Construction of tourism investment risk management model combining big data

The presence of financial risks is a significant aspect of modern financial markets. In recent years, crises in international financial markets and a number of domestic financial events in China have been the consequence of financial risk.

Financial risk is the uncertainty of loss suffered by the actor. Financial risk is often associated with loss. This includes two levels of meaning. First, for an event in financial activity, as long as it has the possibility of loss, it indicates the existence of financial risk, but this does not mean that the possibility of profit does not exist for the visiting event. Secondly, financial risk refers to a possibility, a future event whose outcome is not known.

The cause of financial risk is uncertainty in financial activities. Uncertainty includes “external uncertainty” and “internal uncertainty”. External uncertainty comes from outside the economic system is the process of economic operation, random, accidental changes or unpredictable trends, such as macroeconomic trends, the market supply and demand for funds, the political situation, technology and resource conditions. Intrinsic uncertainty originates from within the economic system and is caused by the subjective decision-making of the actors and the inadequacy of the information they obtain, etc., and is characterised by a clear individuality.

The impact of financial risk on economic activity is complex, and the factors that contribute to it are many and varied. There are various types of financial risks and many ways to classify them. The most common is to divide them into direct and indirect risks according to the content of the risks. Direct risk refers to the risks that need to be directly addressed in investment activities or actual business, mainly market and credit risks. Indirect risk refers to risks that are not directly related to actual business activities but affect the return of an investment entity indirectly. Indirect risks include liquidation risk, liquidity risk, operational risk, legal risk, credit risk, etc.

Risk management, also known as crisis management, is a management process that involves defining, measuring, evaluating, and developing strategies to cope with risks. [24]. The aim is to minimize avoidable risks, costs, and losses. Ideally, risk management is prioritized so that the events that cause the greatest losses and have the highest probability of occurring are dealt with first, followed by events with relatively low risk. In practice, it is difficult to decide on the order of priority because the risk and probability of occurrence are often not the same. Therefore, it is necessary to weigh the two options to make the most appropriate decision. For modern enterprises, risk management is the process of identifying, measuring, forecasting, monitoring and reporting to manage risks and adopting effective methods to reduce costs and deal with risks systematically in order to ensure the smooth operation of the enterprise. This requires the enterprise to identify possible risks in the course of business and to predict the negative impact on resources and operations after the occurrence of various risks in order to ensure the smooth running of production. Thus, risk identification, prediction, and treatment are the main steps of enterprise risk management.

Risk prediction is actually the estimation and measurement of risks, whereby the risk manager applies scientific methods to systematically analyse and study the statistical data, risk information and the nature of the risks at his disposal in order to determine the frequency and intensity of the risks and to provide a basis for choosing the appropriate risk treatment method.

VaR method, also known as the Value at Risk method, refers to the maximum possible loss of an asset or portfolio over a specific period in the future at a certain probability level of confidence [25-26]. The period selected here can be one day, one week, two weeks, one month, etc., while the probability confidence level set is generally 90% to 99%. Using this concept, the market risk of positions of various sizes in the financial markets, from a single asset to multiple assets or even multiple asset classes, from a single traded position to a portfolio of trades, or an entire business or even an entire industry, can be analysed and measured.

The VaR definition can be expressed using the following equation: (1)Prob(ΔP>VaR)=1−β

Where ΔP is the loss of the financial asset or portfolio over the holding period Δt and VaR is the value at risk with confidence probability β. The use of VaR makes it possible to quantify the risk to which an asset is exposed, giving risk managers an intuitive reference for judgement and decision-making.

There are two important parameters in the definition of VaR - the holding period and the confidence probability - for different holding periods and confidence levels different VaR values will be obtained, and any calculation of VaR is meaningful only if these two parameters are given. Therefore, before analysing the VaR of a financial asset it is necessary to first determine the future holding period of the asset and the level of confidence in the probability of risk that is acceptable to the risk manager.

Equation (1) gives only the basic concept, and in practice, it is often defined in other ways.

Now suppose an asset or portfolio, P₀ for the initial value of the portfolio, R for the holding period of the rate of return, then in the holding period of the portfolio value will be P=P0(1+R) , where the expected value of R is μ, volatility is σ, defined at a given confidence level β under the minimum value of the portfolio is P*=P0(1+R*) , VaR can be divided into relative VaR and absolute VaR. the difference between the expected value and the minimum value for the relative VaR. The difference between the beginning value and the minimum value is called absolute VaR. i.e.:

Relative VaR: (2)VaR=E(P)−P*=−P0(R*−μ)

Absolute VaR: (3)VaR=P0−P*=−P0R*

From the above, finding the value of VaR is actually finding the minimum value of an asset or portfolio at a certain confidence level P^* or the minimum return R^*.

The solution to the minimum value P^* or the minimum yield R^* can be obtained directly from the quantile if the historical method or Monte Carlo simulation is used: if the parametric method is used, it is usually necessary to assume the distribution of the yield [27].

The most important feature of the Value at Risk (VaR) model is that it shows the risk that an organisation is exposed to in the market in a simple and understandable figure, and because of this, VaR has become the main tool used by financial and investment institutions to measure trading risk. Typically, VaR can be estimated from a probability distribution using one of two methods: 1) deriving the VaR value from an empirically derived distribution. 2) approximating the distribution with a normal curve, in which case the VaR is derived from the standard deviation only. These processes, sometimes referred to as “reality checks”, are important for regulators to ensure that VaR models within financial or investment institutions are not systematically biased in favour of one party.

The first step in measuring VaR is the selection of two quantitative factors: the length of the underlying time interval and the confidence level. The selection of these two factors is somewhat arbitrary. 1)

VaR in a general distribution

To calculate the VaR in a portfolio, define: W₀ as the initial investment amount and R as the return on investment, so that the value of the portfolio during the target period will be W=W0(1+R) . As before, here the expected return and the volatility of the return are μ and σ, respectively.

