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Analysis to Time-varying β of China Stock Market

Author: LinXinDa
Tutor: GuoJianJun
School: Southwestern University of Finance and Economics
Course: Statistics
Keywords: βTime-varying Multivariate GARCH GMM CAPM
CLC: F832.51
Type: Master's thesis
Year: 2009
Downloads: 83
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Abstract

One of the important areas of Financial Research is to understand why we observed a variety of financial assets have different expectations of return. Asset pricing model can be regarded as a description of the expected return of financial assets. Asset pricing problem is the fastest growing area in the financial theory in West in recent decades. After Markowitz made portfolio theory, his student, Sharp has developed a teacher’s theory, put forward the capital asset pricing model (CAPM).CAPM, as one of foundation of the modern financial theory, has a wide range of applications. CAPM, which Markowitz’s portfolio theory was very important to simplify, claim that any asset’s risk -rewards can be used characteristics of 3 parameters: Mean, standard deviation of the market as well as the combination of sensitivity. Although the portfolios theory suggest that the price of assets is not determined by the total risk, it did not clarify which part of the risk associated with asset pricing. Sharpe actively explore this issue and a major breakthrough, in 1964, "the financial magazine" published by the paper on "Capital asset prices: the risk of a state of the market equilibrium theory" and the subsequent Lintner (1965) and Mossin (1966) to complete independence But come to the same conclusion of the relevant papers constitute the famous capital asset pricing model (Capital Asset Pricing Model, CAPM). The core idea of CAPM, in a nutshell, is a single portfolio of assets or earnings expectations and its systemic risk linear relationship. Market risk factorβis used to measure value. The CAPM considerations can’t spread the risk (market risk) to the requirements of the Securities return, it has assumed that investors can make full diversification of investments can be distributed to spread the risk of (company-specific risk), it is only at this time can’t be dispersed The risks, investors are concerned about the risk and, therefore, only those risks, the risks can be paid.βcoefficient is estimated that the actual use of CAPM model when one of the important part of the group, in actual use, people used single-factor model to estimateβ. Although, strictly speaking, asset pricing model and the value ofβsingle factor model ofβthere is a difference between the value of the former relative to the market as a whole portfolio, and the latter as opposed to a particular market index, but in practice , Since we can’t know the exact combination of market structure, the general market index in place, so we can use single-factor model of the measuredβvalue pricing model to replace the capital value ofβ. Sharpe made since the CAPM model, many of the people CAPM asset pricing models assume that a constraint, that is, assets and earnings expectations of risk assets is a linear relationship. If Sharpe (1964) and Lintner (1965) the conditions put forward by the CAPM model on the assumption that the conditions of assets and earnings expectations of the market portfolio risk premium (minus the risk-free income) is a linear relationship, which is a direct factor of the assets ofβ, Have assets of the portfolio and market conditions covariance portfolio and market conditions for the variance ratio.βcoefficient as input parameters, in theory, should be the next phase of theβvalues. However,βcoefficient is also unknown parameters, the market can’t be directly observed only in the past period of the estimated data for later measurement of value. This approach also implied in fact an important assumption that the coefficientβa certain period of time is completely stable. If the historical data of theβcoefficient estimate does not have good stability, it can’t be used as the next phaseβcoefficient is estimated that an effective, CAPM model in practice will be severely limited. At the same time, in the analysis of the securities and investment management, the systemic risk in advance of the forecast is more important than ex post estimate, and the ability to accurately predict the future of theβcoefficient, the key is to use historical data are estimated from the coefficientβis a certain Stability. Therefore,βfactor is the stability of the research has highlighted the theoretical and practical significance, many scholars recognize the importance of the issue, they have a variety of methods to test the stability of the coefficientsβ,βcoefficient analysis of changes in the characteristics. Some scholars put forward a "time-varying coefficientsβ" (time-varying beta) concept, they used some of the dynamic approach to the study and the estimated time-varying coefficientsβof the positive changes in the characteristics of the study results show that,βin the long