Applications of Risk Analysis in the Financial Sector

RISK ANALYSIS

Abstract

This review paper presents the applications of Risk analysis in the financial sector. Financial risk analysis is an important tool for companies for decision-making processes, which has played a significant role during and after the financial crisis. This paper presents an overview of financial risk analysis, explaining its main types, and showing how each of them can be measured. The final part focuses on the importance of this analysis, considering its effects during the financial crisis.

1   Introduction

The history of risk analysis is ancient. Around 3200 B.C., a group called Asipu used to be consultants for decisions involving risk. They studied the problem, collected data and presented different alternatives, assigning likely outcomes to each of them. Another example is the use of the risk assessment by the Athenians, as cited during the Pericles’ Funeral Oration:

We Athenians, in our own persons, take our decisions on policy or submit them to proper discussions: for we do not think that there is an incompatibility between words and deeds; the worst thing is to rush into action before the consequences have been properly debated. And this is another point where we differ from other people. We are capable at the same time of taking risks and of estimating them beforehand.

In previous years, in order to assess the risk, many developed mathematical methods that are used to estimate the effect of one action, but there is still a link between the past and the present, that is the basic form of the trial and error method [1]. Nowadays, our society is built on risk management and every field has its own risk modelling: in medicine, for example, it is used to analyse the effect of a treatment on a disease; in engineering, many constructions would not exist without the risk assessment, neither all the modern technology that we have.

With the economy, it is important to analyse the risk of a decision, i.e. the introduction of new market policy, price changing, investment risks and so on. In finance, the management sector looks at the wealth of the company, trying to estimate the effect of the interaction with external and internal factors.

This review paper is organized as follows: section 2 presents a brief overview of risk analysis and financial risk; section 3 illustrates the main financial risk types, defining each of them, and presenting an overview of some quantitative methods to calculate them. In section 4, the case study focuses on the financial crisis, and it shows the importance of the right management of these indicators, especially for credit and liquidity risk. Furthermore, some regulations about it are discussed and compared. Section 5 summarizes the paper, concluding with a personal review.

2 Risk Analysis

Risk analysis can be defined as the process of identifying sources of potential negative outcomes and estimating the likelihood, in order to define which outcome requires actions and how to implement them. Giving a quantitative definition of risk [2]:

It can be defined as a triplet (S_i, P_i, X_i), where S_i a scenario identification or description, P_i is the probability of that scenario, and X_i is the consequence or evaluation measure of that scenario, i.e., the measure of damage.

The following table shows all possible scenarios with the related likelihood and consequence.

The risk analysis process can be summarised:

2.1 Financial Risk

Risk assessment is essential for financial institutions, and without effective risk management the company would fail: the financial crisis is an example. Financial risk analysis aims to reduce the effects of market price fluctuations, the negative impact of internal and external factors, and to prevent crises as bankruptcy. It can be divided into different categories, based on the type of risk that might affect the company, and on the type of the organization. The main categories are:

– Market risk

– Liquidity risk

– Credit risk

– Operational risk

Due to the fact that an organisation faces many risks, the measurement process is not unique. A good framework is to calculate an absolute risk value aiming to price it, to allocate capital to cover the excepted losses, and to identify how to reduce the risk with a minimum capital charge.

Nowadays, many methods are used as described in the next section, but it is essential to have a critical approach on quantitative methods, because the risk analysis is not a precise science [3], and the excessive dependence on these methods can result in crisis (case study). In order to preserve the company health, it is important to confront its own results with the market ones. Institutions as banks have their own set of rules, one of these is Basel regulation. It has been emitted by Basel Committee on Banking Supervision, and three different accords have been developed, Basel I (1988), Basel II(2004) and Basel III(2010). These regulations represent an obligation for the banks in terms of capital requirements, risk requirements (credit risk, operational risk, market risk), supervision and reporting. This set of rule has played an important role during the financial crisis; as a result, from the Basel II weakness, a further extension, Basel III, was developed.

