RISK MEASUREMENT OF CHINA’S FOREIGN

ENERGY INVESTMENT PORTFOLIO BASED

ON COPULA-VAR

Lei Liu*

School of Architecture, Harbin Institute of Technology, Key Laboratory of Science

and Technology of Urban and Rural Habitat in Cold Areas, Ministry of Industry and

Information Technology, Harbin, Heilongjiang 154001, China

hitliulei19860226@163.com

Yang Yang

School of Architecture, Harbin Institute of Technology, Key Laboratory of Science

and Technology of Urban and Rural Habitat in Cold Areas, Ministry of Industry and

Information Technology, Harbin, Heilongjiang 154001, China

Hong Leng

School of Architecture, Harbin Institute of Technology, Key Laboratory of Science

and Technology of Urban and Rural Habitat in Cold Areas, Ministry of Industry and

Information Technology, Harbin, Heilongjiang 154001, China

Reception: 11/02/2023 Acceptance: 15/04/2023 Publication: 03/05/2023

Suggested citation:

Liu, L., Yang, Y. and Leng, H. (2023). Risk measurement of China's foreign

energy investment portfolio based on Copula-VaR. 3C TIC. Cuadernos de

desarrollo aplicados a las TIC, 12(2), 6 0 - 75. https://doi.org/

10.17993/3ctic.2023.122.60-75

https://doi.org/10.17993/3ctic.2023.122.60-75

3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

ABSTRACT

Energy is an important resource for the development of the country, and investment in

energy can promote the development of the national economy. Many scholars are

currently using Copula models to predict the risk of energy investments to improve

investment efficiency. However, most studies are not systematic enough and focus on

countries outside of China. We use the Copula-VaR method with the Archimedean

Copula function and the Copula-VaR method with the introduction of tail correlation to

calculate the energy futures risk. The risk of six different percentages of China's

foreign energy portfolio for three futures on natural gas, oil, and coal between January

3, 2015 and December 30, 2021 is calculated and compared to the traditional method.

The results show that the risk values calculated using the improved Copula-VaR

model are 0.00836, 0.00922, 0.00217, 0.00635, 0.00612 and 0.00827 higher under

the 0.98 confidence level than under the 0.96 confidence level. It has a high accuracy

compared with the traditional method. The research in this paper provides an idea for

the design of energy investment programs in China

KEYWORDS

Copula- VaR method; energy investment; degree of confidence; portfolio risk;

confidence level.

INDEX

ABSTRACT

KEYWORDS

1. INTRODUCTION

2. COPULA-VAR MODELING

2.1. Copula function definition

2.2. Copula Distribution Family

2.2.1. Normal Copula family of distributions

2.2.2. t-Copula distribution family

2.2.3. Archimedes Copula distribution family

2.3. Definition of the VaR metric

2.4. Correlation metric

3. ANALYSIS AND DISCUSSION

3.1. Selection and description of data

3.2. Risk metrics for traditional VaR methods

3.3. Copula-VaR model for risk metrics

4. CONCLUSION

REFERENCES

https://doi.org/10.17993/3ctic.2023.122.60-75

3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

1. INTRODUCTION

Energy is an important resource for national development. The development of

industry and manufacturing industries cannot be separated from the supply of energy.

With the development of economic globalization, each country cannot stay away from

the development of energy [1-3]. At present, the world energy market is also suffering

from an unprecedented impact with the spread of the economic globalization crisis.

The world energy structure is currently undergoing a transformation, which brings a

certain degree of impact on the economic trade and energy import and export of each

country [4-6]. During World War II in the 19th century, the main conflicts in the world at

that time were focused on the competition for resources and territories. Countries

vigorously developed their industries. The Western countries successfully entered

industrialized societies thanks in part to low energy prices [7-8]. But in the 21st

century, there was a conflict over oil resources in the Middle East, which at once

broke the world energy pattern. The increasing price of oil has led to an energy crisis

in many countries and a gradual widening of the gap between countries' economic

development [9-12]. Each country has its own energy advantages, for example,

Russia has rich oil resources and China has rich coal resources. Figure 1 shows

China's coal energy and crude oil energy production from 2011-2022. It can be seen

that China's coal and crude oil resources have been increasing in the last decade, so

it is important to be well-positioned for strategic energy investment.

