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GMJACS, Spring 2022, Volume 12(1)
Global Management Journal for Academic & corporate Studies (GMJACS)
Spring 2022, Vol 12 No. 1, PP. 130-140
(Electronic) Copyright 2022 – Global Management Journal for Academic &
Corporate Studies
Published by Bahria Business School, Bahria University Karachi Campus
POST-COVID-19 VOLATILITY OF EXCHANGE RATE RETURNS
A CASE STUDY OF PAKISTAN
Anum Hayat1, Marium Mazhar2, Urooj Aijaz3, Dr.Saghir Pervaiz Ghauri4, Kishwer Sultana Lodhi5
Corresponding Author: Urooj Aijaz6
ABSTRACT
The purpose of the study is to forecast the volatility for returns of the exchange rate of Pakistan
concerning US dollars along with the impact of covid-19 so that we can find out the feasibility of holding
this asset along with the risk and returns associated with it. For this purpose daily data has been taken
from the State bank of Pakistan on a period from February 01, 2001, to June 30, 2021, where covid-19
is used as a dummy variable. Furthermore, in methodology, we applied GARCH models after finding
the presence of the ARCH effect which is at ARCH (6) in the series. It is found in all GARCH models
that the past volatility of the exchange rate returns has a statistically significant influence on the current
volatility of the exchange rate means there is time-varying and time-correlated volatility associated with
exchange rate returns. According to GARCH-M, GARCH-M (variance) (1,1) and GARCH-M (SD) (1,1)
results it is concluded that average returns of exchange rate are small but significant and there is no
risk factor associated with exchange rate returns but the past square residual terms have a significant
impact on risk volatility. Furthermore, Both T-GARCH and E- GARCH depicts that the impact of covid-
19, which is bad news, although has a significant impact but its magnitude has a lesser influence on
exchange rate volatility than the good news.
Keywords: Exchange rate, covid-19, GARCH model, volatility, Pakistan
JEL classification codes: F31, O16
1 Faculty JUW
2 Faculty JUW
3 Ph.D. Scholar JUW
4 HoD Dept, of Economics, JUW
5 Ph.D. Scholar JUW
INTRODUCTION:
Traditionally, Volatility models are used to
determine the economic health of any country
for portfolio allocation and risk management. In
the case of risk management analysis exchange
rate volatility (ERV) is the major determinant,
which is noticeable for the investors, as it
impacts local and foreign investment, while
GMJACS, Spring 2022, Volume 12(1)
policymakers monitor ERV to formulate
appropriate fiscal and monetary policies.
Volatility in ER is equally important for both
exporting and importing nations, as it catalyses
trade in both directions (positive and negative).
According to Taylor (2005), it is observed that
ERV is sometimes better for the financial
market if it deals with hedging, risk
management, etc. Sometimes, it affects the
long-term policies of the state. It is also evident
that investors’ confidence to invest in the
market in some countries is negatively related
to ERV, which is the main reason behind the
use of the volatility model. This paper is an
attempt to examine the volatile behaviour of ER
before and during the pandemic of COVID-19
which originates from China but jolt the global
financial market. It is an already known fact
that the pandemic leaves its harmful effects on
every facet of life including ER market and
being the worldwide accepted currency ERV of
Rupee versus Dollar always leaves strong
footprints on Pakistan’s economy. This paper
attempts to evaluate the unprecedented effects
of ERV in Pakistan. The study hypothesized
that the Pandemic has a strong impact on the
performance of the stock exchange and is one
of the major causes of ERV during the COVID.
This paper evaluated the performance and
volatility of ER by using the high-frequency
daily data and forecasted by GARCH family
model including M-GARCH, T-GARCH, and
E-GARCH.
LITERATURE REVIEW:
Accuracy in high-frequency data is required for
future values and improved forecasting results.
Therefore it is of utmost importance to analyse
the volatility of the exchange rate as it affects
the macroeconomic variables of a country like
international trade flows, the flow of capital,
etc. Due to these reasons researchers,
governments and policymakers are keen to
analyse and inspect the volatile behaviour to
control and manage the exchange rate risks
involved in the growth of the economy.
Different researchers have examined the
volatility on different exchange rates. Jarque-
Bera test rejects the null hypothesis proving
normality does not exist, the curve was found to
be leptokurtic and therefore different Arch-
Garch type models are applied (Ravanoglu
2020, (Mohsin et al., 2019).,(Hung, 2018).
Most Recently (Ravanoglu, 2020) investigated
the model for the nominal exchange rate of
Turkey by the ARCH and GARCH
methodology. The data has been collected from
2002-2017. The Garch (1,2) model is most
appropriate. Although the effects of variance
are symmetric in exchange rate data volatility
clusters can be found.
