Time-varying beta: a boundedly rational equilibrium approach

The conditional CAPM with time-varying betas has been widely used to explain the cross-section of asset returns. However, most of the literature on time-varying beta is motivated by econometric estimation using various latent risk factors rather than explicit modelling of the stochastic behaviour of betas through agents’ behaviour, such as momentum trading. Misspecification of beta risk and the lack of any theoretical guidance on how to specify risk factors based on the representative agent economy appear empirically challenging. In this paper, we set up a dynamic equilibrium model of a financial market with boundedly rational and heterogeneous agents within the mean-variance framework of repeated one-period optimisation and develop an explicit dynamic behaviour CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the two most commonly used types of investors, fundamentalists and chartists, into the model, we show that there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas. We also show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta.     

New estimates of time-varying currency betas: A trivariate BEKK approach

This paper examines the conditional time-varying currency betas from five developed markets and four emerging markets. We employ a modified trivariate BEKK-GARCH-in-mean model of Engle and Kroner (1995) to estimate the time-varying conditional variance and covariance of returns of stock index, the world market portfolio and changes in bilateral exchange rate between the US dollar and the local currency. It is found that currency betas are more volatile than those of the world market betas. Currency betas in emerging markets are more volatile than those in the developed markets. Moreover, we find evidence of long-memory in currency betas. The usefulness of time-varying currency betas are illustrated by two applications.     

Option implied beta and option return

We study the information content of option-implied betas for future equity option returns, using data on the S&P 500 index options and all of the component stock options. We find a significantly strong relation between option-implied betas and option returns cross-sectional. The paper presents evidence that call (put) option returns increase (decrease) with the option-implied betas of the underlying stock. A trading strategy of buying high (low) implied beta call (put) option portfolio and selling low (high) implied beta call (put) option portfolio generates a statistically and economically significant return. Our results are robustly persistent even after controlling for various cross-sectional effects and are not explained by the risk factors in asset pricing.     

The macroeconomic drivers in hedge fund beta management

We investigate how macroeconomic indicators alter the dynamic risk exposure of different hedge fund style strategies. We implement a multifactor model to estimate the unobservable time-varying risk exposure conditional on macroeconomic information and a VAR to measure the impact of macroeconomic predictors on different time horizons. Using monthly returns on a cross-section of 10 different style indices from February 1997 to August 2019, we find that, on average, macroeconomic indicators explain approximately 30%, 55%, and 75% of the variability of betas at 1-, 6-, and 36-month horizons, respectively. Although macroeconomic predictors play a critical role at every horizon, at 1 month, the dominating effect comes from idiosyncratic shocks, which indicates that in the short run, hedge fund managers rely mostly on their own reallocation signals. Moreover, consistent with the fundamental drivers of the smart beta factors, we find that the interest rate level and GDP growth similarly impact hedge fund exposures across styles.     

THE SYSTEMATIC RISK OF DEBT: AUSTRALIAN EVIDENCE*

This paper examines systematic risk (betas) of Australian government debt securities for the period 1979–2004 and makes three contributions to academic research and practical debate. First, the empirical work provides direct evidence on the systematic risk of government debt, and provides a benchmark for estimating the systematic risk of corporate debt which is relevant for cost of capital estimation and for optimal portfolio selection by asset managers such as superannuation funds. Second, analysis of reasons for non‐zero (and time varying) betas for fixed income securities aids understanding of the primary sources of systematic risk. Third, the results cast light on the appropriate choice of maturity of risk free interest rate for use in the Capital Asset Pricing Model and have implications for the current applicability of historical estimates of the market risk premium. Debt betas are found to be, on average, significantly positive and (as expected) closely related, cross sectionally, to duration. They are, however, subject to significant time series variation, and over the past few years the pre‐existing positive correlation between bond and stock returns appears to have vanished.     

Empirical tests on the asset pricing model with liquidity risk: An unobserved components approach

The aim of this paper is to test empirically the conditional liquidity-adjusted capital asset pricing model (L-CAPM) developed by Acharya and Pedersen (2005). Accordingly, we propose to estimate the L-CAPM using unobserved components methodology, which allows us to take into account the main stylized facts characterizing liquidity. Based on a sample of firms listed on the NASDAQ, our empirical analysis reveals several findings. Firstly, we show that liquidity is time-varying and exhibits strong seasonality. Secondly, we highlight the impact of the liquidity level premium on asset prices. Thirdly, we show that the most important liquidity risk is related to the covariance between portfolio illiquidity and market returns. Fourthly, we observe a negative relationship between portfolio returns and market illiquidity. Fifthly, we find that liquidity risk and illiquidity level are not always positively correlated.     

