Analysis of Stock Price Risk Measurements with the Variance Covariance and Historical Simulation Models Approach

Oct 13, 2025 by wbrum.org 83 views

Analysis of Stock Price Risk Measurements with the Variance Covariance and Historical Simulation Models Approach

Introduction

The stock market is a complex and dynamic environment where investors and portfolio managers face numerous risks. One of the most significant risks is the potential loss of investment due to fluctuations in stock prices. To mitigate this risk, it is essential to measure and manage stock price risk effectively. This study aims to analyze the price risk of banking shares by measuring the maximum potential loss in one day, five days, and twenty days using the Variance Covariance and Historical Simulation models approach.

Background

The stock market is a highly volatile environment where stock prices can fluctuate rapidly. This volatility can result in significant losses for investors and portfolio managers. To manage this risk, it is essential to measure and understand the potential losses that may be faced. The Value at Risk (VAR) is a widely used risk measurement tool that estimates the maximum potential loss in a given time period with a specified confidence level. The VAR is calculated using two methodologies: the Variance Covariance and Historical Simulation approaches.

Methodology

Variance Covariance

The Variance Covariance method calculates risks by utilizing the average and standard deviation of stock returns. This approach is based on the assumption that stock returns follow a normal distribution. The advantage of this approach is its simplicity in calculation and speed in processing data. However, this method has limitations, one of which is the assumption of normal distribution from return, which often does not reflect the reality in the market.

The Variance Covariance method is calculated using the following formula:

VAR = (Σσ^2 * (1 - ρ))^(1/2)

where:

VAR is the Value at Risk
σ is the standard deviation of stock returns
ρ is the correlation coefficient between stock returns
Σ is the sum of the standard deviations of stock returns

Historical Simulation

On the other hand, historical simulation uses historical data to calculate potential losses. By analyzing past data, this method can provide a more realistic picture of the risks that might be faced. However, the weakness of this approach is its dependence on existing historical data, which may not always be relevant in the future.

The Historical Simulation method is calculated using the following formula:

VAR = (Σ|Rt| * (1 - ρ))^(1/2)

where:

VAR is the Value at Risk
Rt is the return of stock t
ρ is the correlation coefficient between stock returns
Σ is the sum of the absolute returns of stock t

Data and Sample

The object of research includes ten banking shares listed on the Indonesia Stock Exchange (IDX) during the period January 3 to February 29, 2012. The data used in this study is the daily closing prices of the ten banking shares.

Results and Analysis

From the research conducted, it was found that there was a significant difference between the VAR values calculated using the Variance Covariance and Historical Simulation methods. The Historical Simulation method tends to show a greater potential loss compared to the Variance Covariance method. This may be caused by the ability of historical simulation in capturing extreme movements in the market that cannot be captured by the Variance Covariance method.

The validity of the two methods is tested using back testing and Kupiec test, which compares the maximum potential loss with actual losses. The test results show that both methods, although they produce different values, are still valid to measure the maximum potential loss of banking stocks.

Conclusion

In conclusion, both the Variance Covariance and Historical Simulation methods have advantages and disadvantages of each stock price risk measurement. For investors and portfolio managers, it is essential to understand the differences between these two methods in order to make more appropriate decisions in risk management. The use of both methods simultaneously can also provide a more comprehensive picture of the potential losses that may be faced in investment in the banking sector. Thus, this research is expected to contribute to the development of risk management strategies in the stock market, especially in the context of banking shares.

Recommendations

Based on the findings of this study, the following recommendations are made:

Investors and portfolio managers should use both the Variance Covariance and Historical Simulation methods to measure stock price risk.
The use of both methods simultaneously can provide a more comprehensive picture of the potential losses that may be faced in investment in the banking sector.
The Historical Simulation method should be used in conjunction with the Variance Covariance method to capture extreme movements in the market.
The use of back testing and Kupiec test can help to validate the results of the two methods.

Limitations

This study has several limitations, including:

The use of a small sample size of ten banking shares.
The use of historical data, which may not always be relevant in the future.
The assumption of normal distribution from return, which often does not reflect the reality in the market.

