Syntax Literate: Jurnal Ilmiah Indonesia
p�ISSN: 2541-0849 e-ISSN: 2548-1398
Vol. 7, No. 11, November 2022
VALUE AT RISK (VAR) AND EXPECTED SHORTFALL (ES) MEASUREMENTS FOR FOREIGN
CURRENCY PORTFOLIO USING EWMA AND GARCH (1,1)
Firly Armanda, Fatwa Aulia, Jodi Surya Gustanto, Jalil Mujib Tan Ismail, Jonatan Halomoan�,
Dianita Fitriani Pogram,
Girindra Chandra Alam, Dewi Hanggraeni
Master of Management students Universitas Indonesia, Jakarta, Indonesia
Faculty of Economics and Business Universitas Indonesia, Universitas
Pertamina
E-mail: dewi.hanggraeni@ui.ac.id
Abstract
This study assesses the Value at Risk (VaR)
and Expected Shortfall (ES) methods in gauging exchange rate risk in PT Telkom
Indonesia Tbk, using historical Bank Indonesia
closing rates USD/IDR and JPY/IDR from January 2022 - December 2022. Results
demonstrate that the ES calculation with Confidence Level (CL) 99%, using the
Exponentially Weighted Moving Average (EWMA) and Generalized Autoregressive
Conditional Heteroskedasticity (1,1) (GARCH (1,1))
models, provides conservative measures for USD and JPY exposures. These
measures, reflecting the highest potential losses, are consistent with
management's cautious approach towards currency exchange market risk.
Furthermore, based on the ES calculations in this study, it is suggested that
PT Telkom Indonesia retains a minimum deposit of 30,000,000,000 IDR, equivalent
to roughly 1.007% of its short-term liabilities, which is substantially below
the stipulated 25% minimum deposit to efficiently navigate potential foreign
exchange risks.
Keywords: Value at Risk, Estimated Shortfall, EWMA, GARCH, Telkom
Indonesia, Market Risk.
As
Indonesia's largest telecommunications company, PT Telkom Indonesia Tbk operates in multiple currencies and faces market risk,
including foreign exchange rate fluctuations (Pristiwantiyasih
& Setyawan, 2020). The company's risk management
program aims to minimize potential losses resulting from currency and interest
rate fluctuations (Settembre-Blundo
et al., 2021). Based on the 2022 audited
financial report, PT Telkom Indonesia Tbk's total
liabilities in foreign currencies amount to IDR 3,899 billion or 3.10% of total
liabilities. This shows that transactions in foreign currencies, especially
liabilities, are not Telkom's core business considering the small portion (Mburu
& Rotich, 2017). However, with the covid pandemic and the anticipation of the economic crisis,
it is necessary to mitigate market risk for liabilities in foreign currencies,
especially short-term liabilities (Devi
et al., 2020).
PT
Telkom Indonesia Tbk's market risk management is
implemented to minimize the loss of short-term liabilities in foreign currencies,
as a result of exchange rate movements (Jatiningtyas
& Iradianty, 2016). The form of risk mitigation is in
the form of placement of time deposits and hedging for 3-12 months of at least
25% of total short-term liabilities in foreign currency, in anticipation of
fluctuations in foreign currency values during this period (Battilossi,
2020).
Total
short-term liabilities in foreign currencies of PT Telkom Indonesia Tbk in 2022 which consist of trade payables, other
payables, accrued expenses, customer advances, and long-term loans with
maturities of less than one year amounting to USD 163, 54 million; JPY 798.45
million; and other foreign currencies equivalent to USD of USD 15.89 million (Damanik
et al., 2023). In accordance with the implemented
risk management policy, placement of time deposits in foreign currencies is at
least 25% of the foreign currency short-term liabilities, namely USD44.85
million and JPY199.61 million.
This
study analyzes PT Telkom Indonesia Tbk's foreign
currency risk management using Value at Risk (VaR)
models, specifically Exponentially Weighted Moving Average (EWMA) and GARCH
(1,1), based on Malz (2011) [8] financial risk
management framework. PT Telkom's financial strategy prioritizes meeting its
short-term liabilities, which comprise a significant percentage of its total
liabilities. Researchers used data from the 2022 financial report to assess the
company's foreign currency exposure and risk management practices (Chong
et al., 2014).
