The pricing of time-varying beta

We generalize an asset pricing model based on the Arbitrage Pricing Theory (APT) allowing beta to be time-varying. Making beta a random variable adds flexibility to the model because permits a non-linear relation between individual returns and the set of factors, and accounts for the effect of possible omitted variables. We integrate the conditional APT with a general linear stochastic process for beta. We analyze the behavior of the conditional expected return, the conditional variance and conditional covariance of individual asset returns as functions of the conditional moments of beta. On considering time-varying betas we introduce another source of uncertainty (risk) independent of the factors. We need to disentangle if this extra risk is systematic or non-systematic. To this end, we introduce a modified conditional APT model that rationalizes why the time variation of beta may represent extra systematic risk. For a sample of individual stocks, we test the hypothesis of time-varying beta and the feasibility of the modified conditional APT. We present a test for time-varying beta based on the conditional second moments of returns. We find that there is strong evidence against constancy of betas in favor of a random coefficient model, and that the time variation of beta is due to non-systematic behavior of the firms and investors should be able to diversify this risk away.     

Mean-semivariance behavior: Downside risk and capital asset pricing

For over 30 years academics and practitioners have been debating the merits of the CAPM. One of the characteristics of this model is that it measures risk by beta, which follows from an equilibrium in which investors display mean-variance behavior. In that framework, risk is assessed by the variance of returns, a questionable and restrictive measure of risk. The semivariance of returns is a more plausible measure of risk and can be used to generate an alternative behavioral hypothesis, mean-semivariance behavior; an alternative measure of risk for diversified investors, the downside beta; and an alternative pricing model based on this downside beta. The empirical evidence discussed in this article for the entire MSCI database of developed and emerging markets clearly supports the downside beta and the pricing model based on it over beta and the CAPM.     

THE DISTRIBUTION OF BETAS IN PRESENCE OF NONTRADED ASSETS

This study considers a capital assets pricing model (CAPM) in an incomplete financial market wherein not all risky assets are traded and the risk from non‐traded assets is not orthogonal to that of the existing or traded assets. The model shows the extent of the divergence of the CAPM betas (true betas) from the traditional CAPM betas (perceived betas) in market equilibrium conditions in an incomplete market. Specifically, it implies that the more incomplete a financial market is, the wider is the discrepancy between the true and perceived betas, and the distribution of the perceived betas tends to centre more around 1 in an incomplete market than that of true betas. Empirical evidence in various settings support these results.     

Asset pricing with time-varying betas for stocks traded on S&P 500

This study uses a novel approach for capturing time variation in betas whose pattern is treated as a function of market returns. A two-factor model (TFM) is constructed using estimated coefficients of a nonlinear regression. The model is tested against the CAPM and the Fama and French three-factor model in the context of time series regressions. The used stocks are traded on S&P 500. The period spans from 1993 to 2011. The time series regression results depict the superiority of the TFM in explaining portfolio returns including momentum ones. We also provide evidence that the particular portfolios employed at the construction of the new model accommodate different fundamental characteristics and different risk levels.     

Non-parametric and semi-parametric asset pricing

We find that the CAPM fails to explain the small firm effect even if its non-parametric form is used which allows time-varying risk and non-linearity in the pricing function. Furthermore, the linearity of the CAPM can be rejected, thus the widely used risk and performance measures, the beta and the alpha, are biased and inconsistent. We deduce semi-parametric measures which are non-constant under extreme market conditions in a single factor setting; on the other hand, they are not significantly different from the linear estimates of the Fama-French three-factor model. If we extend the single factor model with the Fama-French factors, the simple linear model is able to explain the US stock returns correctly.     

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.     