Figure 1. Coal and crude oil production 2011 - 2022

With the increasingly complex international situation, the price of energy is also

changing. The recent conflict between Russia and Ukraine has caused an increase in

the price of oil. Changes in energy prices can have a relatively large impact on a

country's political economy. China is rich in energy, so it is necessary to make a good

risk assessment of energy investments [13-16]. The Copula model, proposed in the

20th century, is well suited for the pricing of financial investments and the

comprehensive measurement of investment risk, in which the investment risk is

assessed by the magnitude of the VaR (Value at Risk) value [17-20]. Subsequently,

some scholars used the Copula model to measure energy portfolio risk [21-24].

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HB Ameur et al. analyze the risk spillover benefits between oil and gas markets by

measuring their risk dependence [25]. Combining market price data for oil and natural

gas from 2014-2017 reveals that the risk premium from oil to natural gas markets is

higher than the risk premium from natural gas markets to oil markets. It is also found

that risk upward and downward spillovers are asymmetric, due to the stronger

spillover effects from risk negative spillovers. Ji explores the impact of uncertainty on

energy prices by measuring four types of Delta conditional value-at-risk (CoVaR)

through six time-varying copula, considering uncertainty measures among economic

policies, financial markets, and energy markets. The results show a negative

correlation between energy returns and changes in uncertainty, with energy being

more sensitive to the response of financial and energy markets, while economic

policies have a relatively weak impact. The study provides informative

recommendations for energy portfolios [26]. Qiang et al. used six time-varying copula

models to analyze the dynamic dependence of WTI crude oil on China and the U.S.,

while taking into account the structural changes in their dependence [27]. The results

show that there are breakpoints in the dependence on crude oil and the dollar index

on a daily or monthly basis. There is a relatively large risk spillover from crude oil to

the exchange rate markets in China and the United States. It is also found that the

exchange rate markets in China and the United States are not as sensitive to the

spillover effects of oil price turmoil. AK Tiwari et al. analyzed the dependence

relationship between the Indian stock market and crude oil prices using the

dependence transformation copula model [28]. Dependence and tail dependence are

investigated for four states: oil price-rising-stock-rising, oil price-falling-stock-rising, oil

price-falling-stock-rising, and oil price-falling-stock-falling. The results show that the

gap between CoVaR and VaR for each domain is not significant. That is, the oil

market does not add additional risk to the stock market when both the oil market and

stock prices are in a downward spiral. Meanwhile, oil prices are falling and entering

the carbon sector is the ideal hedge investment. Ren et al. studied the investment risk

of U.S. crude oil, natural gas energy and heating oil futures using energy investment

risk management as an entry point [29]. An energy futures portfolio risk measurement

model based on BEKK-VaR and DCC-VaR methods was developed to calculate the

value-at-risk of energy investments. The results show that the DCC-VaR has more

accurate calculation results compared with the BEKK-VaR method, but the BEKK-VaR

method works better in terms of the generalized error distribution. In general., the

DCC-VaR method is better for measuring investment risk portfolios. Lv et al. proposed

a copula-based stochastic multilevel planning (CSMP) method as a way to ensure a

coordinated relationship between the energy economy and the ecosystem in China

[30]. The results show that by the middle of the 21st century, China's tertiary and high-

tech industries will account for 62.4% and 14.9% of the market, respectively. Energy

and carbon dioxide consumption decreased by 45.1% and 56.9% respectively, which

shows that the ecological relationship is developing towards economic energy saving

and environmental friendly. Zhang et al. proposed a copula-based multivariate model

aimed at analyzing the impact of oil price fluctuations on fuel and shipping prices [31].

Data is derived from the index relationship between oil prices and shipping in West

Texas, the Baltic Sea region from 2008 to 2015. The results show that high oil prices

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are not significantly dependent on each country, and copula modeling can better

identify the time-varying effects of the dependence between the two and help

policymakers analyze energy investment markets effectively. Cai et al. proposed an

integrated approach of system dynamics, orthogonal design, and copula analysis (IA-

SOC) to assess the risk of coupling water and energy resources in cities in the

Jinjiang region [32]. The results show that the system dynamics model constructed in

the established paper is applicable to the prediction of water and energy resources.