(Mohsin et al., 2019), Showed the exchange
rate uncertainty against U.S. dollar in Pakistan.
The daily data from January 2005 to December
2018 of volatility exchange rate was taken for
using GARCH family models. The symmetric
and asymmetric effects were checked in
exchange rate of Pakistan against dollar. The
uncertain and high volatility conditions of
exchange rate were observed in this research. It
is also observed that, volatile behaviour of
GMJACS, Spring 2022, Volume 12(1)
dollar against Pakistani Rupee is the main
reason behind high risk factor of erosion in
capital market of Pakistan. (Sharma & Pal,
2019), in their study, took 73 Commodities
from 2013 to 2016 in India for testing the
relationship between exchange rate and imports
of these commodities. The heteroscedasticity
and time series model were used for testing this
relationship. All the imports of the commodities
declined in long run by 12%.In short run the
agriculture sector was more sensitive than
manufacturers sector.
((Abdullah et al., 2017) and (Dung, 2018))
analysed the volatility of exchange rates by
assuming student’s- terror assumptions and
found to have better results compared to normal
or Gaussian method as student’s t test captures
the non-normality of the series involved.
Further the researchers’ results depict a general
view where the curve had leptokurtic curve.
AR, ARMA, GARCH (1, 1) and GARCH (1, 2)
models are used. Trade in both cases was found
to be significant and therefore the impact of
these rates had serious impacts on growth.
Additionally (Epaphra, 2017) explored the
exchange rate of Tanzania on daily basis from
2009-2015.Volatility clustering, non-
normality, non-stationarity and serial
correlations are all found in the series therefore
ARCH, GARCH and EGARCH models were
used. It was also found that exchange rate
volatility is dependent on the volatility on its
lag. Since asymmetric volatility is estimated it
can be concluded that compared to negative
shocks the positive shocks suggested next
period conditional variance.
(Olowe, 2009) investigated Nairo’s exchange
rate on fixed and floating regimes both before
and after deregulation of currency. He found to
have the same results for both regimes. Results
of the asymmetric models were found to reject
any leverage effects. The persistent high
volatility that was found in the fixed exchange
rate was considered due to import dependence
on Nigerian economy.
Both symmetric and asymmetric models are
considered by (Abdalla, 2012) of volatility
clustering and leverage effects for nineteen
Arab countries. The empirical results show that
the volatility is explosive for seven while
persistent for ten countries. Leverage effects
were found in all of them except for Jordanian
dinar. In conclusion it was found that the Garch
model is appropriate for exchange rate models
for the nineteen Arab countries.
(Thorlie et al., 2012) explore the volatility
model including ARMA, GARCH and
asymmetric GARCH in Sierra Leone. The
parameters of the model were found to be
statistically significant. It was further found that
no serial correlation exists in the series of
exchange rate return. Furthermore Arch effect
does not have a significant appearance in the
return series neither is the variance equation
correctly specified.
The US exchange rate volatility due to the
impact of Covid-19 cases and related deaths is
investigated using a GARCH (1, 1) model in
this paper. According to the findings, a boost in
GMJACS, Spring 2022, Volume 12(1)
the number of cases and deaths in the United
States has a positive impact on the USD/EUR,
USD/Yuan, and USD/LivreSterling. While In
another paper by (Omari et al., 2017), both
symmetric and asymmetric GARCH models
are used. The paper finds strong evidence that
the aforementioned models can characterize
daily returns. In the residuals series, the
USD/KES data showed a significant departure
from normality and the presence of conditional
heteroscedasticity.
METHODOLOGY:
Daily data for variable exchange rate has been
taken from State bank of Pakistan which spans
from Tue, Jan 02, 2001, to Wed, Jun 30, 2021.
Here covid-19 is used as a dummy variable.
Therefore, in this research paper our data set
consists of total 5535 observations.
In this research study we tried to find out the
risk factor and time varying volatility
associated with exchange rate returns with
respect to US dollars. For this purpose, we used
GARCH model (Bollerslev, 1986) by using
following steps:
Step 1: Generation of exchange rate returns
series.
Step 2: Identification of volatility clustering by
using conditional variance graph or simple
graph of the series.
Step 3: ARCH effect has been checked by
applying hetroscedasticity test ARCH of OLS
method. The lag of ARCH effect helps in opting
between ARCH and GARCH method.
Step 4: Estimation of GARCH method to find
out the risk factor and time varying volatility
associated with exchange rate returns.
