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There are usually great demands for risk control in the banking industry. Value at risk (VaR) is an important risk measurement in the Basel Accords, and Monte-Carlo simulation is a common method for VaR measurement. We conduct a series of Monte-Carlo simulation for VaR measurement based on the banks listed in the China stock market. Our study thinks that it is reliable to use Monte-Carlo simulation to measure VaR in Chinese banks. Therefore, we think that such VaR measurement works in China.

A famous American movie in 2015, The Big Short, refreshes people’s miserable memories to the 2008 global financial crisis. iFeng.com^{1} says in 2016 that another global financial crisis may come again when commenting on the movie. The website lists American financial data and compares with those in 2008 crisis to demonstrate its comments.

The movie arouses world-wide concerns again to the risk control in the banking industry. VaR, or value at risk, is an important risk indicator for the banking industry in the international risk management agreement, the Basil Accords. The Monte-Carlo simulation is one of the major algorithms in calculating VaR. China has accepted Basil Accord I in 2004, and started to accept Basil Accord II

Items | 2008 crisis | 2016 |
---|---|---|

Government debt | $9.6 trillion | $19.0 trillion |

Consumer credit increase | 44% | 44% |

Fed balance sheet increase | 33% | 462% |

Central bank capital | 4.50% | 0.80% |

Interest rate | 4.66% | 0.25% |

Bank balance sheet | No money down | Negative interest |

Bubble size | $1.3 trillion | $7 trillion |

Derivatives market | $182 trillion | $533 trillion |

Data source: http://finance.ifeng.com/a/20160320/14278609_0.shtml.

in 2007. China also promotes a great plan to accept Basil Accord III in 2018. However, there is an issue about China from the beginning: Basil Accords is designed for free market economies. However, China is not a free market economy yet. Is VaR and the corresponding Monte-Carlo simulation method suitable for China? In other words, does the VaR measurement using Monte-Carlo simulation work in China banking industry?

In order to answer this question, we test the monthly stock price risk of all the 16 listed banks from the year 2011 to 2015 using the VaR measurement based on Monte Carlo simulation. Our research finds that such VaR measurement is reliable in general. There are a few failures of VaR measurement in our study, especially in those years with significant market recessions. However, these VaR measurement failures are still acceptable in terms of yearly basis. Therefore, the VaR measurement based on Monte-Carlo simulation works in the Chinese banking industry.

We organize this paper in six sections: Section 2 for literature review, Section 3 for research methodology, Section 4 for sample description, Section 5 for Monte-Carlo simulation and test analysis, Section 6 concludes this paper.

There are three popular methods to calculate VaR, and they are the parameter method, historic simulation, and Monte-Carlo simulation. In the parameter method, the calculation of VaR bases on an assumption that the possible loss complies with a specified distribution, e.g. a normal distribution. However, Zangari (1996a, 1996b) points out that financial statistics do not follow a normal way in terms of the skewness with a fat tail. Therefore, the calculation based on the normal distribution assumption may underestimate the risk. Hull & White (1998) and Guermat & Harris (2001) use non-normal distributions and resolve the problem of fat tail.

The historic simulation and Monte-Carlo simulation are nonparametric approaches. One of the major advantages of using nonparametric methods are that they can avoid the misspecification of probability density functions of risk factors in an era of frequent financial disturbance (Yun and Powell, 2012) .

The historic simulation method assumes that the future loss goes in the similar pattern to its past. It does not request the distribution of loss in a normal way. Therefore, it bypasses the problem of fat tail (Jorion, 1997; Dowd, 1998) . However, another concern may arise. Stock prices in the nearer past, if compared with those in far history, usually have larger influences on how it performs today (Engle, 1982). However, the historic simulation method does not take time into consideration, which results in biased estimation.

The Monte-Carlo simulation method has the similar nonparametric characteristics with the historic simulation method, but it abandons the possibility of more extreme situation such as unexpected economic recession or booming. According to Jorion (1997) and Dowd (1998) , although Mont-Carlo simulation takes the nonlinear price risk and volatility risk into consideration, it has a limitation that the accuracy and reliability of the result heavily rely on the number of times in the simulation. The more number of times the simulation performs, the higher accuracy and reliability it achieves.

The Monte-Carlo simulation method also needs an assumption on the multivariate statistical distribution of price changes of the asset discussed, in this case the stock prices. This assumption comprises three factors?the expected change in value, the degree of uncertainty, and the type of distribution (Vlaar, 2000) .

Kupiec (1995) develops an approach to use the frequency of failures in risk management. This approach provides an easy way to evaluate the accuracy of VaR estimations. In this approach, a failure incurs when the actual loss exceed estimated VaR; a success happens when the actual loss is below VaR. In this way, we can compare the occurrence of success versus failures in large number of Monte-Carlo simulations. Then we can examine if the VaR measurement using Monte-Carlo simulation works.