Define the minimum value of the portfolio at a given confidence level c as: W*=W0(1+R*) .

Define VaR as the loss of the portfolio, i.e., related to zero and independent of the expected value, then: (4)VaR(Zero)=W0−W*=−RW0

In this case, finding the minimum value or minimum return on investment is equivalent to finding the VaR. The most common form of the VaR can be obtained from the probability distribution of the future portfolio value f(w). At a given confidence level c, the least probable W^* can be found, i.e: (5) c=∫W*∞f(w)dw

Or expressed as a probability ρ=P(W≤W*) of 1 − c below W^*. (6)1−c=∫−∞w*f(w)dw=P(W≤W*)=p

The standard deviation is not used here to find VaR, which is valid for any continuous or interval distribution. 2)

VaR in parametric distribution

In a normal distribution, the calculation of VaR can be greatly simplified by obtaining it directly from the standard deviation of the portfolio, taking into account a multiplier that depends on the confidence level. This method is known as the parametric method because it incorporates the estimation of the standard deviation and the parameters, rather than the quantile from an empirically obtained distribution.

The general distribution f(w) is first transformed into a standard normal distribution Φ(ε), ε having the meaning of zero and unit standard deviation. Expressing W^* in terms of the minimum return R^* yields W*=W0(1+R*) . R^* is usually negative and can be written −|R*| , and further R^* is used to denote the standard normal deviation α > 0.

−α=|R*|−μσ is equivalent to setting: (7)1−c=∫−∞W*f(w)dw=∫−∞|R*|f(r)dr=∫−∞−αΦ(ε)dε

In this way, the problem of finding the value-at-risk VaR translates into deviating from α so that the area to the left of it is equal to 1 − c. This can be done by using the table of cumulative standard normal distribution functions, where the values represent the area to the left of the standard normal variable in position d: (8)N(d)=∫−∞dΦ(ε)ε

To find the standard normal variable VaR, the desired confidence level is chosen, e.g., a 95% confidence level corresponds to a value of α of 1.65, which allows the calculation of the minimum rate of return R^* = −ασ + μ. To be more general, parameters σ, μ can be obtained assuming that they are based on a yearly basis, with time interval Δt: (9)VaR=−W0(R*−μ)=W0ασΔt

In other words, the VaR value is the product of the standardised variance for a given distribution and an adjustment factor directly related to a confidence level. When VaR is defined as absolute loss, the formula is: (10)VaR(0)=−W0R*=W0(ασΔt−μΔt)

This approach is applicable to normal and other cumulative probability distribution functions as long as σ all uncertainties are included. The other distributions do not limit the different values of α. The normal distribution is the easiest to deal with as it represents many empirical distributions. This approach is particularly suitable for portfolios with large sample sizes and high levels of diversification, but not for portfolios with a large proportion of options and fewer financial risks.

1)

Basic Definition

A portfolio is a combination of a certain number of risk factor holdings [28]. When disaggregated, the return of a portfolio is a linear combination of the returns of the various underlying assets, with the weight of each asset determined by the proportion of the initial investment in that asset. The VaR of the portfolio can then be had derived from the risky combination of the various marketable fund shares it contains:

The return of the portfolio during the period from time t to t + 1 is: (11)Rp,j+1=∑j=1Nwi,jRi,j+1

Here the weighting coefficients w_i,t are initially determined and sum to 1. Simplifying the expression in matrix form: (12)Rρ=[w1w2⋯wN][R1R2⋮RN]=W′R

where w′ represents the transpose of the vector of weight coefficients and R represents the longitudinal measure of individual asset returns.

The return expectation of the portfolio: (13)E(Rρ)=μ=∑i=1Nwipi

The variance is: (14)V(Rρ)=σρ2=∑i=1Nwipi+∑i=1N∑i=1,j,j=1Nwiwjσ=∑i=1Nwi2σi2+2∑i=1N∑j=1Nwiwjσ

This result illustrates not only the risk of individual fund shares σt2 but also the risk of any two different assets, i.e., cross terms, for a total of N(N−1)/2 different covariances, represented by the matrix: (15)σp2=[w1⋯wN[σ112⋯σ1N2⋮⋯⋮σN12⋯σNN2][w1⋮wN]

With Σ representing the covariance matrix, the portfolio variance can be abbreviated as: (16)σp2=W′∑W

Using a normal distribution yields a value of VaR that is ασ_p times the initial investment.

Portfolio risk can be reduced in two ways: by combining assets with low correlation, and by increasing the number of asset classes.

If the portfolio variance is expressed in terms of VaR, it is necessary to know the distribution of portfolio returns. In the “Δ-normal” model it is assumed that the returns on individual assets are normally distributed. Since the portfolio is the result of a linear combination of random variables, it is natural to assume that the portfolio returns are also normally distributed. For a given level of confidence, the portfolio’s VAR = ασ_p. 2)

Incremental VaR

Calculating VaR is all about understanding which portfolio poses the most risk. With this in hand, it is possible to effectively correct the VaR value by adjusting the share of individual assets. To achieve this goal, it is not enough to have the VaR of individual assets; in the case of individual assets, volatility measures the uncertainty of the return of that asset, which will have an impact on the risk of the portfolio when that asset becomes part of the portfolio.

Assume that a portfolio is composed of N − 1 marketable fund shares labelled j = 1, 2, …, N − 1 respectively. Adding a security i to the portfolio yields a new portfolio with marginal risk induced by the addition of an asset. This can be obtained by differentiating the variance equation V(Rp) with respect to w_t: (17)∂σp2∂wi=2wiσi2+2∑j=1Nwjσj2