Asset pricing and downside risk in the Australian share market

As downside risk has been identified as a separate risk exposure to investors, we investigate whether downside beta and co-skewness exposure impact on the return to investors in Australian equities. Although considered as a developed market, the Australian Securities Exchange merits separate investigation, as it is small and concentrated on some sectors, when compared with the major developed markets. As realized returns are a proxy for expected returns, we separately examine conditional returns in upturn and downturn periods. We find that both downside risks are separately priced by investors, and that our results are unaffected by the inclusion of a range of company characteristics. We subsequently confirm that returns to each downside risk are not related. In robustness tests, we conclude that the return to downside risk cannot be explained by a size, a value, or a momentum premium. Although it also has explanatory power, the inclusion of a leverage factor also does not reduce the explanatory power of downside risk.     

The capital asset pricing model in economic perspective

The capital asset pricing model (CAPM) is theoretically incomplete in its demand-side focus, risk-averse investors and internally inconsistent homogeneous beliefs; is not conclusively supported empirically; and yet it legitimizes a notion that investors can earn higher returns by bearing undiversifiable risk. Our article does not merely extend the CAPM with more realistic assumptions, it completes its original framework by including (1) risk-taking investors in the investor population, (2) investors who can have heterogeneous expectations or beliefs – an overlooked but required condition for the CAPM to be an internally consistent and meaningful model of competitive financial asset pricing under uncertainty and (3) a positive-sloped short-run supply curve based on a reasonable interpretation of the nature of financial asset trade. Upon a complete economic interpretation, it is shown that the equilibrium (systematic) risk-rate of return relationship depends on whose aggregate trading activity dominates, risk-averse or risk-taking investors’. There is no universal, or even general, positive relationship between systematic risk and rate of return. This has far-reaching implications for investors and investment advisors who serve them.     

The instantaneous capital market line

Summary. We show that if the intercept and slope of the instantaneous capital market line are deterministic, then investors will not hold any hedge portfolios in the sense of Merton [9, 11]. They will choose portfolios that plot on the capital market line, and they will slide up and down the capital market line over time as their wealth and risk tolerance change. This result allows us to aggregate over investors and derive a single factor CAPM where the first and second moments of security returns may change stochastically over time and markets are potentially incomplete.Received: 21 June 2004, Revised: 10 December 2004, JEL Classification Numbers: G11, G12.An earlier version of this paper was presented at the Econometric Society Meeting in Pasadena (1997) under the title “Portfolio selection and asset pricing with dynamically incomplete markets and time-varying first and second moments”.     

Mesdames et Messieurs,momentum performance is not so abnormal after all!

This article provides evidence regarding the performance of momentum investment strategies that is consistent with the Neoclassical Theory. More specifically, while momentum investment returns appear orthogonal to systematic risk in the extant literature, this article illustrates that they are due to correlated changes of hedge portfolio systematic risk exposures with market conditions. Momentum portfolios are excellent market timers in both expanding and contracting markets. Their returns however are generally not abnormal when timing is considered in an augmented unconditional Capital Asset Pricing Model (CAPM), while the standard version erroneously considers them to be so, possibly explaining why momentum studies have so far rejected the Neoclassical Theory.     

How strong is the global integration of emerging market regions? An empirical assessment

This paper attempts to evaluate the time-varying integration of emerging markets from a regional perspective based on a conditional version of the International Capital Asset Pricing Model (ICAPM) with DCC-GARCH parameters that allows for dynamic changes in the degree of market integration, global market risk premium, regional exchange-rate risk premium, and local market risk premium. Our findings reveal several interesting facts. First, the time-varying degree of integration of four emerging regions under consideration, satisfactorily explained by the regional level of trade openness and the term premium of US interest rates, has recently tended to increase, but these markets still remain substantially segmented from the world market. Second, the local market risk premium is found to explain more than 50% of the total risk premium for emerging market returns. Finally, we show that conditional correlations usually underestimate and overstate the measure of time-varying market integration. The empirical results of this study have some important implications for both global investors and policymakers with respect to dedicated portfolio investments in emerging markets and policy adjustments.     

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.     