VaR
has been extensively used in the financial industry to quantify potential
losses associated with financial variables, such as foreign exchange rates on Bredin & Hyde (2014) and Kurita (2013) paper. Both EWMA and GARCH (1,1)
models have been widely applied to estimate VaR for
portfolios with foreign currency exposures (Yasin
et al., 2020). These models capture the
time-varying nature of financial market volatility, which is particularly
relevant for managing foreign currency risk (Yasin
et al., 2020). Malz (2011) provides a comprehensive overview
of risk management models, including EWMA and GARCH (1,1), and their
application in various financial institutions. The present study applies the
Exponentially Weighted Moving Average (EWMA) and GARCH (1,1) models to measure
the VaR of the foreign currency portfolio of PT
Telkom Indonesia Tbk, using the framework discussed
in Financial Risk Management Models, History, and Institutions by Malz (2011). The present study concentrates
exclusively on these market risks, particularly the potential for default due
to foreign exchange rate fluctuations.
Using
2022 financial report data, researchers estimate the VaR
of Telkom Indonesia's foreign currency portfolio with EWMA and GARCH (1,1)
models. The study provides insights into these models' effectiveness in
predicting potential losses and offers valuable information for the company's
risk management efforts, benefiting other companies in similar contexts and
aiding policymakers in promoting effective risk management practices in the
telecommunications industry. Given an annual interest rate of 7% on Telkom
Indonesia's IDR 653 billion fixed-term deposit, the potential losses from
currency fluctuations, calculated using the most conservative values, only
account for about 59.32% of the interest income, indicating that the deposit's
earnings could cover the entire foreign exchange risk and still yield a
surplus.
Applying
EWMA and GARCH (1,1) models to measure the VaR of
Telkom Indonesia's foreign currency portfolio, the study compares their
performance in capturing foreign currency risk dynamics and offers insights for
risk management practitioners in the telecommunication industry. The study
concludes that the EWMA with 99% confidence level (CL) is more conservative
than the GARCH (1,1) method in calculating VaR and ES
for USD exposure. In contrast, for JPY exposure, the GARCH (1,1) method with
99% CL is more conservative than EWMA. The performance of the GARCH (1,1) model
for JPY and the EWMA model for USD was determined through the Kupiec statistical test.
Theoretical Model
Value at Risk�
and Estimated Shortfall
Value
at Risk (VaR) and Expected Shortfall (ES) are
employed to assess potential losses in investments or portfolios. While both
methods focus on quantifying potential losses, their approaches and the
information they offer on risk differ. VaR estimates
the maximum possible loss a portfolio or investment can incur over a specified
time frame and at a certain confidence level. The formula for VaR is:
�������������������.(1)
where μ is the mean return, z
is the z-score corresponding to the chosen confidence level, and σ is the
standard deviation of the returns.
ES,
alternatively referred to as Conditional Value at Risk (CVaR),
calculates the average loss expected in the tail distribution of portfolio
returns beyond a specific confidence level. The formula for ES is:
������������.(2)
where α is the chosen
confidence level, and f(x) is the probability density function of the returns.
In
essence, ES determines the average loss likely to occur in extreme scenarios,
surpassing the VaR threshold (Malz,
2011).
Three primary techniques are
employed for calculating VaR and ES: historical,
parametric, and Monte Carlo simulation methods. The historical method involves
deriving calculations based on the historical data of asset or portfolio
returns. The first step entails determining the VaR
value at the desired confidence level, followed by calculating the average
return worse than the obtained VaR value. This
average value is known as the Expected Shortfall. The parametric method, on the
other hand, presumes that asset or portfolio returns adhere to a specific
distribution (e.g., normal). The initial phase involves selecting the
appropriate distribution, estimating the statistical parameters (mean, standard
deviation), and determining the desired confidence level. Subsequently, the VaR value is determined using the formula mentioned above,
and the ES value is calculated according to the chosen distribution. Lastly,
the Monte Carlo simulation method utilizes random sampling simulations to
generate various scenarios for the returns of owned assets or portfolios. This
technique allows for multiple simulations, producing a range of VaR or ES values. These scenarios can then be averaged to
yield the final result. Jorion (2009) ; McNeil, Frey & Embrechts (2015).
Exponentially Weighted
Moving Average (EWMA)���������
In
VAR estimations, it is usual to assume that logarithmic returns have a normal
distribution with mostly a mean of zero. As a result, the volatility must be evaluated
as the key factor. There are various ways to determine volatility. The majority
are founded on past return information, although implied volatility is an
alternative. Data volatility that is not constant is called heteroscedasticity.
