Principles Of Risk Management PDF

PRINCIPLES OF RISK MANAGEMENT Directed by: Jesús M. López Zaballos | Chairman, European Federation of FinancialAnalyst Societies Collection: EFFAS Manuals 4 Block Certification Path Collection Coordinators: Jesús M. López Zaballos | Chairman, European Federation of Financial Analyst Societies Prof. Dr. Leef H. Dierks | Professor for International Capital Markets, Lübeck University of Applied Sciences Dr. Valeria Fauner | Director Training & Qualifications, European Federation of Financial Analyst Societies Jorge Valencia | Training & Qualifications, European Federation of Financial Analyst Societies Authors: Roberto Knop Muszynski | (PhD, CESGA, MRICS). Associate Director Analistas Financieros Internacionales. Domum Real Estate Fund Advisor. Consejo EFA Academic Council (Escuela de Finanzas Aplicadas del Grupo Analistas Financieros Internacionales S.A). Head of the Derivatives and Fixed Income Area of CEFA qualification IEAF; Spain English translation: Catalina Sherwell | Certified Translator Review performed by: Jesús López Zaballos | President of the European Federation of Financial Analysts Societies (EFFAS). Managing Director of the Escuela de Escuela FEF. PhD in Business Administration, Universidad San Pablo CEU Published by: The European Federation of Financial Analysts Societies (EFFAS), 2021 Sophienstrasse 44 DE60487 Frankfurt am Main, Germany ISBN: 978-3-949300-13-4 Contents 1. FINANCIAL RISKS 11 1.1 Introduction: Overview of risk and risk management in banking 11 1.1.1 Definition 1.1.2 Types of risks 12 13 1.1.2.1 Credit 1.1.2.2 Market 1.1.2.3 Balance sheet (structural) 13 14 16 1.1.3 Fundamental Methodologies 16 1.1.3.1 Exposure 1.1.3.2 Sensitivity 1.1.3.3 Value At Risk 16 17 22 1.1.4 Capital implications 26 1.2 Risk framework 28 1.2.1 Risk appetite definition 1.2.2 Risk governance 1.2.3 Defenses lines 1.2.4 Limits definition 28 31 33 33 1.3 Credit risk 34 1.3.1 Definition 1.3.2 Types 34 37 1.3.2.1 Issuer 1.3.2.2 Counterparty 1.3.2.3 Delivery risk 1.3.2.4 Settlement 37 37 37 37 1.3.3 Measurements and indicators 38 1.3.3.1 Probability of default 1.3.3.2 Exposure 1.3.3.3 Add-ons 38 38 40 1.3.4 Limits definition 1.3.5 Key Risk indicators for the credit portfolio 42 44 1.4 Market risk 45 1.4.1 Definition 1.4.2 VaR metholologies 45 50 1.4.2.1 Parametric VaR 1.4.2.2 Historical simulation VaR 1.4.2.3 MonteCarlo simulation VaR 51 51 52 1.5 Asset liability risk 56 1.5.1 Definition 1.5.2 Types 1.5.3 Interest rate risk 56 56 57 1.5.3.1 Interest rate risk metrics 59 1.5.4 Liquidity risk 61 1.5.4.1 Liquidity risk metrics 62 1.5.5 Limits definition 64 2. DERIVATIVE INSTRUMENTS 67 2.1 Objectives 67 2.1 Introduction to derivatives 68 2.1.1 Typology of derivatives 68 2.1.1.1 Futures and forwards 2.1.1.2 Swaps 2.1.1.3 Options 68 68 68 2.1.2 Typology of markets 69 2.1.2.1 Organised 2.1.2.2 Unorganised 69 69 2.2 Futures and forwards 70 2.2.1 Definition 2.2.2 Forward contract 2.2.3 Futures contract 2.2.4 Underlying typologies 70 71 71 77 2.2.4.1 Equities 2.2.4.1.1 Equity futures 2.2.4.1.2 Stock options 2.2.4.1.3 Equity swaps 2.2.4.2 Currency 2.2.4.2.1 Forward exchange deal 2.2.4.2.2 Non-delivery forward 2.2.4.3 Short and long-term interest rates 2.2.4.3.1 Main markets 2.2.4.3.2 The FRA 2.2.4.4 Bond futures 77 78 78 78 79 79 80 81 81 81 83 2.2.5 Valuation 2.2.6 Management 89 90 2.2.6.1 Hedging 2.2.6.2 Speculation 2.2.6.3 Arbitrage 2.2.6.4 Portfolio management with bond futures 90 91 92 93 2.3 Swaps 99 2.3.1 Definition 2.3.2 Underlying typologies 99 99 2.3.2.1 Short and long-term interest rates 2.3.2.1.1 Coupon swaps (standard IRS) 2.3.2.1.2 The basis swaps 2.3.2.1.3 Non-generic Interest Rate Swaps (Interest Rate Swaps) 2.3.2.2 Currency 2.3.2.2.1 Standard currency swaps 2.3.2.2.2 Floating-rate currency swaps 2.3.2.2.3 Cross-currency coupon swaps 2.3.2.3 Equities 2.3.2.3.1 Total return swap 2.3.2.3.2 Dividend swaps 99 99 101 101 102 102 103 104 104 105 105 2.3.3 Valuation 2.3.4 Management 105 108 2.3.4.1 Hedging 2.3.4.2 Speculation 2.3.4.3 Arbitrage 108 108 109 2.3.5 Credit Default Swaps 110 2.3.5.1 Introduction and Basic Concepts 2.3.5.2 Credit Events 2.3.5.3 Conventions 2.3.5.4 ISDA Protocols 2.3.5.5 Accounting Constraints 2.3.5.6 Valuation 110 110 113 114 115 116 2.4 Options 121 2.4.1 Definition 2.4.2 Underlying typologies 121 127 2.4.2.1 Equities 2.4.2.2 Currency 2.4.2.3 Interest rates 127 127 128 2.4.3 Valuation 128 2.4.3.1 The Binominal Model 131 2.4.4 Management 137 2.4.4.1 Hedging 2.4.4.2 Speculation 2.4.4.3 Arbitrage 2.4.5 Exotic options 2.4.5.1 Digital Options 2.4.5.2 Compound Options 2.4.5.3 Chooser Options 2.4.6.4 Exchange Options 2.4.5.5 Asian Options 2.4.5.6 Barrier Options 2.4.5.7 LookBack Options 140 140 141 159 160 160 161 162 162 164 166 2.5 Self-evaluation questions 167 3. BIBLIOGRAPHY 169 1 FINANCIAL RISKS 1.1 Introduction: Overview of risk and risk management in banking Bank risk is