A two-regime threshold model with conditional skewed Student t distributions for stock returns

This paper proposes a two-regime threshold model for the conditional distribution of stock returns in which returns follow a distinct skewed Student t distribution within each regime: the model allows capturing time variation in the conditional distribution of returns, as well as higher order moments. An application of the model to daily U.S. stock returns illustrates the advantages of the proposed model in comparison to alternative specifications: the model performs well in terms of in-sample fit; it more accurately estimates the conditional volatility; and it produces useful risk assessment as measured by the term structure of value at risk.     

Single Beta Models and Currency Futures Prices

The conditional capital asset pricing model is applied to foreign currency futures prices, covariance risk being measured relative to excess returns from a broadly diversified international portfolio of equities. Positive time-varying risk premia are found in all five currencies tested when the difference between the US and the average foreign interest rates is used as an instrumental variable for the expected excess return from the common stock portfolio.     

An examination of the economic significance of stock return predictability in UK stock returns

We explore the out-of-sample performance of domestic UK asset allocation strategies that use forecasts of expected returns from a linear predictive regression and those that are implied by asset pricing models such as the capital asset pricing model (CAPM) or arbitrage pricing theory (APT). Our findings suggest that using forecasts of expected returns from the predictive regression generate significant benefits in out-of-sample performance. We find the performance of the strategies using expected return forecasts implied by the CAPM or APT is lower than the predictive regression strategy. However, with binding investment constraints, the performance of the APT matches that of the predictive regression.     

Nonparametric methods for estimating and testing for constant betas in asset pricing models

In this article, we study the performance of a smoothing spline method in estimating and testing for constant betas in two well-known asset pricing models, the usual market model and the three-factor model. The spline estimator is computed taking into account the conditional heteroscedasticity of the errors. Using the right model and estimation procedure for the variance term plays a crucial role in gaining efficiency in beta estimators. A simulation study shows the good performance of our method; in all the scenarios simulated, it outperforms the benchmark rolling estimator. The method enables users to obtain confidence intervals and to test for the significance and constancy of betas. Finally, the method is applied to US data, comprising 25 portfolios formed based on size and the ratio of book equity to market equity. The results show that the time-variability of the betas plays an important role, mainly when sensitivity to the HML factor is considered.     

Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash

Modelling of conditional volatilities and correlations across asset returns is an integral part of portfolio decision making and risk management. Over the past three decades there has been a trend towards increased asset return correlations across markets, a trend which has been accentuated during the recent financial crisis. We shall examine the nature of asset return correlations using weekly returns on futures markets and investigate the extent to which multivariate volatility models proposed in the literature can be used to formally characterize and quantify market risk. In particular, we ask how adequate these models are for modelling market risk at times of financial crisis. In doing so we consider a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and show that the t-DCC model passes the usual diagnostic tests based on probability integral transforms, but fails the value at risk (VaR) based diagnostics when applied to the post 2007 period that includes the recent financial crisis.     

Evidence of Stock Returns and Abnormal Trading Volume: A Threshold Quantile Regression Approach

This paper presents a capital asset pricing model‐based threshold quantile regression model with a generalized autoregressive conditional heteroscedastic specification to examine relations between excess stock returns and “abnormal trading volume”. We employ an adaptive Bayesian Markov chain Monte Carlo method with asymmetric Laplace distribution to study six daily Dow Jones Industrial stocks. The proposed model captures asymmetric risk through market beta and volume coefficients, which change discretely between regimes. Moreover, they are driven by market information and various quantile levels. This study finds that abnormal volume has significantly negative effects on excess stock returns under low quantile levels; however, there are significantly positive effects under high quantile levels. The evidence indicates that each market beta varies with different quantile levels, capturing different states of market conditions.     

The role of sentiment in global risk premia

This article examines the role of sentiment for global risk premia. We analyse whether the global risk premia on macroeconomic fundamentals can be estimated more thoroughly if sentiment is included as additional conditioning information. The analysis is performed in the framework of a conditional multiple beta pricing model. The focus of analysis is the asset excess returns of the G-7 stock markets in the period from February 1999 to February 2012. The obtained results indicate that sentiment as conditioning information is able to contribute to the explanation of the general macroeconomic risk premia.     

