Quantitative Methods for Financial Markets (ETF3300) Financial Econometrics (ETF9300) Semester 2, 2008 Tutorial Week 13 Modelling Stock Return VolatilityWe use the data set from week 12 tutorial “stockprices.wf1” containing daily stockprices of Hong Kong, Japan (jp) and Singapore (sg) markets from 1990 to 2005.We will further examine the volatility of stock returns from Singaporean marketanswering the questions below. The cases of Hong Kong and Japanese markets areleft as your own exercise.1. Estimate the Threshold GARCH(1,1) model and discuss the nature of volatility in relation to asymmetry of volatility2. Estimate a GARCH(1,1)-in-mean model. Is there any evidence of the return-risk relationship3. As further extensions, estimate TGARCH(1,1)-in-mean. Comment on the result in relation to asymmetry and return-risk relationship.
EVIEWS InstructionsTo estimate a Threshold GARCH(1,1) or TGARCH(1,1) model.Choose the GARCH/TARCH model with the threshold value 1. The threshold valueis usually set to one, although it can take a higher value. Click OK, then you will seeAgain note that the form of the variance equation estimated is given above the resulttable. All coefficients are statistically significant including the one which is related tothe leverage effect.The GARCH-in-mean model specifies that the volatility (or risk) which follows aGARCH model appears in the return equation as an explanatory variable. There arethree possible forms of GARCH-in-mean model that EVIEWS can estimate,
depending on the form of the volatility in the return equation. It can appear as thestandard deviation, variance or natural log of the variance. In many cases, the choiceis purely statistical, as there is no apparent economic reasons as to which form is themost appropriate.The window below is for the estimation of GARCH(1,1) model. The field ARCH-Mwas set to None so far. To estimate a GARCH-in-mean model,choose one of the options in ARCH-M field, say Standard Deviation. Click OK, thenyou will seeYou can see that the return equation now has @SQRT(GARCH) term, which meansthat the time-varying standard deviation from GARCH(1,1) estimation is included inthe return equation. The coefficient of @SQRT(GARCH) is insignificant, indicatingthat there is no evidence of return-risk relationship in the case of Singaporean market.You may try to use variance or log of variance instead of standard deviation to
examine whether these alternative measures of risk are related significantly withreturn.The case of variance in the return equation shows the following result:The coefficient of variance in the equation is found to be positive and statisticallysignificant at 5% level, indicating the presence of return-risk relationship or time-varying risk premium.You can try many other combinations such as TGARCH(1,1)-in-mean models withdifferent forms of risk in return equation. This means that that there are many possibleforms and specifications, but you can choose the final model based on a number offactors including statistical significance of coefficients, correctness of the signs ofestimated coefficients, and the use of information criterion such as AIC or BIC.