Based on the above literatures, we use the Monte-Carlo simulation method in order to avoid the drawbacks in the parameter method and the historic simulation method. In this study, we also conduct large number of times of simulations to overcome the limitation of the Monte-Carlo method.

In this section, we construct the research methods and processes for the VaR measurement based on Monte-Carlo simulation.

Traditionally, risk is measured by the standard variance that suggests the instability. However, human beings are by nature risk-averse. Given a certain amount of gain or loss, people react more to loss than the gain. Loss brings larger suffering than the satisfaction that gain gives. From this perspective, VaR serves well for this concern because it defines risk as the possible worst loss instead of the variance.

In the calculation of VaR, a distribution of possible loss is firstly attained. This distribution is assumed to be the probable loss in the future. From the distribution, one comes out the possible worse loss in an investment given a certain level of significance (e.g. 5%). This possibly worse loss is the value at risk (VaR) of the investment. The mathematical expression is Equation (1) as below (Wang et al, 2000) :

In the equation, the variable loss means the losses in the holding period of an asset. The variable VaR is the value at risk under the confidence level of. The concept of loss in the definition of VaR should be taken as negative return^{2} to daily context. The calculation of VaR becomes easy when we attain the distribution of possible losses. Therefore, the most important preparatory work is to attain a distribution of loss. There are several methods for this purpose, the parameter method, historic method and Monte-Carlo simulation method. As Monte-Carlo simulation is more objective, we use Monte-Carlo simulation to evaluate its suitability or reliability in the Chinese banking industry. We expect to examine the reliability of the VaR measurement based on Monte-Carlo simulation.

We use two methods to evaluate the reliability: first, examining the frequency of VaR prediction failures. Then we can tell the percentage of VaR prediction failures. Second, checking the significance of the difference between a VaR prediction and the actual number. We predict the month-end stock price based on that at the beginning of a month using the VaR measurement based on Monte Carlo simulation. Then we can find out if the VaR measurement works.

Suppose that a stock price is S_{0} at the starting point, we simulate how this price changes in the following 20 transactional days (the average transactional days in a month in the China stock market, after removing weekends and public holidays). We use the Geometric Brownian Motion (GBM) in the underlying process. GBM is mostly described by a Stochastic Differential Model (SDE), which connects the prices of two adjacent time points. However, most SDEs do not have an unambiguous solution, in other words, they cannot offer an explicit relation between two adjacent stock prices. Therefore, we resort to the most frequently used SDE, which is Equation (2) as below:

The variable S_{t} indicates stock price in the time point of t, and

The exp expression of Equation (2) is a combination of various situations. The first part

there were no risk and volatility. The second part

The combination of the two parts depicts how a stock price is “ought” to be in the future. The last but most important part is

We use all the 16 banks listed in China stock market from RESSET financial database for the VaR measurement based on Monte-Carlo simulation. These banks are Bank of Beijing, ICBC Bank (Industrial and Commercial Bank of China), Everbright Bank, Huaxia Bank, CCB Bank (China Construction Bank), BOCOM (Bank of Communication), Minsheng Bank, Bank of Nanjing, Bank of Ningbo, ABC Bank (Agricultural Bank of China), Ping’an Bank, SPD Bank (Shanghai Pudong Development Bank), CIB Bank (Industrial Bank, abbreviated as CIB for historical reasons), CMB Bank (China Merchant Bank), Bank of China, CITIC Bank (Citic Industrial Bank). Data items include daily stock price, risk-free return, and daily volatility of a stock. The time period of the sample is from Jan. 2011 to Dec. 2015, totaling 60 months. We take a month (usually 20 transactional days) as the unit of time period for the Monte-Carlo simulation. In other words, we pick up the stock price of a bank at the beginning of a month, and then follow a GBM for 20 steps to reach the possible stock price at the end of the month. The difference between stock prices at the end and beginning of a month makes the return to an investment. Then we have simulated or forecasted return using predicted month-end stock price and actual return using actual month- end price.

We assume that the

At the end of every month, we repeat the process for 70 times^{3} for each bank, and attain 70 simulation results of stock prices for each bank of each month. Therefore, we can obtain 70 possible monthly returns from Monte-Carlo simulation for each bank of each month in the sampling period for further analysis.

For every bank of every month during the 5 sampling years, the 70 possible returns constitute a distribution that we are able to calculate the value at risk at the significance level of 95% (70 × 5% = 3.5). In this way, we have a value at risk for each bank of every month. We consider these values as the reference to the risk measurement at the beginning of a month for each bank because of the data availability at that time. In the meantime, we attain the real monthly returns to the same bank and the same month, and compare the actual returns the simulated VaRs to check the significance of their differences.

