Linear beta pricing with inefficient benchmarks in a given factor structure*

ABSTRACT

We show the equivalence between the zero-beta version of a multi-factor arbitrage pricing model and a linear pricing model utilizing undiversified inefficient benchmarks in a given factor structure. The resulting linear model is a two-beta model, with one beta related to the inefficient benchmark and another adjusting for its inefficiency. This linear model shows that there are only two distinctive and computable sources of risk, affecting security expected returns, despite the existence of several risk factors. In a short empirical example we demonstrate that the model can be employed to provide guidance and allow researchers to test for the validity of their selection of the underlying risk factors driving variations in security returns.     

An Examination of Alternative Factor Models in UK Stock Returns

This paper examines the mean-variance efficiency of a number offactor models in UK stock returns. The paper also explores, using theapproach of MacKinlay (1995), whether missing risk factors ornonrisk-based explanations best explain the pricing errors of thedifferent factor models. The evidence in the paper suggests that themean-variance efficiency of each factor model is rejected and missing riskfactors are unable to explain the pricing errors of any of the models.Some nonrisk-based explanations, which posit a wide spread in abnormalreturns, may be a more plausible source of explaining the pricing errorsof the factor models.     

Do Beta Pricing Models Explain January Mean Reversion in Stock Returns?

Jegadeesh (1991) finds evidence of January mean reversion in stock returns. In this paper we attempt to distinguish between two competing economic explanations of January mean reversion in returns: (1) mispricing in irrational markets versus (2) predictable time variation in security risk premia. Excess portfolio returns are decomposed into “explained” and “unexplained” components using the Fama-French (1993) pricing model. The explained excess returns exhibit January mean reversion. The unexplained excess returns are not mean reverting. Mean reversion is therefore consistent with rational pricing in the framework of the Fama-French model. Mean reversion can be attributed to the component of return related to a relative distress factor (SMB). A comparison with the Chen, Roll, and Ross (1986) macroeconomic factors reveals that mean reversion is due to the components related to SMB and bond default premium.     

On the Number of Factors in the Arbitrage Pricing Model

Recent theory has demonstrated that the Arbitrage Pricing Model with K factors critically depends on whether K eigenvalues dominate the covariance matrix of returns as the number of securities grows large. The purpose of this paper is to test whether sample covariance matrices can be characterized as having K large eigenvalues. Using all available data on the 1983 CRSP tapes, we compute sample covariance matrices of returns in sequentially larger portfolios of securities. Analyzing their eigenvalues, we find evidence that one eigenvalue dominates the covariance matrix indicating that a one-factor model may describe security pricing. We also find that, for values of K larger than one, there is no obvious way to choose the number of factors. Nevertheless, we find that while only the first eigenvalue dominates the matrix, the first five eigenvalues are growing more distinct.     

Quantile regression analysis of hedge fund strategies

Extending previous work on hedge fund pricing, this paper introduces the idea of modelling the conditional quantiles of hedge fund returns using a set of risk factors. Quantile regression analysis provides a way of understanding how the relationship between hedge fund returns and risk factors changes across the distribution of conditional returns. We propose a Bayesian approach to model comparison which provides posterior probabilities for different risk factor models that can be used for model averaging. The most relevant risk factors are identified for different quantiles and compared with those obtained for the conditional expectation model. We find differences in factor effects across quantiles of returns, which suggest that the standard conditional mean regression method may not be adequate for uncovering the risk-return characteristics of hedge funds. We explore potential economic impacts of our approach by analysing hedge fund single strategy return series and by constructing style portfolios.     

Investor Psychology and Asset Pricing

The basic paradigm of asset pricing is in vibrant flux. The purely rational approach is being subsumed by a broader approach based upon the psychology of investors. In this approach, security expected returns are determined by both risk and misvaluation . This survey sketches a framework for understanding decision biases, evaluates the a priori arguments and the capital market evidence bearing on the importance of investor psychology for security prices, and reviews recent models.     

Is there a real estate factor premium?