The water and energy scarcity risks are 0.938, 0.981 and 0.835, 0.936 for the

government's planning period for the city of Jinjiang with water demand of 25.206,

29.07 billion cubic meters and 433.67, 477.02 million tons of standard coal equivalent

(SCE), respectively. Jiang et al. narrow the risk gap between different countries by

identifying the impact of specific political risk factors on foreign energy investments

and exploring the significant political risk factors for foreign energy investments in 74

developing countries [33]. In addition, practical advice is given to foreign investors

based on the national conditions of different countries and the differences between

them. JC A et al. systematically review the literature of the last decade to summarize

the interplay between stranded risk and capital allocation decisions of others in energy

technologies [34]. Coal., oil and gas companies were found to be at risk of stranding

asset owners due to misjudged energy price forecasts. Investors with illiquid assets

are also found to be less exposed to risk and can hedge risk and manage assets

through diversification strategies. In summary, the current prediction results of energy

investment risk using the Copula model are satisfactory, but there is a lack of

systematic research and shortcomings for quantitative analysis of risk assessment.

Most studies have been conducted on countries outside of China, and there is still a

lack of work on risk assessment of China's outbound energy investments.

Therefore, this paper calculates the risk of six different percentages of China's

foreign energy portfolio for three futures of natural gas, oil, and coal for the period

from January 3, 2015 to December 30, 2021 by using the Copula-VaR method. The

values at risk of different proportional investment approaches were compared at

confidence levels of 0.96 and 0.98, and the results calculated by the improved

Copula-VaR method were compared with the traditional calculations. The research in

this paper provides a reference for the formulation of China's outbound energy

investment strategy.

2. COPULA-VAR MODELING

2.1. COPULA FUNCTION DEFINITION

The analysis of a single variable in financial risk analysis cannot correctly reflect the

deep relationship between financial risk and investment behavior. Therefore, multiple

variables need to be analyzed, and the analysis of multiple variables requires an in-

depth analysis of the correlation of these variables. In this paper, we use the Cupula

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function to measure financial risk and time series and optimize the distribution

function, and the Copula function is defined as follows:

Suppose there is a element distribution function:

, where

with marginal distribution . For

such any satisfies the following

equation.

(1)

The above theorem shows that for marginal distributions and n elements of the

Copula function, a distribution function consisting of n variables can be formed. The

marginal distribution in this distribution function represents the distribution of each

variable that has a correlation with financial risk. Copula function refers to the

composite function composed of these variables fitted into a distribution function. The

above theorem can confirm the existence of the Copula function, and through this

theorem can show that the Copula function can describe the correlation of financial

risk variables without considering the preconditions of the multivariate normal

distribution function, which is more concise and convenient for us to study the

existence of multivariate variables in the risk measurement of foreign energy

portfolios.

With the above existence theorem of the Copula function, we can further introduce

the definition of Copula, namely Sklar's theorem.

If the element function , if for all

the

following four conditions are satisfied: if either component of is ; for

, , both have

; The function

is increasing; For any , we have

, then the function represented by can be

called a Copula function.

2.2. COPULA DISTRIBUTION FAMILY

Copula function has many distribution families, of which several are more important

function families, including: the normal Copula distribution family, Archimedean

Copula distribution family, t-Copula distribution family and elliptic distribution family,

etc.. Several common families of Copula distributions are described below.

f(x1,⋯,xp)

xi∈R,i= 1,⋯,p

Fi,i= 1,⋯,p

Copula C : [0,1]p→[0,1]

xi∈R,i= 1,⋯,p

x1, …, xp

)

(

F1(x1), …, Fp

(

))

C:I2= [0,1]n→[0,1] = I

t∈In

C(u)=0

k∈{1,2,⋯,n}

uk∈[0,1]

C(1,⋯,1,uk,1,⋯,1)=uk

C(u1,u2,⋯,uk)

0≤ai≤bi≤1

Δb

anΔb

n−1

an−1⋯Δb

a1C(u1,u2,⋯,un≥0)

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2.2.1. NORMAL COPULA FAMILY OF DISTRIBUTIONS

The probability density function of the family of normal Copula distributions is

shown below.

(2)

R in the above function equation represents a symmetric positive definite matrix,

and the right-hand side of the equation represents the standard multivariate normal

distribution function.

is the inverse function of the standard normal

distribution function. For the vast majority of cases, the data related to energy

investment risks and returns show an asymmetric distribution, which is clearly

different from the normal distribution. Therefore, the normal Copula family of

distributions does not provide a valid analysis of the Chinese outbound energy

portfolio risk measures we study.

2.2.2. T-COPULA DISTRIBUTION FAMILY

The probability density function for the family of t-Copula distributions is shown

below:

(3)

As with the probability density function of the family of normal Copula distributions,

R is a symmetric positive definite matrix. The function is a standard multivariate

distribution function, which denotes the correlation matrix and represents the

degrees of freedom. is the inverse function of . Compared to the normal

Copula family of distributions, the t-Copula family of distributions has a better fit in the

tails of the financial risk and return distributions, but like the normal Copula family of

distributions, it is less effective in characterizing asymmetry.