Future Research Directions

Future research directions include:

The use of more advanced risk measurement models, such as the Monte Carlo simulation method.
The use of more comprehensive data, including macroeconomic variables and industry-specific data.
The development of a hybrid risk measurement model that combines the advantages of both the Variance Covariance and Historical Simulation methods.

References

Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill.
Hull, J. C. (2009). Options, Futures, and Other Derivatives. Prentice Hall.
Kupiec, P. H. (1995). Techniques for Verifying the Accuracy of Risk Measurement Models. Journal of Derivatives, 3(2), 73-84.

Appendix

The appendix includes the following:

The list of banking shares used in this study.
The daily closing prices of the ten banking shares.
The results of the back testing and Kupiec test.
Q&A: Stock Price Risk Measurements with the Variance Covariance and Historical Simulation Models Approach

Introduction

In our previous article, we discussed the analysis of stock price risk measurements with the Variance Covariance and Historical Simulation models approach. In this article, we will answer some of the frequently asked questions related to this topic.

Q: What is the Variance Covariance method?

A: The Variance Covariance method is a risk measurement approach that calculates risks by utilizing the average and standard deviation of stock returns. This approach is based on the assumption that stock returns follow a normal distribution.

Q: What is the Historical Simulation method?

A: The Historical Simulation method is a risk measurement approach that uses historical data to calculate potential losses. By analyzing past data, this method can provide a more realistic picture of the risks that might be faced.

Q: What are the advantages and disadvantages of the Variance Covariance method?

A: The advantages of the Variance Covariance method include its simplicity in calculation and speed in processing data. However, this method has limitations, one of which is the assumption of normal distribution from return, which often does not reflect the reality in the market.

Q: What are the advantages and disadvantages of the Historical Simulation method?

A: The advantages of the Historical Simulation method include its ability to capture extreme movements in the market that cannot be captured by the Variance Covariance method. However, the weakness of this approach is its dependence on existing historical data, which may not always be relevant in the future.

Q: How do the Variance Covariance and Historical Simulation methods differ?

A: The Variance Covariance method calculates risks by utilizing the average and standard deviation of stock returns, while the Historical Simulation method uses historical data to calculate potential losses. The Historical Simulation method tends to show a greater potential loss compared to the Variance Covariance method.

Q: What is the Kupiec test?

A: The Kupiec test is a statistical test used to validate the results of the Variance Covariance and Historical Simulation methods. This test compares the maximum potential loss with actual losses.

Q: What is the back testing method?

A: The back testing method is a statistical test used to validate the results of the Variance Covariance and Historical Simulation methods. This test involves recalculating the risk measurement model using historical data to see if the results match the actual losses.

Q: Why is it essential to use both the Variance Covariance and Historical Simulation methods?

A: It is essential to use both the Variance Covariance and Historical Simulation methods because they provide a more comprehensive picture of the potential losses that may be faced in investment in the banking sector. The use of both methods simultaneously can help to capture extreme movements in the market that cannot be captured by the Variance Covariance method.

Q: What are the limitations of this study?

A: The limitations of this study include the use of a small sample size of ten banking shares, the use of historical data, which may not always be relevant in the future, and the assumption of normal distribution from return, which often does not reflect the reality in the market.

Q: What are the future research directions?

A: The future research directions include the use of more advanced risk measurement models, such as the Monte Carlo simulation method, the use of more comprehensive data, including macroeconomic variables and industry-specific data, and the development of a hybrid risk measurement model that combines the advantages of both the Variance Covariance and Historical Simulation methods.

Conclusion

In conclusion, the Variance Covariance and Historical Simulation methods are two widely used risk measurement approaches in the financial industry. While the Variance Covariance method is simple and fast, it has limitations, including the assumption of normal distribution from return. The Historical Simulation method, on the other hand, is more realistic but has limitations, including its dependence on existing historical data. The use of both methods simultaneously can provide a more comprehensive picture of the potential losses that may be faced in investment in the banking sector.