In this section, we conduct the Monte-Carlo simulation first, then compare the differences between the simulated / predicted returns to the actual ones.

We repeat the Monte-Carlo simulation for altogether 67,200 times (16 banks × 12 months × 5 years × 70 times per bank per month). Although we are not able to show all the results of the simulations, we can demonstrate one example of them as in

come less dense, or the less likely such price incurs. Secondly, the longer the dates are away from the starting date, the distribution of the lines becomes less dense, or becomes more random. It usually means to need much more number of simulations to predict the stock prices in the longer period of time.

The concept of VaR is based on a statistical distribution with a certain level of significance. Therefore, there are still definite possibilities that VaR fails to predict the real situation. A consequent question is how efficient VaR works in predicting risk. We answer to this question by a t-test of the gap between VaR and the actual return to stock prices. We demonstrate the result from two ways: the frequency of VaR failures, and the t-test results from the gap between the predicted and actual value.

These VaR failures reveal that, when the market is in a normal situation rather than in an extreme status, VaR is generally reliable as the reference to risk measurement. However, we do not think that the extreme market situation is the concern of VaR. The mechanism of unexpected recession in a stock market is intricate, and it is not likely for Monte-Carlo simulation to predict. In this perspective, it’s not a hasty conclusion that the Monte-Carlo simulation based VaR prediction is reliable in normal market situations.

Month Year | 3 | 5 | 6 | 7 | 12 | Total |
---|---|---|---|---|---|---|

2011 | 0 | 2 | 1 | 1 | 0 | 4 |

2012 | 1 | 1 | 2 | 2 | 0 | 6 |

2013 | 0 | 0 | 15 | 2 | 5 | 22 |

2014 | 0 | 0 | 3 | 1 | 0 | 4 |

2015 | 0 | 0 | 0 | 1 | 0 | 1 |

Total | 1 | 3 | 21 | 7 | 5 | 37 |

Note: Most banks have 0-3 times of VaR failures for the 12-month prediction except for June and December, 2013. On June 2013, the number of VaR failures is 15, 40.5% of total 37 ones; on December 2013, it is 5, 13.5%. On year 2013, it is 22, 59.4%.

Year Banks | 2011 | 2012 | 2013 | 2014 | 2015 | Total |
---|---|---|---|---|---|---|

Bank of Beijing | 0 | 1 | 1 | 1 | 1 | 4 |

ICBC Bank | 0 | 1 | 1 | 0 | 0 | 2 |

Everbright Bank | 1 | 0 | 2 | 0 | 0 | 3 |

Huaxia Bank | 0 | 0 | 2 | 0 | 0 | 2 |

CCB Bank | 0 | 0 | 1 | 0 | 0 | 1 |

BOCOM | 1 | 0 | 2 | 0 | 0 | 3 |

Minsheng Bank | 0 | 0 | 1 | 1 | 0 | 2 |

Bank of Nanjing | 0 | 0 | 1 | 0 | 0 | 1 |

Bank of Ningbo | 0 | 0 | 1 | 0 | 0 | 1 |

ABC Bank | 0 | 0 | 2 | 0 | 0 | 2 |

Ping’an Bank | 0 | 0 | 1 | 1 | 0 | 2 |

SPD Bank | 1 | 1 | 1 | 0 | 0 | 3 |

CIB Bank | 1 | 0 | 2 | 0 | 0 | 3 |

CMB Bank | 0 | 2 | 1 | 0 | 0 | 3 |

Bank of China | 0 | 1 | 2 | 1 | 0 | 4 |

CITIC Bank | 0 | 0 | 1 | 0 | 0 | 1 |

Total | 4 | 6 | 22 | 4 | 1 | 37 |

Note: Most banks have 0 - 2 times of VaR failures for the 12-month prediction of a specific year. In terms of the sampling period, four banks have the lowest number of VaR failures, 1 time only; two banks have the highest number of VaR failures, 4 times.