3 Market Risk

It is the risk that an investor (company or individual) could face losses due to fluctuations in the market. It includes different events that could affect the market value, e.g. natural disaster, political instability, terrorist attacks.

The main technique to measure the risk is the “Value at Risk” (VAR). In recent years, it has become the most popular and simplest method to predict losses of an asset, portfolio, or even an entire firm. It measures the maximum average of loss in a defined time. There are many different applications of VAR, most of those consider the historical value to predict the loss, using the probability density functions (PDF), which restrict the prediction for future risk measurements.

If W is the initial portfolio investment, μ be the average return, and R* be the rate of return at a particular confidence level, c, the VAR expression can be expressed as:

$\mathit{VAR}=–W_0\left(1+\mu \right)–W_0\left(1+R^{*}\right)=–W_0(R^{*}–\mu )$

The key is to find the correct cutoff return, R*, [4].

Two methods are used to find it, parametric and non-parametric.

Parametric methods are divided into two groups: Gaussian distribution and Non-Gaussian, the first one is not used frequently because the financial returns do not follow a normal distribution and are characterized by heavier tails and a higher peak than a normal distribution[5]. For Non–Gaussian methods, there are many techniques, two of those are T-student distribution and ARCH method.

Non-parametric method uses the historical returns to predict the new ones so it could not be precise because the future could change from its previous path.

T-test for VAR can be expressed as:

     $\mathrm{ }{\mathit{VAR}}_{t+1|t}=F\left({\left\{\frac{{\mathrm{ϵ}}_{t+1–r|t}}{{\mathrm{\sigma }}_{t+1–r|t}}\right\}}_{r=1}^m;a\right){\mathrm{\sigma }}_{t+1|t}$

Where F (.;a) is the corresponding a^th quantile, σt+1|t is the one‐day‐ahead conditional standard deviation forecast, and ϵt+1|t is the innovation process under a given time horizon, m is the mean of the non‐standardized skewed Student‐t distribution.

Under the t-distribution the tail behaviour depends on the tail index, Bormetti et al. (2007) pointed out that highest sensitivity and fat-tails are related weigh high value of v ( degree’s freedom) of the T-student distribution.

Another method related to T-test is Arch method, which its aim is to capture fat tails and to take conditional volatility in account, for a changing return distribution over time [4].

In Huang, Y. and Lin, B. (2004) research, it is demonstrated that bad news have more effect in increasing future volatility than positive shocks caused by good news.

The generalized model can be expressed as:

$h_t^2={\alpha }_0+\sum _{i=1}^q{\alpha }_i{\epsilon }_{t–i}^2+\sum _{i=1}^p{\beta }_i{h}_{t–i}^2$

Where ${\epsilon }_{t–i}^2$

 is the sample variance, and $h_{t–i}^2$

 is the conditional variance, at time t.

It estimates today’s volatility using a combination of yesterday’s volatility and the squared value of yesterday’s return.

To test if the VAR of a company respects the econometric reliability requirements, the backtesting method is used. It consists on counting the number of exceptions that lie outside the theoretical expectation, then the ratio of exceptions to total that lie within the 99 per cent coverage is determined. Then compare this value with the actual risk levels in the market [6]. 

3.1 Operational risk

Operational risk is defined as the risk of losses due to a failure of a company’s internal sector, it can be caused by employee’s defaults, systems or some external factor as legal risk [7].

Operational risk is different because it is actually from the interior of the company. There are two types of operational risk, the first is “system”, i.e. error in back office and legal procedures, the other one is “agency” e.g. mismanagement [8].

From a mathematical point of view, firstly, we assume that the firm’s value has no cash flows. It means that all revenues generated within the firm are reinvested and not distributed as dividends [7].

Secondly, we assume that a firm is operating in technology, so it means that transforms the assets in more valuable objects. Following this assumption, the starting portfolio value at time t is $S_{t0}$

 , π (t)represents the increasing value due to operating in technology at time t, the aggregate portfolio value $S_t$

is:

$S_{t0}*\pi \left(t\right)=S_t$

Where π (t) is the net present value (or NPV).