One
approach to dealing with heteroscedastic data volatility is the Exponentially
Weighted Moving Average (EWMA) method. The "RiskMetrics
model" - EWMA is an alternate strategy to apply to the return data that
considers time-varying volatility developed by J.P. Morgan in 1994 on their RiskMetrics technical document. In EWMA, each observation
is provided with a decay factor (0, 1), allowing for the weighting of more recent data over
older ones in the volatility calculation. The decay factor is often very
nearly, but not precisely, unity. The final
volatility estimator is stable as long as the decay factor is smaller than
unity. As in RiskMetrics, a value of roughly 0.94 has
received strong empirical confirmation for very short time horizons like daily.
A decay factor of 0.97 has been suggested for slightly longer time frames, like
one month. As the return observations move further into the past, the weights
decrease smoothly. More recent data are given more weight and past observations
are quickly deemphasized if the decay factor is smaller.
The EWMA estimator according to
Morgan (1996) can be written in this form:
�����..��������������.(3)
������ = Variance of
return on day t
�������� =� Decay factor
����� = Return on day
t-1
For large time series data of n, the following formula is used where m is n-1.
The greater the value of m, the
smaller the value of the decay factor multiplied in past data.
������..�����������...(4)
After the EWMA model is formed using
this formula, the generated variance value () is used to calculate VAR and ES in the VAR parametric
formula.
Generalized Autoregressive Conditionally
Heteroscedastic (GARCH)
The
generalized autoregressive conditionally heteroscedastic (GARCH) model can be
seen as a generalization of the EWMA model. It highlights conditional
volatility estimation time series rather than profit series (Malz,
2011). This paper use the GARCH (1,1) to
estimates the volatility of return in each day. A conditional mean equation in
GARCH model can be given by
for t = 1�..t �����..����������.(5)
where yt
denote the dependent variable analyzsed , �t
is its conditional mean, xt-1 represents the k-dimensional vector of
the explanatory variables. Simply, the variable yt
represents the daily return of a financial asset. A conditional variance
equation related to the GARCH structure (p, q) can be given by :
����������������.�������.(6)
����������.�������.(7)
the model is introduced by Bollerslev (1986) , and the paper on ARCH by Engle (1982)
this equation is re expressed as :
�����������.�.������(8)
where L is denoting a lag operator.
In his book, Malz (2011) explains the equation
details the process of updating the estimation of current volatility by
incorporating new return information , is:
�������������..������(9)
Previous Research
There
are several studies that examine the calculation of value at risk on exchange
rates as was done by Anjuma and Malik (2020), with the topic "Forecasting
risk in the US Dollar exchange rate under volatility shifts". This
research examines the movement of the US Dollar exchange rate compared to seven
major trading partners based on data from the US Federal Reserve Bank from 1
January 2020 - 07 December 2018. The author believes that "volatility
shift" must be considered in estimating volatility because it will affect
the estimated var value. By comparing seven models to
estimate VAR value, the research performs results that indicate the
GARCH-volatility shift model is the most accurate compared to other methods to
VAR in Dollar Exchange Rate.
Another
research was conducted by Kurita (2013) with the topic "Dynamic
characteristics of the daily yen-dollar exchange rate". This research
examines the JPY-USD Exchange rate quantitative information on technical
trading. Kurita compares some volatility-based models such as GARCH (1,1),
FIGARCH, FIAPARCH. The result of this research is that the difference between
the highest and lowest value plays a significant part. Also, in order to decide
the best model to estimate a VaR based on volatility,
one has to pay attention to the skewness as well as the leptokurtosis.
Bredin and Hyde (2014) assessed Various Value-at-Risk (VaR) methodologies using a portfolio centered around the
foreign exchange exposure of a small open economy, specifically Ireland. The
study employed both parametric and non-parametric Value-at-Risk models for this
investigation. Based on advanced evaluation methods, the findings suggested
that the Orthogonal GARCH model provided the highest accuracy, while the
exponentially weighted moving average (EWMA) model offered a more conservative
approach.
Results and Discussion
It
is suggested in Telkom Indonesia's financial statement that the risk of foreign
currency exchange rate fluctuations can be mitigated by the company maintaining
fixed deposits and receivables in foreign currencies. These should constitute
at least 25% of its total short-term foreign currency-denominated liabilities.
The hedging strategy emphasized in the financial statement can offset any
potential losses due to currency fluctuations, thereby ensuring the company's
financial position's stability. The computation of potential losses for Telkom
Indonesia's short-term liabilities due to currency fluctuations was carried out
by researchers based on this understanding of the company's financial
statement. Valuable insights into potential risks that could impact the
company's financial performance can be provided by focusing on short-term liabilities.
