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A GARCH analysis of the excess returns on the FTSE All Share Index
The objectives of this seminar are to:
• Test for ARCH effects in a series of excess returns on the FTSE All 代写留学生论文Share Index (excess market returns).
• Estimate and test a GARCH model for the excess market returns.
• Test for leverage effects and estimate asymmetric GARCH models for the excess market returns.
• Test for a time varying risk premium in the excess market returns using different versions of GARCH-in-Mean (GARCH-M) models.
The learning outcomes will be to develop your understanding of:
• Testing for ARCH effects in Eviews.
• Estimating GARCH models in Eviews.
• Misspecification testing of GARCH models and their application in Eviews.
• GARCH models which allow for an asymmetric response of volatility to past shocks.
• GARCH models which incorporate a time varying risk premium in the conditional mean (GARCH-M).
• Estimating and testing asymmetric GARCH and GARCH-M models in Eviews.
The workfile for this analysis is ftse_all_sem5.wf1 which contains daily data on the FTSE All Share Index and the 3-month Treasury Bill rate (converted to a daily rate) for the period 1st January 2003 – 19th January 2006.
1. Background and overview
The basic GARCH model for the excess market returns can be written as follows:
()1,0~,212102,NIDvvrrtttttttttftm−−++==+=−βσαεασσεεμ
The first equation is the conditional mean equation. We will begin the analysis by assuming a constant risk premium ()μand relax this assumption subsequently. The other three equations describe the conditional variance.
In particular, in the above specification, we’ve assumed that:
i) The conditional variance follows a GARCH(1,1) model (a common assumption in empirical finance).
ii) The conditional error distribution is Gaussian:
()()21,0~1,0~ttttNNIDvσε−Ω⇒
As always, we need to test whether these assumptions relating to the statistical model hold for our data i.e., we need to carry out misspecification testing. For the GARCH model this will involve:
• Testing whether the NID assumption holds for the standardized residuals.
• Estimating and testing extensions to the basic GARCH model.
We will go through the tests on the standardized residuals below. On the second point, an important extension to the basic GARCH model is to allow for an asymmetric response of volatility to past shocks. Typically volatility may respond more to bad news (negative shocks) than good news (positive shocks) of the same magnitude. In the context of equity returns this asymmetry may be due to leverage effects: negative shocks cause the value of the firm to fall which raises the debt-equity ratio thereby increasing the risk of bankruptcy (debt-equity ratios are a key predictor of the probability of default in credit scoring models).
There are two main models which are useful for modelling asymmetric volatility: Threshold ARCH (TARCH) and Exponential GARCH (EGARCH) (see lecture 6). The asymmetry analysis begins with a general test for asymmetries in volatility called a Sign and Size Bias Test. Then, based on the evidence of this test, we will estimate and test for asymmetries in TARCH and EGARCH models.
The analysis culminates with the estimation of a time-varying risk premium model for the excess market returns. Applying CAPM to the market portfoli