In this paper, we study the variation of expected returns on five different asset portfolios in a multi-factor model. We found the presence of a real estate factor, in addition to both a stock factor and a bond factor in asset pricing. This suggests that mutual fund managers should seriously consider including real estate assets in their portfolios, since one cannot capture the real estate factor premium without having some kind of real estate exposure. Another result is that the market segmentation found in previous studies disappears in a more general model of asset pricing in which we allow for multi-factors other than the market factor to affect asset returns. This implies that real estate assets can be treated just like other assets as far as mean-variance efficient asset allocations are concerned. We also have some preliminary evidence that equity REITs and the Russell-NCREIF index are driven by the same underlying real estate factor.     

上市公司综合盈利水平与股票收益

本文基于2000-2017年上市公司的财务及股票交易数据,研究了上市公司综合盈利水平与股票收益之间的关系。我们使用目前资产定价文献中较新的偏最小二乘法和组合预测法,从12个衡量公司盈利能力的指标中提取了一个测度上市公司综合盈利水平的指标。研究结果显示,上市公司综合盈利水平能够显著预测未来股票收益。使用单因子偏最小二乘法、取12个月斜率的平均值构造的综合盈利水平最有效,以其构建的多空对冲投资组合能产生15%的年平均收益,夏普比率达到0.75。与此对应,组合预测法提取的上市公司综合盈利水平的预测能力稍低,但依然显著。在控制了其他公司特征变量后,综合盈利水平对于股票收益的解释能力依然稳健。本文还从经济机制的角度出发,探讨了综合盈利水平对收益的预测来源。我们发现,上市公司综合盈利水平与股票预期回报的正向关系在投资摩擦更低的组中更高,而在错误定价程度更高的组通常更低。这些结果支持了基于投资摩擦的Q理论,而与行为金融的错误定价理论相悖。     

On the differences in measuring SMB and HML in the UK – Do they matter?

The Fama–French (FF) three factor model expands the capital asset pricing model (CAPM) to include two additional factors to the market factor – SMB, employed to capture a firm size effect in returns and HML employed to capture book-to-market effects in returns. In the UK, different researchers use different ways of calculating SMB and HML in the context of empirical applications of the three factor model, or extensions of it, perhaps because they believe the differences in the construction of the SMB and HML factors to be relatively unimportant from an empirical standpoint. We investigate whether indeed factor construction methods are unimportant. Our conclusion is that they do matter.     

The impact of exchange rates on stock market returns: new evidence from seven free-floating currencies

This paper provides evidence of a significant exchange rate effect on stock index returns using data from seven selected countries practicing free-floating exchange rate regimes. This research uses parity and asset pricing theories, thus placing it within the monetary-cum-economics framework for international asset pricing. In this study, we apply a system of seemingly unrelated regression to control for unobserved heterogeneity and cross-sectional dependence. The findings constitute evidence of a statistically significant exchange rate impact on stock index returns across selected countries. These findings can be considered as falling under the arbitrage pricing approach of the international capital asset pricing model of Solnik who also used the parity-theoretical framework on exchange rate determination.     

中国大宗商品期货市场定价机制研究

大宗商品期货市场是我国资本市场的重要组成部分,其定价有效性关系到投资者套期保值和价格发现等功能的实现。本文对国际前沿研究中常用的定价因子进行全面系统梳理,并对这些因子对我国商品期货合约收益率的解释和预测能力进行检验。在此基础上,本文构建了适用于我国大宗商品期货市场的包含市场、基差以及基差动量的三因子定价模型。进一步研究表明,基于大宗商品存储理论和现货存货数据构建的投资组合收益率可以被本文三因子模型有效解释,验证了经典的存储理论在我国的适用性。此外,本文对基差与基差动量两个重要因子的经济学意义进行了阐释。本文研究为进一步厘清大宗商品期货市场定价机制提供了一定参考。     

An International Asset Pricing Model with Time-Varying Hedging Risk

This paper employs a two-factor international equilibrium asset pricing model to examine the pricing relationships among the world's five largest equity markets. In addition to the traditional market factor premium, a hedging factor premium is included as the second factor to explain the relationship between risks and returns in the international stock markets. Moreover, a GARCH parameterization is adopted to characterize the general dynamics of the conditional second moments. The results suggest that the additional hedging risk premium is needed to explain rates of return on international equities. Furthermore, the restriction that the coefficient on the hedge-portfolio covariance is one smaller than the coefficient on the market-portfolio covariance can not be rejected. This suggests that the intertemporal asset pricing model proposed by Campbell (1993) can be used to explain the returns on the five largest stock market indices.     