Step 5: Forecasting of the series has been done
by using both dynamic and static method.
Step 6: Finally, we have applied normality test
by using histogram.
The table 1 above summarizes the descriptive
information of returns on exchange rate
volatility for 20 years on daily basis. The mean
of log is 86.082. Standard deviation shows
returns of exchange rate deviation by 1.04 from
its mean. Since the skewness is a little greater
than 1 the distribution can be concluded as
skewed. Kurtosis is greater than 3 this means
the series is leptokurtic depicting that the curve
has flatter tails and is wider therefore it is
portrayed that impact of Covid-19 is extensive
on exchange rate returns. The Probability of
Jarque-Bera test <0.05 which means the
distribution is normal.
Mean 86.08
Median 84.10
Maximum 168.20
Minimum 57.19
Std. Dev. 28.29
Skewness 1.04
Kurtosis 3.58
Jarque-Bera 1037.64
Probability 0.000
Observations 5347
Table 1: Descriptive Statistics
GMJACS, Spring 2022, Volume 12(1)
Volatility Clustering:.
Identification of the ARCH effect in the above
graph takes place by recognizing the clusters. It
is the time when large changes are assisted with
additional larger change and smaller changes
are assisted with additional smaller changes.
While conditional Variance acts in different
phases of time series model and corresponds
with actual plot of the given series.
Here it is observed from 2000-2002; 2008-2010
and 2019-2020 clusters are present. These are
the time periods where exchange rate volatility
is very frequent.
Table 2 shows results of ADF unit root test for
stationarity according to which p-value of ADF
test is less than 0.05 that means null hypothesis
mentioned in table 3 should be rejected
indicating exchange rate returns are stationary
at 5% level of confidence interval.
The ARCH test of heteroscedasticity results
shown in table 3 stated that p-value of observed
R-squared is statistically significant so, the null
hypothesis mentioned in table 2 has been
rejected indicating that there is ARCH effect at
lag 1,3 and 6 which means there is a
significance heteroscedasticity at 5%
confidence level, so if we apply ARCH model
at lag six it will increase coefficients and model
will no longer be parsimonious that is why
GARCH (1,1) model has been chosen because
it is parsimonious model as compare to ARCH
(6) model.
General equation of GARCH model:
This model can be generalized to a GARCH (p,
q) model in which there are p lagged terms of
the conditional variance and q lagged terms of
squared error term:
T-STATS PROBABLITY
Augmented Dickey-Fuller test
statistic
-45.875 0.0001
Test critical value s:
1% level -3.431
5% level -2.862
10% level -2.567
Table 2: ADF Unit Root Test for Exchange Rate Returns
H0: there is a unit root / the series is non-stationary
At Confidence interval: 5%
Heteroskedasticity Test: ARCH lag 1 lag 3 lag 6
F-statistic 84.48 45.9 23.23
Obs*R-squared 83.23 134.45 136.17
Prob. F(1,5530) 0.000 0.000 0.000
Prob. Chi-Square(1) 0.000 0.000 0.000
Table 3: ARCH Effect
HO: No heteroscedasticity
Confidence interval: at 5%
GMJACS, Spring 2022, Volume 12(1)
The risk behaviour of the exchange rate return
and volatility is estimated using the GARCH-M
model, in which the conditional mean depends
on its own conditional because of variance if
the risk is captured by the volatility or by the
conditional variance, and then the conditional
variance may enter the conditional mean
function of series (Engle, 1993). In Table 4
results of GARCH –M model depicts that there
are two equations first, the mean equation
which explains the average returns associated
with exchange rate returns which is exhibits by
coefficient of constant term C and in this model
average returns of exchange rate are small but
significant, whereas the R-LEXCH (-1) term
exhibits how previous exchange rates influence
the current exchange rate. While the impact of
covid-19 is statistically significant at 5%
confidence level. Second the variance equation
demonstrates impact of past square residual
term on risk volatility therefore according to the
results both the past square residual term
(RESID (-1) ^2 ) term and past conditional
variance term (GARCH (-1)) are statistically
significant at 5 %, indicating that past square
residual terms have a significant impact on risk
volatility. However, the GARCH (-1)
signifying that past volatility of the exchange
rate returns has a statistically significant
influence on current volatility of exchange rate.
Hence its is concluded that there is no risk
factor associated with exchange rate returns but
there is time varying and time correlated
volatility.