A. Volatility
Estimates vs Return
The analysis of the risks facing
Telkom Indonesia due to foreign currency exchange rate fluctuations was
undertaken using 246 observations of the closing prices of USD/IDR and JPY/IDR
currency exchanges, as specified in the company's financial statement. This
number of observations, covering a span from the start to the end of 2022,
aligns with standard practice in banks for such computations. Volatility
estimates derived from these observations were subsequently plotted against the
returns. This provides a clear illustration of how changes in exchange rates
could impact potential losses for the company's short-term liabilities.
Graphical representations, including estimates from both GARCH (1,1) and EWMA
models, were facilitated to determine the more accurate volatility estimate.
USD/IDR: The plot in Figure 1 shows that the
GARCH (1,1) model line is volatile and follows the EWMA line closely. This
suggests that the volatility of returns is too high, which increases the risk
of potential losses for Telkom Indonesia's short-term liabilities. The fact
that the GARCH (1,1) line is closely following the EWMA line suggests that both
models are providing similar estimates of volatility. This could signify that
the GARCH (1,1) model is not adding any extra value in predicting volatility
over and above the simpler EWMA model.
Figure 1
(USD/IDR) GARCH and EWMA Volatility
vs Return
JPY/IDR: The plot in Figure 2 showing the
JPY/IDR exchange rate with a GARCH (1,1) model line having a slight upward
slope but staying roughly horizontal suggests that the volatility of returns
for this pair is not changing dramatically over time. Instead, it is relatively
stable, albeit with a slight increasing trend. This means that the level of
risk associated with the JPY/IDR exchange rate, as measured by its volatility,
is not undergoing drastic fluctuations but might be experiencing a gradual
increase.
Figure 2
(JPY/IDR) GARCH and EWMA Volatility
vs Returns
B.
Kupiec
Backtesting
The Kupiec
VaR backtesting analysis, a
widely employed method for validating VaR estimates,
serves to gauge the precision of VaR projections for
Telkom Indonesia's short-term foreign currency-denominated liabilities. This is
achieved by comparing the frequency of actual losses exceeding VaR predictions with the expected frequency at a given
confidence level.
In line with this objective, such an
analysis was conducted following the calculation of the VaR
coefficients. The results not only inform the selection of risk mitigation
measures but also provide insights for refining the company's VaR estimation models.
Furthermore, the Kupiec
test assists in identifying the model that best captures the risk dynamics of
these liabilities.
USD/IDR:�
Table 1 presents the results of the Kupiec VaR backtesting for USD/IDR,
utilizing both GARCH (1,1) and EWMA models. These results encompass the VaR method, confidence level, accuracy, p-value, likelihood
ratio, and the number of errors. For both the GARCH (1,1) and EWMA models at
the 90% and 95% confidence levels, the VaR estimates
were found to be inaccurate. This is supported by the p-value and likelihood
ratio results at these levels, which suggest a low degree of accuracy.
Specifically, the p-value for both models at the 90% and 95% confidence levels
were 0.032 and 0.014 respectively, with a likelihood ratio of 4.605 and 5.991,
and each had one error.
However, at the 99% confidence
level, the VaR estimates for both models were
accurate, with no errors recorded. This is corroborated by the high p-value of
0.887 and low likelihood ratio of 0.020, suggesting a high level of accuracy
for both the GARCH (1,1) and EWMA models at this confidence level.
Based on these results, the VaR coefficients derived from the GARCH (1,1) and EWMA
models at the 90% and 95% confidence intervals will be rejected due to their
lack of accuracy. The models, however, perform adequately at the 99% confidence
level, providing accurate VaR estimates. This
indicates that for high confidence levels, both models can be used reliably for
risk estimation.
