Research On Liquidity Adjusted Asset Pricing And Risk Measurement Models And Their Applications

The traditional theory of financial economics usually assumes that the market is perfect,which means there is no any transaction cost.However,this assumption is very far from the real world and thus greatly reduces the explanatory power of the related theory.Due to the existence of the liquidity transaction cost,liquidity changes may have a great impact on the prices of assets,while ignoring these changes would bring great harm to the entire financial market.Because of the importance of liquidity in both theoretical and practical views,and based on the research of Acharya and Pedersen(2005),Engle(1982)and Engle and Manganelli(2004),we consider the nonlinear impact of liquidity on the asset pricing and risk measurement,and propose new liquidity adjusted asset pricing models and risk measurement methods in this thesis.Our studies not only greatly enrich and improve the existing financial theory,but also provide investors with some practical suggestions and useful tools.The exsitentence of liquidity transaction costs in reality will directly affect the calculation of net returns in traditional asset pricing models,which makes these models become invalid.Considering that the nonzero liquidity transanction cost is endogenous,we put it into the balance framework of investor’s consumptions in two periods,and derive the liquidity nonlinearly adjusted capital asset pricing model(LNA-CAPM)in this thesis.The biggest difference between LNA-CAPM and the existing liquidity adjusted CAPM is that the liquidity transaction cost is endogenous and is a compeletely unknown single-index function of the liquidity.This treatment is able to overcome the difficulty of the unobservability of liquidity transaction cost.The nonlinear premium form of the liquidity is our main innovation of this thesis in pricing theory.Based on the theoretical analysis,we do many empirical studies on the LNA-CAPM using both daily and monthly data from Chinese stock market.In the empirical studies based on the daily data,we compare our LNA-CAPM with CAPM,LLA-CAPM(liquidity linearly adjusted CAPM)and have the following results.(1)The relationship between the liquidity cost and liquidity is nonlinear indeed.(2)The liquidity has a significant impact on the excess returns.In details,the unexpected illiquidity has a significantly negative impact on the excess returns,while the impact of the expected illiquidity is not significant.(3)LNA-CAPM performs very well in explaining the cross-sectional differences of excess returns of different portfolios,and can increase the model explanation by 10 percents than that of LLA-CAPM.In the empirical studies based on the monthly data,we compare our LNA-CAPM with CAPM,LLA-CAPM and the three-factor model proposed by Fama and French(1993).In addition to the similar results with above results(1)and(2),we also find that the LNA-CAPM is able to achieve quite similar level of the three-factor model in terms of explaining the cross-sectional differences of excess returns of different portfolios.Additionally,considering the factors of market,liquidity,size and BM simutaneuously,we propose a four-factor mixed model,which has a much better goodness of fit than that of the three-factor model.In the study of risk measurement,we consider two widely used risk measurements.One is volatility of returns.The other is value at risk(VaR).Considering the nonlinear structure of the conditional variance,we gernalize the linear or parametric form assumed by ARCH-type models to a nonlinear single-index form.Futhermore,we consider the impact of liquidity on the volatility,and propose the liquidity asjusted single-index volatility model(LA-SIVM).This model is an important promotion of traditional ARCH-type models.Taking into account the sample size requirements of semiparametric estimation of volatility,we only use daily data from Chinese stock market to do empirical studies.The results show that(1)under the assumption of the semiparametric structure,the volatility also has a significant time series autocorrelattion,which explains the phenomenon of volatility cluster again;(2)the liquidity has a significant impact on the volatility risk.Furthermore,the impact of expected and unexpected liquidity on the volatility are opposite.The former is significantly positive,and the latter is significantly negative;(3)the impact of liquidity on the volatility risk from asset itself is much bigger than that from the whole market.Finally,we compare the LA-SIVM with GARCH(1,1)in terms of volatility calculation,and find that LA-SIVM can well capture impact of liquidity on the returns and adjust the future volatility estimation according to the liquidity changes,which can effectively avoid the underestimation of volatility risk in the period of liquidity sharp deterioration.In studying the liquidity adjusted VaR,we do not follow the existing idea of adding the liquidity risk factor on the traditional VaR directly.In this thesis,we consider the liquidity as a influencing factor of the future VaR.Based on the idea of Engle and Mangannelli(2004),we propose the liquidity adjusted CAViaR model(LA-CAViaR)to calculate the liquidity adjusted VaR directly.LA-CAViaR can efficiently avoid the risk overlapping effect in the exsiting methods.Using LA-CAViaR to study the risk of Chinese stock market,we find that(1)LA-CAViaR is able to well fit the data from Chinese stock market,and immediately adjust the VaR prediction according to the liquidity changes.Especially in times of financial crisis and asset liquidity dropped significantly,LA-CAViaR can capture the increase of liquidity risk so as to effectively avoid future risk of assets being underestimated;(2)In Chinese stock market,the sharp decline in asset liquidity usually leads to significantly increased risk in the future.The risk caused by the decline of positive liquidity is much bigger than that from decline of negative liquidity,and therefore is more worthy of risk managers’attention.Actually,LNA-CAPM and LA-SIVM are the regressive mean and variance functions respectively.Combining LNA-CAPM and LA-SIVM together,we propose a new statistical model,called partially linear single-index volatility model(PLSIVM)hereafter,whose mean function is of a partially linear single-index form and variance function is of another single-index form.PLSIVM is a very general model,which contains many existing models,such as the linear model,partially linear model,single-index model,partially linear single-index model and single-index volatility model and so on.In this thesis,we give the estimation method and prove the consistency and asymptotic normality of the corresponding estimators.Many numerical studies show that the estimators are really robust and effective when the sample size is small,which lays the foundation for practical applications.Finanlly,following the idea of the risk adjusted return and using LNA-CAPM,LA-SIVM and LA-CAViaR respectively for asset pricing and measurements of volatility and VaR risks,we propose liquidity adjusted indexes for portfolio performance evaluation.By applying these indexes in portfolio performance evaluation in Chinese stock market,useful suggestions are provided for Chinese investors.