related to the macroeconomy like ‘‘recession’’. It seems plausible that this is caused by
private investors getting nervous and subsequently overreacting on the stock market,
leading to an increase in volatility.
To cross-validate our results, we study market data on trades of private and
institutional investors from a stock exchange in Section 11.3.2. The special feature of
this dataset is that it entailsalltransactions on the stock market (in Estonia), thus we
have no selection bias in the data. We demonstrate that at times where many private
investors trade, volatility is higher, which confirms our theory.
11.2 What causes volatility asymmetry?
Increased volatility while market prices drop is referred to as volatility asymmetry.
The current section summarizes some of the results of Talpsepp and Rieger (2009)
on measuring and empirically investigating various causes of volatility asymmetry.
11.2.1 Measuring volatility asymmetry
There are a number of approaches to measuring volatility asymmetry. We can derive the
asymmetry from different types of volatility estimation models. A direct approach
compares volatility of up and down markets (which has its drawback when linking
different market periods to corresponding volatility). We favored using more of an ad
hoc model that already incorporates the asymmetry estimation in its original setup. The
choice also depended on data availability and an exact research focus.
Although the current literature on volatility (see, e.g., Andersen, Bollerslev, and
Diebold, 2003) has shifted to using realized volatility from intraday returns, such data
are not available for all markets and longer time periods. As we study a wide range of
markets for a long time period, we use the asymmetric power GARCH (APARCH)
model of Ding, Granger, and Engle (1993) with asymmetrict-distribution. There is a
wide choice of GARCH-type models (see, e.g., Poon and Granger, 2003) that could be
used for the task when using daily returns. But as the APARCH model contains an
asymmetry parameter it is one of the most natural choices for this task. Additionally,
APARCH proved to deliver very accurate VAR forecasts compared with other models,
especially when using asymmetrict-distribution.
We used the following specification of the APARCH model:
t¼aðÞjj"t 1
"t 1 þ t 1 ; ð 11 : 1 Þwhere , , , andare the APARCH parameters to be estimated. We are mainly
interested in the asymmetry parameter. It reflects volatility asymmetry and takes
values from1 to 1. If there were no asymmetry (meaning that volatility is the same
for down-market periods and up-market periods) the estimated would be zero. A
positive value of means that volatility is higher in bear markets and that is exactly what
results show for almost all countries most of the time.
Our choice of the APARCH(1,1) model is motivated by an effort to obtain volatility
asymmetry estimates with higher statistical reliability for a large number of countries
dictated by the data frequency available. We tested various combinations or different
ARMA and APARCH orders with our data. Based on the results the used model proved
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