Global idiosyncratic risk moments

We investigate a global cross-sectional relation between idiosyncratic risk moments and expected stock returns by suggesting three global idiosyncratic volatility, skewness, and kurtosis risk factors. We also suggest two global small minus big and high minus low risk proxies for estimating return residuals of the test assets from a global asset pricing model. To perform robustness checks, we suggest other four global risk factors of momentum, leverage, bid-ask spread, and liquidity. We find a significant negative relation between stock portfolio returns and the global moments, and the cross section of stock returns reflects a significant negative price of risk for global idiosyncratic skewness (?0.13%) and idiosyncratic volatility (?1.85%) and a positive and significant price of risk for global idiosyncratic kurtosis. We find that our suggested risk factors are key drivers of risk premia in stock market and are robust to various checks. These factors also can forecast the gross domestic product growth over the sample period.     

Endogenous time-varying risk aversion and asset returns

Stylized facts about statistical properties for short horizon returns in financial markets have been identified in the literature, but a satisfactory understanding for their manifestation is yet to be achieved. In this work, we show that a simple asset pricing model with representative agent is able to generate time series of returns that replicate such stylized facts if the risk aversion coefficient is allowed to change endogenously over time in response to unexpected excess returns under evolutionary forces. The same model, under constant risk aversion, would instead generate returns that are essentially Gaussian. We conclude that an endogenous time-varying risk aversion represents a very parsimonious way to make the model match real data on key statistical properties, and therefore deserves careful consideration from economists and practitioners alike.     

Some empirical tests of the arbitrage pricing theory using transformation analysis

The purpose of this paper is to test the Arbitrage Pricing Theory (APT) using monthly data for Finnish stock returns during the 1970–1986 period. The first stage involves estimating the systematic risks for each asset using factor analysis. The second stage involves testing by transformation analysis if the number and structure of factors which influence the security returns remain unchanged across various time periods. The third stage involves testing the implications of the APT using cross-sectional regression analysis.     

宏观经济状态对资产定价因子的影响

为刻画资产定价因子随宏观经济状态时变性,本文通过经济增长和通货膨胀两个指标定义经济状态,建立宏观经济状态下的条件资产定价模型。研究发现在中国资本市场上此模型能够显著改进CAPM模型的效力,其定价效力甚至优于多因子模型。进一步研究表明,宏观经济通过两个维度影响资产价格：第一,多数资产在衰退时期对市场风险更敏感,其代表市场因子的贝塔系数大于复苏与过热阶段;第二,小市值公司的贝塔系数均值及波动性大于大公司,在经济衰退时承担更高的风险收益。     

我国基于总收益形式与超额收益形式估计的证券贝塔比较分析

经过简化的基于总收益形式的指数模型被经常用来估计证券贝塔,但这个模型没有理论依据。由于我国无风险利率的方差与市场收益的方差变动比较起来非常小,短期无风险利率的实际变动对贝塔估计值影响很小,因此,从“预测”的角度看,用总收益形式的单指数模型估计贝塔值可以完全替代具有理论基础的超额收益形式的单指数模型估计的贝塔。     

Political and Regulatory Risk: Beta Sensitivity in U.K. Electricity Distribution*

To establish price caps, regulators must determine appropriate returns for utilities capital employed. This paper uses the techniques of the Kalman Filter to estimate daily betas for the U.K.s regional electricity companies in the period from privatization to end-1998. The paper demonstrates that utilities risk is time-variant, and establishes significant political and regulatory influences in the systematic risk faced by shareholders. It finds beta to be mean reverting, with little evidence of cyclical variation across the regulatory review cycle. The paper confirms the prevalence of significant excess returns in U.K. privatized electricity distribution and suggests that over-estimation of the systematic risk faced by investors may imply further excess returns in the next regulatory review period.     

Semi‐Parametric Examination of Industry Risk: The Australian Evidence

This paper examines the time variation form of the systematic risk measurement, beta, in Australian industry sectors. By using a semi‐parametric approach, the systematic risk measurement, beta, is defined as a combination of one stable parametric component and one varying non‐parametric component. Two categories of industries were identified. The Energy, Material, Mining, Industrial and Property Trust industries had a generally increasing beta for most of the sample period, while the Consumer Discretionary, Financials Excluding Property Trust, IT and Telecommunications had a decreasing beta for the same period. The betas of the Health and Utility industries are more stable than others. The variation of industry risk is linked with the market conditions, as well as the change of interest rates.