Currency risk premia and uncovered interest parity in the International CAPM

Zero-investment uncovered interest parity (UIP) portfolio positions provide perfect factor-mimicking portfolios for currency risk in the International CAPM context. Their returns are the currency risk premia. Since the UIP positions on average provide low returns, the currency risk premia must be low so that currency risk appears not to be priced in an unconditional model. However, previous research has shown that UIP returns are predictable and may be quite substantial conditionally. We use this observation to generate a specific conditional version of the International CAPM. A GMM approach shows that the conditional model performs well, while the unconditional International CAPM is (marginally) rejected. The paper thus argues that previous rejections of the International CAPM stem from the fact that currency risk premia are by nature low over extended periods of time and do not provide evidence against the International CAPM.     

A conditional regime switching CAPM

The standard Capital Asset Pricing Model (CAPM) is simple, intuitive, and grounded in sound economic theory. Yet, almost half a century's worth of empirical testing has so far failed to demonstrate its relevance. One major reason given for the CAPM's empirical failure is that beta is not the sole measure of systematic risk. In other words, the standard CAPM does not hold. Another important explanation is that the CAPM may hold conditionally rather than unconditionally. The standard CAPM fails to explain the cross-section of returns because it ignores the fact that both the risk and the price of risk are time-varying. The search for conditional models has led researchers to either disregard the theory behind the CAPM or to use statistical procedures that are too complex to be replicated by other researchers and practitioners. In this paper we propose a conditional model that is compatible with the standard CAPM while remaining simple and accessible to both researchers and practitioners. Beta and the risk premium are assumed to be time-varying, with the latter being associated with bull and bear states. We find strong support for the conditional CAPM with beta explaining both bull and bear markets. While the bear market ex-post risk premium is negative, the weighted average risk premium is positive and highly significant.     

The critical role of conditioning information in determining if value is really riskier than growth

Conditional asset pricing models have been used to determine whether the value premium and other CAPM anomalies are due to risk. We show that the conclusions on whether these anomalies are due to risk are very sensitive to the choice of the information variables used to define good and bad states of the world. We use a conditional CAPM framework allowing for alternative sets of plausible conditioning information and find that value appears to be riskier than growth in only about ten to twenty percent of specifications. We find even less evidence that size, issuance, momentum, and asset growth portfolio returns are due to risk. Overall, our results suggest that common CAPM anomalies are not due to risk.     

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.     

A conditional higher-moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926–2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs.     

The conditional CAPM does not explain asset-pricing anomalies

Recent studies suggest that the conditional CAPM holds, period by period, and that time-variation in risk and expected returns can explain why the unconditional CAPM fails. In contrast, we argue that variation in betas and the equity premium would have to be implausibly large to explain important asset-pricing anomalies like momentum and the value premium. We also provide a simple new test of the conditional CAPM using direct estimates of conditional alphas and betas from short-window regressions, avoiding the need to specify conditioning information. The tests show that the conditional CAPM performs nearly as poorly as the unconditional CAPM, consistent with our analytical results.     

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.     

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.     

Conventional and downside CAPM: The case of London stock exchange

Many studies on asset pricing have highlighted the importance of downside risk, in line with the actual losses of investors. In addition, the capital asset pricing model (CAPM), although presented as a universal theory, may provide significantly different rates of return in bull and bear markets. Using the CAPM under different conditions could be regarded as an alternative measurement and valuation approach to downside risk. This paper investigates conventional and downside approaches to risk taking into account different measures of downside beta coefficients. A further contribution of this research is the development of an alternative approach to testing the CAPM relationship. For this purpose, conditional relationships of the CAPM are proposed in which risk premiums are set separately in bull and bear periods. Using equity data and portfolios from the United Kingdom, we obtained positive and statistically significant downside risk premiums. We observed a slight advantage of downside measures over conventional beta measures. Conditional models provide evidence of a positive risk premium in rising markets and a negative risk premium in falling markets. The robustness analysis in subperiods indicates that these findings are largely unchanged for downside beta coefficients, which is not fulfilled by the model in a variance approach.     

Testing the CAPM with Time-Varying Risks and Returns

This paper draws on Engle's autoregressive conditionally heteroskedastic modeling strategy to formulate a conditional CAPM with time-varying risk and expected returns. The model is estimated by generalized method of moments. A CAPM that allows mean excess returns to shift in January survives generalized method of moments specification tests for a number of omitted variables. However, a residual dividend yield component is found to remain in the excess returns of smaller firms. We find significant monthly and quarterly components in the risk premia and beta estimates.     

The Subjective Valuation of Indexed Stock Options and Their Incentive Effects

We analyze the potential role of indexed stock options in future pay‐for‐performance executive compensation contracts. We present a unified framework for index‐linked stock options, discuss their incentive effects, argue that indexation schemes based on the capital‐asset pricing model (CAPM) are the most suitable for executive compensation, and derive a subjective pricing model for the class of CAPM‐based indexed stock options. Contrary to earlier work, executives would not be motivated to take on investment projects with high idiosyncratic risk once their lack of wealth diversification and degree of risk aversion are factored into the analysis.     

Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM

We amend the conditional CAPM to allow for unobservable long-run changes in risk factor loadings. In this environment, investors rationally “learn” the long-run level of factor loadings from the observation of realized returns. As a consequence of this assumption, we model conditional betas using the Kalman filter. Because of its focus on low-frequency variation in betas, our approach circumvents recent criticisms of the conditional CAPM. When tested on portfolios sorted by size and book-to-market, our learning-augmented conditional CAPM passes the specification tests.     

Temporal Aggregation and the Continuous-Time Capital Asset Pricing Model

We examine how the empirical implications of the Capital Asset Pricing Model (CAPM) are affected by the length of the period over which returns are measured. We show that the continuous-time CAPM becomes a multifactor model when the asset pricing relation is aggregated temporally. We use Hansen's Generalized Method of Moments (GMM) approach to test the continuous-time CAPM at an unconditional level using size portfolio returns. The results indicate that the continuous-time CAPM cannot be rejected. In contrast, the discrete-time CAPM is easily rejected by the tests. These results have a number of important implications for the interpretation of tests of the CAPM which have appeared in the literature.     

Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?

Abstract Markowitz and Sharpe won the Nobel Prize in Economics for the development of Mean‐Variance (M‐V) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected utility (EU) maximisation in the face of risk aversion. Kahneman and Tversky suggest Prospect Theory (PT) as an alternative paradigm to EU theory. They show that investors distort probabilities, make decisions based on change of wealth, exhibit loss aversion and maximise the expectation of an S‐shaped value function, which contains a risk‐seeking segment. Can these two apparently contradictory paradigms coexist? We show in this paper that although CPT (and PT) is in conflict to EUT, and violates some of the CAPM's underlying assumptions, the Security Market Line Theorem (SMLT) of the CAPM is intact in the CPT framework. Therefore, the CAPM is intact also in CPT framework.     

Asset market equilibrium with liquidity risk

This paper derives an equilibrium asset pricing model with endogenous liquidity risk. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Under a strong set of assumptions, we prove that a unique equilibrium liquidity cost process and a unique equilibrium price process exists for our economy. We characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including liquidity risk. We derive a generalized intertemporal CAPM and consumption CAPM for these markets. In contrast to the traditional models without liquidity risk, there is an additional systematic liquidity risk factor which is related to the stock return’s covariation with the market’s stochastic liquidity cost. Traditional transaction costs are a special case of our formulation.     

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。     

Discount-Rate Risk in Private Equity: Evidence from Secondary Market Transactions

Measures of private equity (PE) performance based on cash flows do not account for a discount-rate risk premium that is a component of the capital asset pricing model (CAPM) alpha. We create secondary market PE indices and find that PE discount rates vary considerably. Net asset values are too smooth because they fail to reflect variation in discount rates. Although the CAPM alpha for our index is zero, the generalized public market equivalent based on cash flows is large and positive. We obtain similar results for a set of synthetic funds that invest in small cap stocks. Ignoring variation in PE discount rates can lead to a misallocation of capital.     

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.     

Testing Conditional Asset Pricing Models Using a Markov Chain Monte Carlo Approach

We use Markov Chain Monte Carlo (MCMC) methods for the parameter estimation and the testing of conditional asset pricing models. In contrast to traditional approaches, it is truly conditional because the assumption that time variation in betas is driven by a set of conditioning variables is not necessary. Moreover, the approach has exact finite sample properties and accounts for errors‐in‐variables. Using S&P 500 panel data, we analyse the empirical performance of the CAPM and the Fama and French (1993) three‐factor model. We find that time‐variation of betas in the CAPM and the time variation of the coefficients for the size factor (SMB) and the distress factor (HML) in the three‐factor model improve the empirical performance. Therefore, our findings are consistent with time variation of firm‐specific exposure to market risk, systematic credit risk and systematic size effects. However, a Bayesian model comparison trading off goodness of fit and model complexity indicates that the conditional CAPM performs best, followed by the conditional three‐factor model, the unconditional CAPM, and the unconditional three‐factor model.     

The effect of time-varying covariances on asset risk premia

In this article we examine an intertemporal capital asset pricing model (CAPM) that allows for time-varying conditional covariances that are assumed to follow a multivariate integrated generalized autoregressive conditional heteroscedastic (IGARCH) process. The resulting pricing equation includes idiosyncratic risk premia in addition to the usual market beta. Empirical analysis based on ten size and ten industry portfolios reveals significant idiosyncratic premia for most portfolios. Overall, we reject the static CAPM in favor of the intertemporal CAPM.