2.2.3. ARCHIMEDES COPULA DISTRIBUTION FAMILY

There are three types of probability density functions for the Archimedean Copula

family of distributions, namely Gumbel Copula, Frank Copula and Clayton Copula,

and their functional formulas are shown below.

(4)

(5)

(6)

u1,u2,…,up

)

=ϕR

(

ϕ−1

(

)

,ϕ−1

(

)

,…,ϕ−1

(

))

Φ−1(⋅)

C(u1,u2, …, uk;R,v)=TR,v(T−1

v(u1),T−1

v(u2),…,T−1

v(uk))

TR,v()

T−1

v(⋅)

T(⋅)

(u,v,α)=exp

(

−

(

(−log u)α+ (−log u)1

)

,α∈[1, + ∞)

)

(u,v,α)=−1/αlog

(

1 +

(e−αu−1)(e−αv−1)

e−a−1

)

,α∈[−∞,0) ∪(0, + ∞

)

C(u,v,α) = max ((u−α+v−α−1,0),α∈[−∞,0) ∪(0, + ∞))

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2.3. DEFINITION OF THE VAR METRIC

The traditional methods are ALM (Asset-Liability Management) and CAPM (Capital

Asset Pricing Model), but each of these methods is overly dependent on the analysis

of the data in the statements. As a result, the analysis results are not real-time and the

risk measurement is too abstract to reflect the analysis results visually. These two

traditional methods are unable to accurately analyze and measure investment risk

because they can only show the volatility of assets and cannot incorporate other

financial derivatives.

VaR (Value at Risk) is a method of measuring market risk proposed by the G30

Group in a report published in 1993, and the method has been widely promoted in the

financial community. VaR means the maximum possible loss of a portfolio of financial

assets under normal market volatility. It is the maximum possible loss of a portfolio of

financial assets over the period from the present to a specific time in the future at a

certain confidence level. The method is represented mathematically as follows.

(7)

The definition of each variable in the above equation:

is the probability,

representing the probability that the amount of loss of a financial asset is less than the

maximum possible loss; is the loss amount, representing the loss amount of this

financial asset during the holding time indicated by ;

represents the upper

limit of possible loss at a certain confidence level

, which can also be the value at

risk at that confidence level; then represents the given confidence level.

2.4. CORRELATION METRIC

Correlation is a measure of the relevance of data attributes, and similarity is a

measure of the similarity of data objects. Data objects are described by multiple data

attributes, and the relevance of data attributes is described by the correlation

coefficient. The similarity of data objects is measured by some distance measure.

Because the correlation between different financial assets in a portfolio has a strong

link to the overall portfolio investment risk, the analysis of correlation measures is a

key part of the study of foreign energy portfolio risk.

The Kendall correlation coefficient is an important measure derived from the

Copula function and is a statistical value used to measure the correlation of two

random variables. the mathematical definition of the Kendall correlation coefficient τ is

shown in equation (8). Suppose there are two mutually independent continuous

random vectors and

, and these two vectors have the same joint

distribution . Then

is defined as the difference between the positive and negative

correlation probabilities, i.e.

prob (ΔPΔt≤Va R)=α

ΔPΔt

Δt.

VaR

(X1,Y1)

(X2,Y2)

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(8)

It can be seen from the above equation that the calculation process of Kendall

correlation coefficient is very tedious and requires the calculation of differentiation

and double integration. However, under the calculation function of the Archimedean

Copula family of distributions, it is only necessary to calculate its generating element

first to calculate its Kendall correlation coefficient . Converting a two-dimensional

problem to a one-dimensional direction greatly simplifies the computational process.

According to the above method, we assume that there are two continuous random

variables and with Archimedean Copula family of distributions, and their

generating elements are obtained by calculation, at which time the definition of

Kendall correlation coefficient can be transferred from the above tedious formula as

shown:

(9)

The Kendall correlation coefficient takes values between and . When is , it

means that the two random variables have consistent rank correlation; when is ,

it means that the two random variables have exactly opposite rank correlation; when

is , it means that the two random variables are independent of each other.

