that the expected excess return of a risky asset/portfolio is solely determined by the information-adjusted beta rather than the market beta. The model is then used to analyze empirical anomalies of the classic CAPM, including a flatter relation between average return and the market beta than the CAPM predicts, a non-zero Jensen's alpha, insignificant explanatory power of the market beta, and size effect.     

Can An 'Estimation Factor' Help Explain Cross-Sectional Returns?

Abstract:  We show in a theoretical model that the expected excess return on any asset depends on its covariance not only with the market portfolio, but also with changes in the representative agent's estimate. We test our model using GMM and compare it to the CAPM. The results suggest that adding an 'estimation factor' to the CAPM helps explain cross-sectional returns and that, unconditionally, this estimation factor carries a negative risk premium.     

Estimating the Intertemporal Risk–Return Tradeoff Using the Implied Cost of Capital

We argue that the implied cost of capital (ICC), computed using earnings forecasts, is useful in capturing time variation in expected stock returns. First, we show theoretically that ICC is perfectly correlated with the conditional expected stock return under plausible conditions. Second, our simulations show that ICC is helpful in detecting an intertemporal risk–return relation, even when earnings forecasts are poor. Finally, in empirical analysis, we construct the time series of ICC for the G–7 countries. We find a positive relation between the conditional mean and variance of stock returns, at both the country level and the world market level.     

What Cost of Capital Should You Use? The Market Has an Answer

The most widely used means of estimating a company's cost of equity capital is the Capital Asset Pricing Model (CAPM). But as a growing number of academics and practitioners have suggested, use of the CAPM produces estimates that often fail to reflect the risks of the companies as perceived by current and potential investors. The authors' work, together with other research, also suggests that the cost of equity produced by the CAPM is often too high. To the extent this is so, companies are discounting investment projects at rates of return that may be leading them to pass up value‐adding opportunities. The authors advocate the use of a simple and practical alternative to the CAPM that does not use either an assumed market risk premium or a beta. It uses instead an equity premium that is implied by the current market price of a company's stock and, as such, is implicitly derived from investors' assessments of the firm's risk that are reflected in that price. More specifically, the alternative approach solves for the internal rate of return that equates the present value of expected future cash flows to the current market price. In support of this approach, studies have shown that such market‐implied measures are better predictors than CAPM‐based estimates of future stock returns, both at the individual‐firm and aggregate market levels.     

Time-varying state variable risk premia in the ICAPM

We find that the relation between state variables, such as the t-bill rate and term spread, and consumption growth is time-varying. In the cross-section of U.S. stocks, risk premia for exposure to state variables vary over time accordingly. When a state variable predicts consumption strongly relative to its own history, its annualized risk premium increases by 6% (0.4 in Sharpe ratio). This effect implies that risk premia can switch signs and are increasing in the conditional variance of the state variable. These common drivers of time-varying risk premia are consistent with the Intertemporal CAPM. Benchmark factors contain the same conditional expected return effects as state variable risk premia.     

Equilibrium relations in a capital asset market: A mean absolute deviation approach

We consider the equilibrium in a capital asset market where the risk is measured by the absolute deviation, instead of the standard deviation of the rate of return of the portfolio. It is shown that the equilibrium relations proved by Mossin for the mean variance (MV) model can also be proved for the mean absolute deviation (MAD) model under similar assumptions on the capital market. In particular, a sufficient condition is derived for the existence of a unique nonnegative equilibrium price vector and derive its explicit formula in terms of exogeneously determined variables. Also, we prove relations between the expected rate of return of individual assets and the market portfolio.     

Unbiased estimation of expected return using CAPM

Estimation of expected return is required for many financial decisions. For example, an estimate for cost of capital is required for capital budgeting and cost of equity estimates are needed for performance evaluation based on measures such as EVA. Estimates for expected return are often based on the Capital Asset Pricing Model (CAPM), which states that expected excess return (expected return minus the risk-free rate) is equal to the asset's sensitivity to the world market portfolio (β) times the risk premium on the “world market portfolio” (the market risk premium). Since the world market portfolio, by definition, contains all assets in the world, it is not observable. As a result, an estimate for expected return is commonly obtained by taking an estimate for β based on some index (as a proxy for the world market portfolio) and an estimate for the market risk premium based on a potentially different index and multiplying them together. In this paper, it is shown that this results in a biased estimate for expected return. This is undesirable since biased estimates lead to misallocation of funds and biased performance measures. It is also shown in this paper that the straightforward procedure suggested by Fama and MacBeth [J. Financ. Econ. 1 (1974) 43] results in an unbiased estimate for expected return. Further from the analysis done, it follows that, for an unbiased estimate, it does not matter what proxy is used, as long as it is used correctly an unbiased estimate for expected return results.     

Estimation of expected return: CAPM vs. Fama and French

Most practitioners favour a one-factor model (CAPM) when estimating expected return for an individual stock. For estimation of portfolio returns, academics recommend the Fama and French three-factor model. The main objective of this paper is to compare the performance of these two models for individual stocks. First, estimates for individual stock returns based on CAPM are obtained using different time frames, data frequencies, and indexes. It is found that 5 years of monthly data and an equal-weighted index, as opposed to the commonly recommended value-weighted index, provide the best estimate. However, performance of the model is very poor; it explains on average 3% of differences in returns. Then, estimates for individual stock returns are obtained based on the Fama and French model using 5 years of monthly data. This model, however, does not do much better; independent of the index used, it explains on average 5% of differences in returns. These results therefore bring into question the use of either model for estimation of individual expected stock returns.     

Some Empirical Tests of the Theory of Arbitrage Pricing

We estimate the parameters of Ross's Arbitrage Pricing Theory (APT). Using daily return data during the 1963–78 period, we compare the evidence on the APT and the Capital Asset Pricing Model (CAPM) as implemented by market indices and find that the APT performs well. The theory is further supported in that estimated expected returns depend on estimated factor loadings, and variables such as own variance and firm size do not contribute additional explanatory power to that of the factor loadings.     

USING BAYESIAN BETAS TO ESTIMATE RISK RETURN PARAMETERS: AN EMPIRICAL INVESTIGATION

Since its original development by Sharpe (1964), the Capital Asset Pricing Model (CAPM) has been the focus of great interest, practical usage, modifications, testing, and controversy. The basic hypothesis of the CAPM is that the minimum expected return required by investors on any asset will equal the risk-free rate plus a premium for the asset's contribution to the variance risk of a diversified portfolio as measured by the asset's beta. The model is often utilized by investors to calculate the relevant risk and required return on an asset, while corporate officers widely employ the theory to compute the appropriate discount rate to use in estimating the net present value of capital budgeting projects when evaluating spending decisions (Gitman and Mercurio, 1982).