Table 1
Kupiec
Backtesting USD/IDR
VaR
Volatility Estimate Used |
Confidence Level |
Accuracy |
p-value |
Likelihood Ratio |
Number of Errors |
GARCH (1,1) |
90 |
Not
Accurate |
0.032 |
4.605 |
1 |
EWMA |
90 |
Not
Accurate |
0.032 |
4.605 |
1 |
GARCH (1,1) |
95 |
Not
Accurate |
0.014 |
5.991 |
1 |
EWMA |
95 |
Not
Accurate |
0.014 |
5.991 |
1 |
GARCH (1,1) |
99 |
Accurate |
0.887 |
0.020 |
0 |
EWMA |
99 |
Accurate |
0.887 |
0.020 |
0 |
JPY/IDR:�
Table 2 provides the Kupiec VaR backtesting results for
JPY/IDR, including the VaR method, confidence level,
accuracy, p-value, likelihood ratio, and the number of failures for both GARCH
(1,1) and EWMA models. For all confidence levels - 90%, 95%, and 99% - both the
GARCH (1,1) and EWMA models returned accurate VaR
estimates. No failures were recorded across these levels for either model,
reinforcing their accuracy. The p-value and likelihood ratio results for all
confidence levels further suggest a high degree of accuracy.
These results imply that the GARCH
(1,1) and EWMA models perform effectively in estimating VaR
for JPY/IDR across all examined confidence levels. This reliability suggests
that both models can be utilized confidently for foreign exchange risk
assessment involving the Japanese Yen and Indonesian Rupiah.
Table 2
Kupiec
Backtesting JPY/IDR
VaR Volatility Estimate Used |
Confidence
Level |
Accuracy |
p-value
|
Likelihood
Ratio |
Number
of Errors |
GARCH (1,1) |
90 |
Accurate |
0.646 |
0.211 |
0 |
EWMA |
90 |
Accurate |
0.646 |
0.211 |
0 |
GARCH (1,1) |
95 |
Accurate |
0.749 |
0.103 |
0 |
EWMA |
95 |
Accurate |
0.749 |
0.103 |
0 |
GARCH (1,1) |
99 |
Accurate |
0.887 |
0.020 |
0 |
EWMA |
99 |
Accurate |
0.887 |
0.020 |
0 |
C. Value-at-Risk
(VaR) and Expected Shortfall (ES)
Upon obtaining accurate VaR coefficients from the Kupiec backtesting, the computation of VaR
and ES values for the short-term liabilities ensued. This was done to translate
the findings of the backtesting into practical risk
measures that can be used in real-world risk management.
The provided data revealed that for
JPY/IDR, VaR and ES were calculated at three distinct
confidence levels: 90%, 95%, and 99%. The decision to use these multiple
confidence levels stems from the Kupiec backtesting results, which indicated that both GARCH (1,1)
and EWMA models provided accurate VaR estimates
across all these levels for JPY/IDR.
Conversely, for USD/IDR, VaR and ES measures were only computed at the 99%
confidence level. This was determined by the Kupiec backtesting results, which suggested that accurate VaR estimates for USD/IDR were only obtained at the 99%
confidence level using both GARCH (1,1) and EWMA models.
Therefore, the choice of confidence
levels for each currency pair directly reflects the findings from the Kupiec backtesting, tailoring the
risk measurement approach to the demonstrated accuracy of the models at
different confidence levels. This approach ensures a more accurate and reliable
estimation of potential losses, enhancing the effectiveness of risk management
efforts.
USD/IDR:�
The given data in Table 3 presents the USD/IDR rate, which is computed
based on Telkom Indonesia's total short-term liabilities, 163,540,000 USD. This
rate plays a pivotal role for the company as it provides a critical benchmark
to assess its foreign exchange risk exposure to the US dollar.
It is important to note that
currency exchange rates are subject to fluctuations due to a myriad of factors
including economic indicators, geopolitical events, and market sentiment. In
this context, a strengthening US dollar against the Indonesian Rupiah would
mean a higher value of liabilities when converted back to Rupiah. This would in
turn lead to higher repayment obligations for Telkom Indonesia, potentially
causing financial losses if not properly managed.
In the data provided, potential
losses are expressed in Indonesian Rupiah at the 99% confidence level for both GARCH
(1,1) and EWMA models. The VaR (Value-at-Risk) and ES
(Expected Shortfall) under both methodologies provide different perspectives on
the potential losses.
For the GARCH (1,1) model, the VaR is -15,029,203,960 IDR, and the ES is -21,613,694,523
IDR. This means that, with 99% confidence, the maximum expected loss over the
given time period would not exceed these amounts. It is important to note that
while VaR provides an estimate of potential losses,
ES gives an estimate of the expected loss given that the VaR
threshold is breached.
For the EWMA model, the VaR is -17,573,009,841 IDR, and the ES is -24,908,396,063
IDR. These values are higher than those obtained from the GARCH (1,1) model,
indicating a potentially greater risk according to this model.