Year Bank | 2011 | 2012 | 2013 | 2014 | 2015 | |
---|---|---|---|---|---|---|

Bank of Beijing | 0.107** | 0.123** | 0.147** | 0.172** | 0.231** | |

ICBC Bank | 0.086** | 0.065** | 0.069** | 0.108** | 0.174** | |

Everbright Bank | 0.075** | 0.096** | 0.111** | 0.180* | 0.243** | |

Huaxia Bank | 0.145** | 0.133** | 0.139** | 0.183** | 0.245** | |

CCB Bank | 0.085** | 0.079** | 0.087** | 0.137** | 0.204** | |

BOCOM | 0.081** | 0.108** | 0.098** | 0.179** | 0.216** | |

Minsheng Bank | 0.131** | 0.132** | 0.173** | 0.172* | 0.189** | |

Bank of Nanjing | 0.116** | 0.115** | 0.133** | 0.176** | 0.292** | |

Bank of Ningbo | 0.112** | 0.157** | 0.158** | 0.187** | 0.276** | |

ABC Bank | 0.075** | 0.087** | 0.083** | 0.130** | 0.172** | |

Ping’an Bank | 0.170** | 0.167** | 0.200* | 0.204** | 0.175** | |

SPD Bank | 0.087** | 0.117** | 0.175** | 0.174** | 0.231** | |

CIB Bank | 0.094** | 0.150** | 0.159** | 0.193** | 0.219** | |

CMB Bank | 0.101** | 0.120** | 0.131** | 0.153** | 0.199** | |

Bank of China | 0.059*** | 0.066** | 0.075** | 0.130** | 0.230** | |

CITIC Bank | 0.133** | 0.128** | 0.157** | 0.243* | 0.217** |

Note: ***stands for significance level at 1%, **at 5%, and *at 10%.

Therefore, the Monte-Carlo simulation based VaR measurement does work reliably for the prediction of stock prices in all the listed 16 Chinese banks. However, one may have another concern: are these results heavily relying on the repetition number of the Monte-Carlo simulation?

We change the repetition number of Monte-Carlo simulation and examine the implication to the performance of VaR.

The concern may come from the number of simulation (limited to only 70 times in the previous tests). This may result in a biased distribution of the simulation results. In order to reinforce the results, we enlarge the number of Monte- Carlo simulation from 70 to 1,000 times, and conduct the whole process again.

From these tables, the occurrence of VaR failures does not vary drastically compared to

We study the reliability of VaR based on Monte-Carlo simulation using all the listed 16 Chinese listed banks of the year 2011-2015. The result reveals that VaR based on Monte-Carlo method works in Chinese banking industry especially when there is no drastic unexpected recession in the market. Even in the year with great market recession, the performance of VaR is still acceptable from the perspective of the whole year. Therefore, we believe that the VaR based on Monte-Carlo simulation works in China banking industries.

Month Year | 3 | 5 | 6 | 7 | 12 | Total |
---|---|---|---|---|---|---|

2011 | −1 | −1 | ||||

2012 | +1 | −1 | ||||

2013 | +1 | +1 | ||||

2014 | +1 | +1 | ||||

2015 | ||||||

Total | −1 | +2 | −1 | +1 | +1 |

Note: −1 (+1) indicates that the occurrences of VaR failures by 1000 simulations less that of 70 simulations in

Year Stock | 2011 | 2012 | 2013 | 2014 | 2015 | Total |
---|---|---|---|---|---|---|

Bank of Beijing | ||||||

ICBC Bank | +1 | +1 | ||||

Everbright Bank | −1 | +1 | ||||

Huaxia Bank | +1 | +1 | ||||

CCB Bank | +1 | +1 | +2 | |||

BOCOM | ||||||

Minsheng Bank | ||||||

Bank of Nanjing | ||||||

Bank of Ningbo | ||||||

ABC Bank | ||||||

Ping’an Bank | ||||||

SPD Bank | −1 | −1 | ||||

CIB Bank | ||||||

CMB Bank | −2 | −2 | ||||

Bank of China | ||||||

CITIC Bank | ||||||

Total | −1 | +1 | +1 | +1 |

Note: −1 (+1) indicates that the occurrences of VaR failures by 1000 simulations less that of 70 simulations in

Although there are significant advantages for the VaR measurement using Monte-Carlo simulation, the method still has some challenges. Staum (2009) summarizes two main challenges from the computational perspective. Firstly, this VaR measurement method focuses on the left tail of the distribution. It is worthwhile to pursue variance reduction. Secondly, it may lead to a computationally expensive nested simulation, and it is worthwhile to explore approaches to make the simulation computation more efficient.

From beyond the computational perspective, there are another two shortcomings when using Monte-Carlo simulation to measure VaR. Firstly, Monte- Carlo simulation seems not working well under extreme economic environment like a recession in stock market (more failures in forecasting). Secondly, Monte- Carlo simulation seems unable to factor the behavioral irrationality of market participants.

Monte-Carlo simulation in risk management is an active area of research. Many researchers have been striving for improving the approaches of using Monte-Carlo simulation to measure VaR. We believe that these improvements would make the approach work better for VaR measurement.

These authors thank for the funding support from the Science Research Foundation of Renmin University of China, Project No. 15XNI010.

Wang, D. H., Song, J. B., & Lin, Y. Z. (2017). Does the VaR Measurement Using Monte-Carlo Simulation Work in China?―Evidence from Chinese Listed Banks. Journal of Financial Risk Management, 6, 66-78. https://doi.org/10.4236/jfrm.2017.61006