For the “system” operational risk category , let  N₁(t) be  doubly stochastic (Cox) counting process, that counts the number of system operational risk events that occur between time 0 up to and including time t, and an operational risk event at time t causes a percentage reduction in firm value equal to  ${\delta }_1\left(X_t\right)<0$

. 

So:

${\theta }_1\left(t\right)= \prod _{i=0}^{N_1\left(t\right)}(1+{\delta }_1\left(T_i\right))$

Where ${\theta }_1\left(t\right)$

represents the risk of loss due to a default in the system.

For the “agency” operational risk category , the formula changes in N₂(t) , and the reduction in firm value equal to ${\delta }_2\left(X_t\right)<0$

. So:

${\theta }_2\left(t\right)= \prod _{i=0}^{N_2\left(t\right)}(1+{\delta }_2\left(T_i\right))$

Where ${\theta }_2\left(t\right)$

represents the risk of loss due to an agency default.

Assuming for simplicity that the firm is managed by an agent, and the internal valuation of the portfolio at time T is:

$V_t=S_t*\pi \left(T\right)* {\theta }_1\left(t\right)*{\theta }_2\left(t\right)$

Then for the market value of the firm’s asset, we assume that the market for these assets is arbitrage free so that there exists an equivalent martingale probability measure Q:

$V_t=E_t^Q\left\{S_t*\pi \left(T\right)* {\theta }_1\left(t\right)*{\theta }_2\left(t\right)*e^{{\int }_t^T{r}_c\mathit{dv}}\right\}$

Where $E_t^Q$

is under martingale probability and r_t denote the default free spot rate of interest.

So far, these estimations assume that is possible to calculate operational risk using market prices, but the reality is more complex. As a result, another efficient method to estimate operational risk parameters has been developed:  using both data internal to the firm and collections of internal data aggregated across many firms, the analyst look at two databases as the Operational Riskdata Exchange Association (ORX) and OpVantage [7].

3.2 Liquidity risk

Liquidity risk refers to the inability of a company (firms or banks) to trade an asset (shares, bonds, goods, etc.) in short time, due to a lack of buyers or a default in the market, without erasing its capital and/or income. For example, if a company owns an asset of 5’000GBP, and it needs to sell it quickly but its value in the market decreases, it cannot be sold without losing capital.

There are two different types of liquidity risk: market liquidity risk and funding liquidity risk.

Market liquidity risk refers to the risk that an asset cannot be sold without affecting significantly the market price.

Funding liquidity risk refers to the risk that an institution is unable to settle its liabilities in a short time.

In this section only the market liquidity risk is analysed.

There are traditional methods [9] that can be used in order to quantify the market liquidity risk:

-The bid-ask spread refers to the difference between ask price and the bid price. It can also be expressed in percentage. A low value of this measurement means liquid assets, indeed the bid-ask spread in the currency market is around 0.01%, so 1% means poor liquid assets.

-Depth refers to the number of shares that can be bought without causing a price appreciation, so if the market depth is huge, there will be enough buyers and sellers and the price will not significantly change.

– Resiliency [10] refers to the ability to act a transaction with  minimum influence on the price while taking into account the elasticity of supply and demand of the market. Basically, it is the time that the market needs to go back from incorrect price due to a reaction to large order flow imbalances instigated by noise traders. Therefore, a market is resilient if the traders believe that a price movement adjusts quickly to the price oscillations.

These are the basics and theoretical to analyse  liquidity risk, but there are more sophisticated market risk measurements. For example, one of those is to combine the VAR method with bid-ask spread [11] and since it uses the same method as listed in the market risk section, it is not developed in this section.

3.3 Credit Risk

Credit risk refers to the risk of loss due to borrower’s non-fulfilment. Given a number of borrower companies or individuals that could be labelled as good/bad credit, credit risk aims to estimate the probability of default that can be used for evaluating the performance of a sample of credit risk portfolio [12].