The results of GARCH-M (variance) model in
Table 5 describe that the risk factor/conditional
variance (GARCH) associated with Pakistan
exchange rate with respect to US is not
statistically significant implying that the
previous day's exchange rate does not influence
the current day's exchange rate or the mean
exchange rate returns are not affected by the
risk factor. However average returns of
exchange rate are small but statistically
significant. Second the variance equation
demonstrates impact of past square residual
term on risk volatility therefore according to the
results both the past square residual term and
past conditional variance term are statistically
significant at 5 %, indicating that past square
residual terms have a significant impact on risk
volatility. However, the GARCH (-1)
signifying that past volatility of the exchange
COEFFICIENT PROBABLITY
GARCH -0.962 0.900
C 0.000 0.005
R_LEXCH(-1) 0.287 0.000
COVID_19 0.001 0.000
VARIANCE EQUATION
C 8.03E-07 0.000
RESID(-1)^2 0.298 0.000
GARCH(-1) 0.611 0.000
At Confidence interval: 5%
Table 4: Results of GARCH-M (1,1)
COEFFICIENT PROBABLITY
GARCH -0.963 0.9
C 0.000 0.005
R_LEXCH(-1) 0.287 0.000
COVID_19 0.001 0.000
C 8.03E-07 0.000
RESID(-1)^2 0.298 0.000
GARCH(-1) 0.611 0.000
VARIANCE EQUATION
At Confidence interval: 5%
Table 5: Res ults of GARCH-M (Variance) (1,1)
GMJACS, Spring 2022, Volume 12(1)
rate returns has a statistically significant
influence on current volatility of exchange rate.
Hence its is concluded that there is no risk
factor associated with exchange rate returns but
there is time varying and time correlated
volatility.
The risk behaviour of the exchange rate return
and volatility is estimated using the GARCH-M
model with standard deviation, this model used
to capture the risk by with standard deviation of
the series instead of variance. The results of
GARCH-M (Standard Deviation) model in
Table 6 describe that GARCH M (SD) depicts
same results as of GARCH M model but more
significantly as significance of its variance term
of mean equation is improved. Therefore,
according to GARCH M (SD) there is no risk
factor associated with exchange rate returns but
there is time varying and time correlated
volatility.
Furthermore the risk behaviour of the exchange
rate return and volatility is estimated using the
T-GARCH model, to check the impact of
covid-19 since these types of news or shocks
has significant impact on assets and decisions
of assets holders. The main target of the
TGARCH model is to capture asymmetries in
term of negative (bad news) and positive shocks
(good news) (R. Rabemananjara, 1993). This
model also includes two equations. The results
of mean equation T-GARCH model in Table 7
describe that the risk factor/conditional
variance (GARCH) associated with Pakistan
exchange rate with respect to US is statistically
significant implying that the previous day's
exchange rate does influence the current day's
exchange rate or the mean exchange rate returns
are affected by the risk factor. The sign for the
coefficient of covid-19 is negative which means
it is bad news for investors. According to the
results of variance equation both the past square
residual term (RESID (-1) ^2 ) term and past
conditional variance term are statistically
significant at 5 %, indicating that past square
residual terms have a significant impact on risk
volatility. However, the GARCH (-1)
signifying that past volatility of the exchange
rate returns has a statistically significant
influence on current volatility of exchange rate.
While the coefficient of the asymmetric term
(RESID (-1) ^2*(RESID(-1)<0) is negative and
statistically significant at 5% level of
significance which signify that for the exchange
rate there are symmetries in the news.
Moreover, due to the negative asymmetric term
(b1+γ1=0.164) < (b1=0.350) therefore for this
asset bad news has lesser effect on the volatility
than good news.
COEFFICIENT PROBABLITY
At SQRT(GARCH) 0.014 0.812
C 9.54E-05 0.346
R_LEXCH(-1) 0.289 0.000
COVID_19 0.001 0.000
C 8.14E-07 0.000
RESID(-1)^2 0.297 0.000
GARCH(-1) 0.611 0.000
At Confidence intervel : 5%
VARIANCE EQUATION
Table 6: Results of GARCH-M (1, 1) (Standard Deviation)
COEFFICIENT PROBABLITY
C 0.0001 0.0001
R_LEXCH(-1) 0.297 0.000
COVID_19 -0.0004 0.000
VARIANCE EQUATION
C 7.37E-07 0.000
RESID(-1)^2 0.35 0.000
RESID(-1)^2*(RESID(-1)<0) -0.186 0.000
GARCH(-1) 0.637 0.000
At Confidence intervel : 5%
Table 7: Results of T-GARCH (1,1)
GMJACS, Spring 2022, Volume 12(1)
The E-GARCH model is an asymmetric
GARCH model used to record the leverage
effects of disturbing events. E-GARCH model
directs conditional hetroscedasticity. The E-
GARCH variables displayed in the Table 8
exhibit that variable are significant at 5% level
in the variance equation. The constant c is
significant at 5%. C (5) the ARCH term has a
p-value of 0.000 therefore the magnitude of
covid-19 has a significant impact on the
volatility of exchange rate. C (5) also shows the
larger the magnitude of covid-19 to the variance
larger the volatility. C (6) is also significant as
p value is 0.013 at 5% level so an agreement
can be devised that the sign of covid-19
influences the volatility of exchange rate. The
positive sign of C (6) also specify that bad news
will lower the volatility higher than good news
of the same size. C (7) is also significant as its
probability is 0.000.