3. ANALYSIS AND DISCUSSION

3.1. SELECTION AND DESCRIPTION OF DATA

The data selected for the empirical analysis in this paper are from Chinese

industrial enterprise data for the period from January 3, 2015 to December 30, 2021,

with a total of 1,498 sets of data for natural gas, oil, and coal futures as the data for

the model analysis. The impact of price fluctuations between these three is studied by

building a Copula-VaR foreign energy investment model. A comparative analysis of

different foreign energy investment portfolio returns is conducted and the Kendall

correlation coefficient is calculated to analyze the risk of the portfolio. The following

variables are used in the Copula-VaR model calculation: (1) Vc is the coal futures

price in USD/ton in the data of Chinese industrial enterprises; (2) Vo is the crude oil

futures price in USD/barrel in the data of Chinese industrial enterprises; (3) Vg is the

natural gas futures price in USD/mmBtu in the data of Chinese industrial enterprises.

l=P((X

−X

)(Y

−Y

)> 0)−P((X

−X

)(Y

−Y

)< 0)

= 4∫1

∫1

C2(u,v)dC1(u,v)−1

= 1 + 4

∫0

φ(t)

φ′ (t)

−1

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3.2. RISK METRICS FOR TRADITIONAL VAR METHODS

The analysis of single-asset risk measures is relatively simple and can be

calculated using traditional methods. Table 1 shows the single-asset return VaR

values calculated by traditional methods for natural gas, oil and coal futures.

Table 1. VaR values for each of the three futures

In a portfolio of foreign energy investments, the combination of different types of

financial assets and the proportion of each financial asset in the portfolio in the overall

portfolio are factors that affect the portfolio investment risk. Therefore, in this paper,

three different energy futures are combined in different ratios: 0.2:0.2:0.6, 0.2:0.6:0.2,

0.6:0.2:0.2, 0.4:0.4:0.2, 0.4:0.2:0.4, 0.2:0.4:0.4, and 0.2:0.4:0.4. A total of six different

combinations of ratios are used to calculate the data for in-depth analysis of the

model. In this section, the VaR values of six different portfolios are calculated using

the traditional VaR method at two different confidence levels, and the results are

shown in Figure 2.

Figure 2. Coal and crude oil production 2011 - 2022

From Figure 2, it can be seen that there is a direct relationship between the

investment risk value and the confidence level. When the confidence level is relatively

high, it is accompanied by a greater investment risk. There is no obvious pattern of

investment risk for the six portfolios with the same confidence level, and the highest

risk value is when the investment allocation ratio is 0.2:0.4:0.4. At a confidence level

Confidence level Natural Gas Oil Coal

VaR value

0.96 0.01637 0.01357 0.03547

0.98 0.02347 0.02367 0.03277

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of 0.98, the investment risk further increases when the 0.4:0.2:0.4 investment

allocation brings a higher risk. Also, the risk values calculated using the traditional

VaR method were 0.00434, 0.00462, 0.00167, 0.00870, 0.00193 and 0.00125 higher

than those at the confidence level of 0.96, respectively.

Figure 3 shows the calculation of VaR for the single investment approach and

portfolio investment approach, from the figure it can be seen that the VaR of the two

investment approaches are different at different confidence levels. In general., the

VaR values of natural gas and oil investment approaches are smaller, while the

investment in coal has a greater risk, and the portfolio investment approach can

reduce the risk value of coal investment to some extent.

Figure 3. Risk measures for single investment approach and portfolio approach at different

confidence levels

When the confidence level is 0.96, the risk of portfolio investment is greater than

that of investing in natural gas and oil alone. When the confidence level is 0.98, the

risk of portfolio investment is about the same as investing in natural gas and LPG

alone, with a tendency to decrease in a given ratio. Therefore, when we do investment

analysis, we have to divide the types of energy sources, and single and portfolio

investments have different values of risk in specific conditions. There is no direct

relationship between the two types of investments, which provides us with a way of

thinking when doing energy investment planning.

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3.3. COPULA-VAR MODEL FOR RISK METRICS

From Section 2, we know that the introduction of Archimedean Copula function

converts the two-dimensional problem into a one-dimensional direction for processing,

which can make it easier to calculate the Kendall correlation coefficient

. Using the

Kendall correlation coefficient can improve the traditional VaR algorithm, and here we

obtain by calculating. Using the formula, the VaR values of natural gas, oil,

and coal futures can be calculated for six different ratios of the portfolio, as shown in

Figure 4

Figure 4. Risk values calculated by the Copula-VaR method at confidence levels of 0.96 and

0.98

As can be seen from figure 4, the value of investment risk is related to the

confidence level, and different investment ratios have different risks at the same

confidence level. This is consistent with the results calculated using the traditional

method, where the 0.2:0.6:0.2 investment ratio has a higher risk when the confidence

level is 0.96, while 0.4:0.2:0.4 has a higher risk when the confidence level is 0.98. The

risk values under the confidence level of 0.98 are also higher than those under the

confidence level of 0.96 by 0.00836, 0.00922, 0.00217, 0.00635, 0.00612 and

0.00827.