Regional stock market integration in Singapore: A multivariate analysis

This paper evaluates the time-varying integration of the Singapore stock market in the ASEAN-5 region based on a conditional version of the International Capital Asset Pricing Model (ICAPM) with c-DCC-FIAPARCH parameters. This model allows for dynamic changes in the degree of market integration, regional market risk premium, regional exchange-rate risk premium, and domestic market risk premium. Our findings show several interesting facts. First, the time-varying degree of integration in the Singapore market is satisfactorily explained by the level of trade openness and the term premium of US interest rates, which have recently tended to increase, however these markets remain substantially segmented from the world market. Second, the local market risk premium is found to explain a significant proportion of the total risk premium for emerging market returns. Our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity markets. Our results are also of interest for both policymakers and investors, with respect to regional development policies and dedicated portfolio investment strategies in the ASEAN-5 region.     

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。     

A Model of Creative Destruction with Undiversifiable Risk and Optimising Households

This paper studies optimal household behaviour in a model of creative destruction. The saving technology is characterised by stochastic returns that follow a Poisson process. It is shown that equilibrium conditions with optimising households differ substantially from equilibrium conditions where investment in R&D is determined by firms. Three out of four market failures disappear and a new market failure resulting from a complementarity in financing R&D is identified. Studying the social optimum shows that it contains as the special case of risk neutrality the social optimum derived in the literature.     

Return patterns of South Korean stocks following large price shocks

This study tests the market efficiency of the South Korean stock market by examining returns on stocks of the constituents of the KOSPI 50 from 2000 to 2014 following large 1-month price decreases and increases. An exponential GARCH (EGARCH) event study framework is used to analyse the stock returns. The results show that large price shocks, positive and negative, are likely to be followed by positive market returns. Moreover, the results show an increase in the beta of stocks in the years following a large price shock. The overall results therefore support the Uncertain Information Hypothesis. However, beginning in 2008, return patterns more closely reflect those hypothesised by the Efficient Market Hypothesis, possibly due to increased participation by international investors. The observed returns following large price increases and decreases can be partially explained by changes in the Korean won to US dollar exchange rate and the trading behaviour of foreign investors.     

Tests of the CAPM under structural changes

Abstract

In accordance with the empirical regularity of time-varying betas we estimate and test for the Sharpe–Lintner CAPM by allowing for structural change(s) in betas. Empirical applications using BM- and size-sorted decile portfolios suggest the following interesting results. Firstly, there exists at least one break for all the portfolios under consideration. Secondly, the estimated break dates are quite similar for some of the portfolios, indicating the possible existence of a common break using multivariate time series. Finally, we find the CAPM can be consistent with the data in some regimes but may appear to be inconsistent with the data in some other regimes. This particularly appealing feature has been completely ruled out under the conventional single-equation framework.     

Option-implied preferences adjustments, density forecasts, and the equity risk premium

The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two-lognormals and several alternative risk adjustments. Our results show that, between October 1996 and March 2000, we can reject the hypothesis that the risk-neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at 4- and 8-week horizons. When forecasting through risk-adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. We show that risk adjustments based on a power specification for the stochastic discount factor—which is the approach used so far in the literature that derives the objective density function from option prices- generates an excessive volatility of risk premia. We use alternative risk adjustments and find that the forecasting performance of the distribution improves slightly in some cases when risk aversion is allowed to be time-varying. Finally, from October 1996 to December 2004, the ex-ante risk premium perceived by investors and that are embedded in option prices is between 12 and 18% higher than the premium required to compensate the same investors for the realised volatility in stock market returns.      

Stability and bifurcation in a simple heterogeneous asset pricing model

Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. We develop a simple pricing model with two types of rational traders, fundamentalists and chartists, in order to study well price behavior in financial markets, we use student t distribution to replace traditional normal distribution to describe fundamental price process. We study the stability and bifurcation of the underling deterministic system and use numerical simulation to study the dynamic of the stochastic system, including autocorrelations structures and high kurtosis of the returns. It is found that the fundamental price becomes stable (unstable) when the activities from both types of traders are balanced (unbalanced).