Table 9 depicts dynamic and static forecasting
and stability of volatility for GARCH models.
According to dynamic forecasting volatility is
steady, as it is evident that volatility lies
between the standard error bands, the dynamic
approach assesses forecasting for periods after
the initial sample period, using the past fitted
values from the lags of the variable that is
dependent. While the static analysis uses the
true values of regress and variable. Therefore,
it is safe for investors and asset holder to hold
this asset (exchange rate).
The above Table 10 depicted the result of
histogram normality test of the GARCH models
indicates that the null hypothesis of Jarque-bera
is rejected and shows that there is no normality
as p-value is less than 0.05. So, it can be
concluded that exchange rate of dollar is
volatile.
CONCLUSION:
In this research study GARCH symmetric and
asymmetric models GARCH-M (1,1),
COEFFICIENT PROBABLITY
C 0.0002 0.000
R_LEXCH(-1) 0.279 0.000
COVID_19 0.0007 0.000
VARIANCE EQUATION
C(4) -2.871 0.000
C(5) 0.445 0.000
C(6) 0.019 0.0134
C(7) 0.787 0.000
At Confidence intervel : 5%
Table 8: Res ults of E-GARCH (1,1)
MODELS JARQUE-BERA PROBABLITY
GARCH M (1,1) 34825386 0.000
GARCH M (1,1) (Standard
Deviation)
32477848 0.000
T-GARCH (1,1) 35240246 0.000
E-GARCH (1,1) 33412654 0.000
At Confidence intervel : 5%
Table 10: Results Normality test : Histogram
GMJACS, Spring 2022, Volume 12(1)
GARCH-M (SD) (1,1), T-GARCH and E-
GARCH have been used to analyse the
volatility and risk associated with daily
exchange rate returns of Pakistani rupees
against US dollars. According to GARCH-M
(1,1) and GARCH-M (SD) (1,1) results it is
concluded that GARCH term of mean equation
is statistically insignificant which means there
is no risk factor associated with exchange rate
returns but the variance equation states that the
past square residual term (RESID (-1) ^2 ) term
and past conditional variance term are
statistically significant at 5 %, indicating that
past square residual terms have a significant
impact on risk volatility. However, the GARCH
(-1) signifying that past volatility of the
exchange rate returns has a statistically
significant influence on current volatility of
exchange rate means there is time varying and
time correlated volatility.
While asymmetric model T-GARCH shows
that all coefficients of the model are statistically
significant at 5% level of confidence which
describe that the risk factor/conditional
variance (GARCH) is statistically significant
implying that the previous day's exchange rate
does influence the current day's exchange rate.
The sign for the coefficient of covid-19 is
negative which means it is the bad news for
investors. According to the results of variance
equation indicate that past square residual terms
have a significant impact on risk volatility.
However, the GARCH (-1) signifying that past
volatility of the exchange rate returns has a
statistically significant influence on current
volatility of exchange rate. While the
coefficient of the asymmetric term (RESID (-1)
^2*(RESID (-1)<0) is negative which signify
that for the exchange rate there are symmetries
in the news. Moreover, due to the negative
asymmetric term (b1+γ1=0.164) < (b1=0.350)
therefore for this asset bad news has lesser
effect on the volatility than good news.
However another asymmetric model E-
GARCH shows c (4) is ω which is the constant,
c(5) is the arch term is positive and significant,
It depicts the magnitude of covid-19 has on
exchange rate returns. In our case it shows that
α is positive and significant which depicts that
larger the magnitude of Covid -19 larger will be
the volatility. The coefficient of leverage term
is also positive and significant representing that
since Covid -19 is considered a negative shock
it will affect the future volatility of exchange
rate returns less than a positive shock.
Therefore covid-19 is statistically significant
which is depicted by probability which is less
than 5% but all models indicate that the
magnitude of covid-19 has an insignificant
impact on the volatility of exchange rate.
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