There are two types of decision that a company has to make, the first is about granting credit to new applicants, and the second one is how to act with existing customers. For the first decision, credit scoring methods are used, for the second one, behavioural scoring techniques are used.

3.3.1 Credit Scoring

There are different methods to estimate credit risk. Such as:

 -Statistical methods as univariate methods, survival analysis, classification tree, discriminant analysis or essentially linear regression, and logistic regression.

-Operational research methods as linear programming [13].

-Neural method [14] which is a technology that offers significant support in terms of organizing, classifying, summarizing data, and requires few assumptions achieving a high degree of prediction accuracy.

There are many other newly developed techniques but the above listed are still used. Capon, N. (1982) [15] highlights that in credit scoring there is not a precise method to use, but it depends on if the technique works on that case.

An example of a statistical method:

-          Survival analysis is a statistical technique which its aim is to estimate when an event of interest will occur, the probability of surviving at one event through the time. Suppose that T is the length of time before a facility defaults, the probability that the default will occur in time t is:                                       

$f\left(t\right)=\underset{∆t\to 0}{\lim }\left(\frac{\mathit{Prob}(t\le T\le t+∆t}{∆t}\right)$

Another way to use survival analysis is the hazard function which aims to estimate the probability that the event immediately affects the facility after a defined time t:

$h\left(t\right)=\frac{f\left(t\right)}{1–F\left(T\right)}=\frac{f\left(t\right)}{S\left(t\right)}$

Where f(t) is the time to (first) failure distribution and S(t) = 1- F(t),  the probability of no failure before time t. So the probability of default increases by the time as shown below.

In this case, this method aims to estimate the likelihood of customer’s default based on time, other tools as linear and logistic regression estimate the outcome using explanatory variables ( i.e. past defaults, income, age, civil state).

3.3.2 Behavioral scoring

[13] Its aim is to decide the credit limit to lend, whether to give new products to customers and if the account turns bad how to manage it. Behavioural scoring models are divided into two different approaches: one uses credit scoring models with additional variables which describe the behaviour, while the other one looks at the probability models of customer behaviour, and it is a Markov chain.

Behavioural scoring tries to estimate the state of a customer after a period, which its estimation is crucial to build a strong model.

The probability models classify different consumer’s states, using variables that describe current and recent behaviour as balance outstanding, number of periods since  payment was made, and average balance.

A practical example built on this is [13]:

A customer is paying and ordering new products at the same time. The states that describe the customer account are u=(b,n,i), where b is the balance outstanding, n is the number of periods since the last payment and i is any other relevant information. Assuming that the aim is to set the credit limit L, and that the account performance may be affected by the limit.

It is necessary to estimate the probability p^L (u,u’) and r^L (u’), where p^L (u,u’)  are the probability of the account moving form state u to u’ under a credit limit L in the next period ,and r^L (u) is the likely reward obtained in that period. These can be estimated using:

-          t^L (u,a), the probability that an account in state u with credit limit L repays a next period;

-          q^L (u,o), the probability that an account in state u with credit limit L orders o next period;

-          w ^L (u,i), the probability that an account in state u with credit limit L changes its information state to i’.

After this estimation, with dynamic programming, it is demonstrated to find Vn(u), the expected profit over n periods given the account is state u, so the optimal credit limit policy can be calculated by solving the optimality equation:

$V_n\left(u\right)={\mathit{max}}_L\left\{r^L\left(u\right)+{\sum }_u{p}^L\left(u,u^{‘}\right)V_{n–1}\left(u^{‘}\right)\right\}$

4 Case Study

-          Financial crisis

The crisis that took place in 2008 has caused significant  financial sector crises. Among the other causes, there were excessive risk-taking incentives, so in observance of risk regulations, failure of risk management, and major focus on financial sector over the economic growth.