A Semiautoregression Approach to the Arbitrage Pricing Theory

This paper developes a semiautoregression (SAR) approach to estimate factors of the arbitrage pricing theory (APT) that has the advantage of providing a simple asymptotic variance-covariance matrix for the factor estimates, which makes it easy to adjust for measurement errors. Using the extracted factors, I confirm the finding that the APT describes asset returns slightly better than the CAPM, although there is still some mispricing in the APT model. I find that not only are the factors “priced” by the market, but the factor premiums move over time in relation to business cycle variables.     

Asset pricing,time-varying risk premia and interest rate risk

This paper investigates the role of interest rate risk in explaining security price changes. We develop and test a two-factor linear beta pricing model of security returns in which the factors are the excess returns on the long-term, riskless bond and the equal-weighted equity market index. We find that time-variation in the interest rate and market risk premia influence expected security returns. Furthermore, conditional interest rate volatility affects security returns, particularly during periods of substantial interest rate movements.     

Linear beta pricing with efficient/inefficient benchmarks and short-selling restrictions

We provide two security pricing models that can be used when short sales of risky securities are not permitted. The first model uses a benchmark located on the expected return-standard deviation efficient frontier without short sales and presents security expected returns as a weighted linear function of two betas, one induced by the benchmark and the other adjusting for the short-sale constraints. The second model uses a benchmark that is inefficient relative to the efficient frontier, does not allow short sales, and expresses security returns as a weighted linear function of three betas:one induced by the inefficient benchmark, and the other two adjusting simultaneously for the short-sales restrictions and the benchmark's inefficiency.These results complement the linear pricing models that link expected returns and betas by allowing, for efficient or inefficient expected return-standard deviation, benchmarks with restricted short sales.     

In America's thrall: the effects of the US market and US security characteristics on Australian stock returns

Can Australian equity returns be modelled by ‘home‐grown’ factors? We examine the indigenous capital asset pricing model, the indigenous Fama–French three‐factor model, and extensions to the latter, and find them all wanting. We find evidence of domestic market segmentation in Australia. For the smallest firms, all the models we study fail. For the largest Australian firms, we find that the US Fama–French three factors (downloaded from French's website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ ) provide a successful model of Australian returns. It is as if the largest firms in the Australian market are simply part of the larger US market.     

Findings from a Cross-Sectional Housing Risk-Factor Model

Housing data from the last 25 years show that returns to residential real estate in the U.S. can be volatile and vary significantly among locations. The variations in returns are driven by economically as well as geographically and psychologically motivated factors, but so far, no asset pricing model that adequately explains systematic risks in cross-sectional housing returns is widely accepted. This paper proposes an asset pricing model for housing returns that includes a market-wide return factor, an economically motivated factor derived from income growth, a geographically based factor derived from land supply elasticity and a momentum factor, which is psychological in nature. The model explains well the systematic risks in housing returns and is robust to different portfolio segmentations. Moreover, the model illustrates that local risk factors indirectly capture the risk previously attributed to market-wide price changes. While housing is not actively traded when compared to other financial assets, understanding the risk-factors that explain housing return in cross-section provides important insight for real estate investors, builders, real estate future traders, homeowners, banks and other mortgage lenders.     

Extending the capital asset pricing model: the reward beta approach

This paper offers an alternative method for estimating expected returns. The proposed reward beta approach performs well empirically and is based on asset pricing theory. The empirical section compares this approach with the capital asset pricing model (CAPM) and the Fama–French three‐factor model. In out‐of‐sample testing, both the CAPM and the three‐factor model are rejected. In contrast, the reward beta approach easily passes the same test. In robustness checks, the reward beta approach consistently outperforms both the CAPM and the three‐factor model.     

The Cross Section of Expected Real Estate Returns: Insights from Investment-Based Asset Pricing

Motivated by investment-based asset pricing, we show that two firm fundamentals, investment and profitability, have substantial predictive power for REIT returns. The return predictability of investment and profitability is not subsumed by conventional models and can be useful for understanding the cross section of expected REIT returns. To illustrate, we construct an investment-based factor model for REITs that consists of a market factor, an investment factor, and a profitability factor. The investment-based model outperforms conventional models in capturing well-known cross-sectional patterns in REIT returns. Our findings suggest that incorporating investment-based asset pricing can be a promising direction for future real estate finance research.