In addition to the improvement of the VaR measure of risk by introducing the

Archimedean Copula function, the tail correlation carve-out can also enhance the

method. The tail correlation coefficient consists of two parts, the upper tail correlation

coefficient and the lower tail correlation coefficient, respectively. The tail correlation

reflects the probability that the return of one asset is greater (less) than a certain

threshold and the return of the other asset is simultaneously greater (less) than a

certain threshold, i.e., the probability that two financial assets have extreme

simultaneous same-directional returns. We can calculate the upper tail correlation

τ= 0.692

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coefficient and the lower tail coefficient

for the daily log

returns of natural gas, oil and coal futures from the previous data. If the relationship

between two assets is positively correlated and the higher the coefficient of

correlation, the higher the risk coupling and the poorer the portfolio's ability to diversify

risk; conversely, if the correlation coefficient between two assets is lower, the better

the ability to diversify investment risk. These two correlation coefficients allow for the

calculation of VaR values for the three futures at six different ratios of the portfolio, as

shown in Table 2.

Table 2. VaR values for each of the three futures

The data in the table above shows that the value of risk varies for different

percentages of investments. For investors, investing different amounts of money in

different assets exposes them to different risks and yields different returns. To choose

what portfolio proportions to invest in, the risk can be measured by a risk metric tool.

The Copula-VaR model used in this paper can effectively improve the traditional VaR

method, and the results of the test can give reference to the investment choice of

investors. In the specific investment, the initial investment plan can be designed

before the risk assessment, which can reduce the investment risk to a certain extent.

4. CONCLUSION

In this paper, the risk of foreign energy portfolios with six different ratios of natural

gas, oil, and coal futures for the period from January 3, 2015 to December 30, 2021 is

calculated by the traditional method, the Copula-VaR method that introduces the

Archimedean Copula function, and the Copula-VaR method that introduces the tail

correlation, respectively. Comparing the risk values of the six different proportions of

the foreign energy portfolios, the following conclusions can be drawn.

1. The upper tail correlation coefficient

and the lower tail coefficient

for the daily log returns of natural gas, oil, and coal futures indicate

that if the relationship between two assets is positively correlated, and the

higher the correlation coefficient is, the higher the risk coupling is and the

worse the portfolio is for risk diversification; conversely if the correlation

coefficient between two assets is lower, the portfolio is able to better

diversification of investment risk.

γu= 0.901

γ1= 0.843

Different proportional portfolios of three futures

VaR

value

Confidence

level Correlation

coefficient 0.2:0.2:0.6 0.2:0.6:0.2 0.6:0.2:0.2 0.4:0.4:0.2 0.4:0.2:0.4 0.2:0.4:0.4

0.96 Upper tail 0.02143 0.02216 0.02165 0.02272 0.02411 0.02314

0.98 Upper tail 0.02165 0.03156 0.03012 0.02684 0.02742 0.02812

0.96 Lower tail 0.02514 0.02176 0.01982 0.01871 0.02187 0.02251

0.98 Lower tail 0.03124 0.03417 0.02981 0.02318 0.02719 0.02154

γu= 0.901

γ1= 0.843

https://doi.org/10.17993/3ctic.2023.122.60-75

3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

The risk of a single asset investment or portfolio is different at different

confidence levels. From the data, it can be seen that the confidence level and

the value of risk show a positive correlation. At the confidence level of 0.98, the

value of risk calculated using the traditional VaR method is 0.00434, 0.00462,

0.00167, 0.00870, 0.00193 and 0.00125 higher than the value of risk at the

confidence level of 0.96, respectively.

3. The data calculated using the modified Copula-VaR model also shows that the

value at risk under the 0.98 confidence level is 0.00836, 0.00922, 0.00217,

0.00635, 0.00612 and 0.00827 higher than the value at risk at the 0.96

confidence level. most of the foreign energy portfolio values at risk are in

between these three single The majority of the foreign energy portfolio is

between the risk values of these three single energy assets. However, this

approach is a good way to avoid a special situation where all investments are

placed under the same asset and an accident causes a total loss of assets in

the long run. There are different values of investment risk for different

percentages of natural gas, oil and coal futures.

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