1. Quantitative Methods for Financial Markets (ETF3300)
Financial Econometrics (ETF9300)
Semester 2, 2008
Tutorial Week 13
Modelling Stock Return Volatility
We use the data set from week 12 tutorial “stockprices.wf1” containing daily stock
prices of Hong Kong, Japan (jp) and Singapore (sg) markets from 1990 to 2005.
We will further examine the volatility of stock returns from Singaporean market
answering the questions below. The cases of Hong Kong and Japanese markets are
left as your own exercise.
1. Estimate the Threshold GARCH(1,1) model and discuss the nature of volatility in
relation to asymmetry of volatility
2. Estimate a GARCH(1,1)-in-mean model. Is there any evidence of the return-risk
relationship
3. As further extensions, estimate TGARCH(1,1)-in-mean. Comment on the result in
relation to asymmetry and return-risk relationship.

2. EVIEWS Instructions
To estimate a Threshold GARCH(1,1) or TGARCH(1,1) model.
Choose the GARCH/TARCH model with the threshold value 1. The threshold value
is usually set to one, although it can take a higher value. Click OK, then you will see
Again note that the form of the variance equation estimated is given above the result
table. All coefficients are statistically significant including the one which is related to
the leverage effect.
The GARCH-in-mean model specifies that the volatility (or risk) which follows a
GARCH model appears in the return equation as an explanatory variable. There are
three possible forms of GARCH-in-mean model that EVIEWS can estimate,

3. depending on the form of the volatility in the return equation. It can appear as the
standard deviation, variance or natural log of the variance. In many cases, the choice
is purely statistical, as there is no apparent economic reasons as to which form is the
most appropriate.
The window below is for the estimation of GARCH(1,1) model. The field ARCH-M
was 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, then
you will see
You can see that the return equation now has @SQRT(GARCH) term, which means
that the time-varying standard deviation from GARCH(1,1) estimation is included in
the return equation. The coefficient of @SQRT(GARCH) is insignificant, indicating
that 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

4. examine whether these alternative measures of risk are related significantly with
return.
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 statistically
significant 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 with
different forms of risk in return equation. This means that that there are many possible
forms and specifications, but you can choose the final model based on a number of
factors including statistical significance of coefficients, correctness of the signs of
estimated coefficients, and the use of information criterion such as AIC or BIC.