Table 3
USD/IDR VAR & ES
Confidence
Level |
VaR |
ES |
VaR |
ES |
99% |
-15,029,203,960 |
-21,613,694,523 |
-17,573,009,841 |
-24,908,396,063 |
JPY/IDR:�
the provided data in Table 4, the JPY/IDR rate is computed based on
Telkom Indonesia's total short-term liabilities in JPY, 798,450,000 JPY. This
rate offers a significant benchmark for the company to assess its foreign
exchange risk exposure to the Japanese yen.
Similar to the USD/IDR analysis, a
strengthening Japanese yen against the Indonesian Rupiah would lead to higher
repayment obligations for Telkom Indonesia when these liabilities are converted
back to the local currency. This could potentially lead to financial losses if
the company doesn't have an effective risk management strategy in place.
The potential losses are denoted in
Indonesian Rupiah at three confidence levels: 90%, 95%, and 99%. For each of
these confidence levels, the Value-at-Risk (VaR) and
Expected Shortfall (ES) are calculated using two methodologies: GARCH (1,1) and
Exponentially Weighted Moving Average (EWMA).
At the 90% confidence level, the GARCH
(1,1) model estimates a VaR of -911,927,393 IDR and
an ES of -1,302,288,224 IDR, while the EWMA model projects a VaR of -321,553,350 IDR and an ES of -715,112,045 IDR. This
indicates that the GARCH (1,1) model foresees a higher risk of loss at this
confidence level compared to the EWMA model.
A similar pattern is observed at the
95% and 99% confidence levels. The GARCH (1,1) model consistently estimates a
higher VaR and ES compared to the EWMA model. At the
99% confidence level, for example, the VaR for the GARCH
(1,1) model is -1,640,025,172 IDR compared to -568,343,442 IDR for the EWMA
model.
This discrepancy between the two
models suggests that they capture different aspects of the market risk. The GARCH
(1,1) model, which accommodates volatility clustering and leverage effects,
might be capturing more potential for extreme events in the JPY/IDR exchange
rate, while the EWMA model, which assigns a decreasing weight to older data,
might be more sensitive to recent changes in volatility.
Table 4
JPY/IDR VAR & ES
Confidence
Level |
VaR |
ES |
VaR |
ES |
90% |
-911,927,393 |
-1,302,288,224 |
-321,553,350 |
-715,112,045 |
95% |
-1,165,105,378 |
-1,451,651,092 |
-407,368,497 |
-819,297,224 |
99% |
-1,640,025,172 |
-2,205,458,957 |
-568,343,442 |
-1,006,773,784 |
The potential losses due to currency
fluctuations were estimated using the most conservative values from the
provided tables. These values are -24,908,396,063 IDR (ES-EWMA@99CL for
USD/IDR) and -2,205,458,957 IDR (ES GARCH@99CL for JPY/IDR), resulting in a
total potential loss of 27,113,855,020 IDR.
Concurrently, according to the financial
report, Telkom Indonesia holds 653,000,000,000 IDR in fixed short-term
deposits. These deposits can serve as a contingency fund to offset any
potential losses from the fluctuations of their foreign currency-denominated
short-term liabilities.
In this context, the potential
losses constitute merely about 0.0042% of the total contingency funds
available. This suggests that Telkom Indonesia's strategy, as stipulated in
their financial report, of maintaining fixed deposits and receivables in
foreign currencies equal to at least 25% of their total short-term foreign
currency liabilities, could be more conservative than necessary given the
actual risks posed by currency fluctuations, even in the worst-case scenarios.
Conclusion
This
study concludes that the Kupiec statistical test
validates the effective performance of the Expected Shortfall (ES) calculation
using the GARCH (1,1) model at a 99% Confidence Level (CL) for JPY exposure.
For USD exposure, the ES using the Exponentially Weighted Moving Average (EWMA)
model at a 99% CL was found to be more effective.
The
ES calculation using the EWMA model at 99% CL provides a more conservative
measurement of exchange rate risk for USD exposure, with an IDR of
24,908,396,063. Similarly, for JPY exposure, the ES calculation using the GARCH
(1,1) model at a 99% CL offers a more conservative risk measurement, with an
IDR of 2,205,458,957.
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Copyright holder: Firly
Armanda, Fatwa Aulia, Jodi Surya Gustanto, Jalil Mujib Tan Ismail, Jonatan Halomoan�,
Dianita Fitriani Pogram, Girindra Chandra Alam, Dewi Hanggraeni
(2022) |
First publication right: Syntax Literate: Jurnal Ilmiah
Indonesia |
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