 Before the crisis many banks had invested in credit risk management improvement, as innovative models, techniques, process to monitor and to quantify their credit risk.  Besides, they had  regulations about regulatory requirements, and followed the idea to optimize risk management  by quantitative models [18].

In Ashby, S. (2010) research [16], an interview with 20 financial professionals was conducted, and it shows that there was not a “failure” in risk management, but:

-The management of low probability high impact events.

 -Use of enterprise-wide risk management frameworks that can be very difficult to implement effectively.

 -Excessive dependence on complex quantitative risk assessment tools, which were too difficult for non-experts to understand.

-Poorly implemented risk appetite frameworks that exposed financial institutions to a level of risk over their capacity to manage it.

Furthermore, the management had lack in areas such as back-testing, stress testing, wrong way risk, and scenario analysis, which are important tools to reveal hidden risks.

In  Cannata, F. and Quagliarello, M. (2009) study [17], other causes have been related to the Basel ll regulation , specifically:

-          The level of capital required  was inadequate;

-          The assessment of credit risk was delegated to non-banking institutions, such as rating agencies, subject to possible conflicts of interest;

-          The key assumption that banks’ internal models for measuring risk exposures were superior to any other has proved wrong;

-          It provided incentives to intermediaries to separate from their balance some very risky exposures.

After the crisis, the new Basel III has been developed and it has changed risk regulation. The main changes have concerned the definition of higher Risk Weighted Assets (RWA), the new Credit Value Adjustment (CVA) charge, identification of Wrong Way Risk and upgrading stress test [18].

Besides, many researchers have agreed with the relation between credit risk and liquidity risk. Indeed, Basel III highlights the importance of evaluating the asset quality, and credit risk taking in consideration liquidity risk management.

As a result, the new approach aims to analyse the data not just from a quantitative point of view, and to underline the importance of introducing reverse stress tests, scenario analysis, and risk measurement models for structured credits [19].

5 Conclusion

Risk analysis has ancient origins, and it has been used as an essential tool for the decision-making process. During its history, it has experimented different developments and applied to many fields with complex or simpler methods. Theoretically, it can be used even with simple approaches, i.e. when we choose which clothes to wear, we actually use a risk analysis approach: in fact, checking the weather forecast we choose the best outfit based on the most likely weather, so we actually give “a score” to each outfit.

When it comes in sectors like finance, the complexity is essential, in the sense that many factors must be taken into consideration, and to use efficient methods. In this paper, different authors and theories have been revised, besides, the methods described do not represent the totality but just a part of it. Another point to highlight is that the different types of financial risk have been treated separately, but in reality, some of them are combined to analyse a particular situation (i.e. credit risk and liquidity risk for banks, see the case study). Financial risk is not a pure science [3], because there is not a unique method to measure the risk, and each method can be applied to some cases while not in others, so the financial analyst has to use a critical approach, not based only on quantitative methods, even with the most innovative ones. Furthermore, the past events teach us not to underestimate the risk assessment and to simplify the language in order to communicate effectively the results to other departments. There is another issue to underline, especially when it comes in credit scoring. The aim of it as discussed in section 3 is to “score” the customer (companies or individuals) in order to understand if it will be a “good” credit. Institutions as banks, when they come to set it, use customer databases, where data as how and where customers spend their money, past defaults, civil state, address and so on. Each data has its own particular significance, for instance: the address is a wealth parameter, in the sense that customers can live in a wealthy zone, so it is likely that the customer is wealthy; the way that customers spend their own money can be used to analyse what type of loan or credit card limit can be applied. There are other variables that do not depend on customers, and on the company’s side it is important to categorize its customers in order to avoid defaults, however, it would seem to be a too objective approach. Other companies use scoring methods to employ the best employees.

To conclude, financial risk analysis has played a great role in our society, as finance is common for many companies, and as the innovation in this field is constantly growing, it is important to adapt it to the continuous development of society, adopting a broad vision, and using  variety of methods  depending on the type of risk that companies face.

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