term will not be a constant. Since the Japanese factor is not completely stable fixed parameters, people need to know more once factor in the time series on the changes in the characteristics that if theβcoefficient of a certain change in the law, then theβcoefficient on a certain degree of predictability.In this paper, the use of the 4 models to estimate the coefficientsβ, are estimated to use residual conditions CAPM model, the standard deviation of the use of the product is estimated that the conditions CAPM model, as well as multi-GARCH model based on the conditions of CAPM model, in the multi-GARCH model, the side Poor play a core of the matrix, the matrix is used to describe the dynamic characteristics of the fluctuations and multi-GARCH model of the general classification are based on the other side of the poor matrix different set of division. VEC model of a single model GARCH extended to the vector form. This is a very direct expansion, but there are a lot of problems. Diagonal-VEC model made only rely on its own first-order lag and of the first order lag value. Variance that is only dependent on each of the past residual square, then only covariance and cross-term residual value related to the past. BEKK model by cross-term and a common identity within the limit, greatly simplifies the need to estimate the parameters. CCC model in the correlation coefficient fixed under the assumption that the correlation coefficient matrix of the maximum likelihood estimator correlation coefficient equal to the sample matrix. As long as the sample matrix positive correlation, covariance matrix will remain positive. This correlation coefficient matrix can be excluded from the likelihood function, can make the likelihood function can be easily optimized. DCC-MVGARCH model and its estimated that in order to better study the fluctuations in the number of time series, the expansion of the CC model, so that time-varying correlation coefficient matrix. Than the previous model relatively thrifty, has a good advantage of the calculation can be used to estimate the large-scale correlation coefficient matrix.In this paper, data, risk-free interest rate announced by the People’s Bank of China adopted the one-year deposit interest rate. The study used a large number of domestic commercial banks deposit interest rates as a risk-free interest rates. This consideration is based on China’s banking system dominated by state-owned commercial banks, the smaller the risk of default. And any individuals and enterprises can be taken to a bank, there is no question of market segmentation. China’s short-term bond market and a lack of market transactions, subject to a lot of debt, so that the domestic risk-free interest rate of bank deposit interest rates generally, in this article. Based on one-year bank deposit rate for conversion, calculated on interest rates and the market as a risk-free interest rates. Market yield Shanghai and Shenzhen 300 index of the selected rate of return in place of. In this paper, taking into account the object of study for the Shanghai and Shenzhen A shares, so the choice to select markets in Shanghai and Shenzhen 300 Index index. The portfolio yield on May 31, 2006’s stock market value as the standard, according to the Shanghai and Shenzhen stock sorting market size, and divided into 5 groups from each division within the market value of randomly selected 10 A stock portfolio, and the use of Section 5 of this portfolio of transaction data on the rate of return to form as a sequence of our R_it.Compare this article we discussed the estimation of 4, we can see that the first estimates for various methods is estimated by the results of the comparison is rough. Covariance constant assumption obviously can not be given the time-varying coefficientsβresearch good results, and will covariance as a residual product of a process of regression since the method results achieved better results, We have also noted that the estimated results of the model, the residual presence of the square from correlation. We therefore be extended so that the portfolio yield is also subject to a process of ARCH. In this paper, the latter two as it should be said that there have a better sense for information, guidance can be used in the actual analysis of theβ. But the focus of the two methods still have some differences, and a third on a single method can yield a good combination of different periods reflect the different volatility, and the fourth method can not only reflect the different combinations betweenβThe coefficient of comparison, but also in value, we can also be seen with relatively close to the true value ofβ. But we also noticed that in many cases, a portfolio of significant regression coefficient is very low, that is, the larger the market value of the portfolio’s return to the results were not good enough. This may be due to larger market shares in more yield on the extent of the company’s own situation, being a relatively small impact on the market.

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