usually referred to as the potential loss to a bank due to the occurrence of particular events. Key risks in banking include credit risk, interest rate risk, market risk, liquidity risk, and operational risk. The main purpose of risk measurement is to estimate potential losses that may occur in the different activities that are adopted. In the case of financial risks, it is fundamentally the identification, quantification, estimation and management of the risks that are induced as a result of the activity in the financial markets. The level of risk usually assumed will have direct implications on the levels of capital required for the adoption of such risks. There is a close relationship between the positioning in the different assets weighted by their corresponding risk and the level of capital that will be required for this activity. The definition by the senior management of financial institutions of the levels of risk appetite is therefore conditioned by access to the capital that allows these activities to be carried out. They will have to be able to generate sufficient profitability to cover the implicit costs and generate a financial margin that remunerates the shareholder. 12 PRINCIPLES OF RISK MANAGEMENT Risk management in financial markets ultimately involves managing the risks inherent in these activities. Basically, these risks are market, credit or solvency and operational. In this sense, financial institutions currently have units that individually or globally address the monitoring, analysis and control of limits necessary to undertake the business plans associated with Treasury activities in the financial markets. It should be noted, and as a previous step to the measurement of the different types of risks, that the correct valuation of assets and liabilities is crucial since, ultimately, the quantification of risks is the estimation of changes in these values. The risk function must establish an orderly process for identifying, locating, analyzing and monitoring the entity’s risk. To this end, all risks must be “inventoried”, assigned to the business units and obviously delimited in terms of potential impact. Assuming an assignment of limits to each of the identified risks, 4 phases are clearly distinguished: Only support from the highest level of the organization allows the proper performance of the risk function. The entity’s top management will define the STRATEGY, the implementation of which requires the definition of an execution PROGRAM. This program requires certain implementation decisions based on processes and OPERATIONS. All phases are subject to UNCERTAINTY, and therefore to the risk function. Any risk assumption decision shall define tolerance thresholds in terms of IMPACT and PROBABILITY of occurrence of the consequence of the identified risks. The thresholds shall be established on the basis of these 2 fundamental dimensions. 1.1.1 Definition Risk is associated with the change in the value of an asset or liability induced by exogenous variables that potentially have a negative impact on us, thus generating losses. Identification: qualitative identification of each of the risk factors. Evaluation: quantitative evaluation of each of the risk factors, according to generally accepted methodologies. Conduct: adequate in form and quantity according to the entity’s risk appetite. Reporting: orderly, recurrent and with a methodology approved by the entity of all risk factors, in such a way as to facilitate risk taking. Uncertainty about the possible results of the management of an entity, agency or corporation generates the existence of risks. Therefore, in a very broad context, risks are associated with uncertainty whose origin could be classified between those that are given (EXOGENIC) and those that result from the management itself (ENDOGENIC). The risk function in any entity is of strategic importance and must therefore be supported from the highest organizational hierarchy. Improvement in the planning of processes, putting more focus on the central objective of the corporation. The main benefits of the existence of an effective risk policy are: 13 Reduction of potential unforeseen costs. It contributes to a better allocation of resources. It contributes to increased efficiency and performance. It contributes to the development of a positive organizational culture. It improves accountability, transparency and good governance in decision making. 1.1.2 Types of risks There are a number of questions that are essential to answer for any financial institution or risk management entity: Essentially, credit risk is the possibility, with greater or lesser uncertainty, of incurring a loss when the counterparty totally or partially defaults on its financial commitments as stipulated in the governing contract. Default, non-payment of a debt or bankruptcy are situations typically considered as credit risk. Credit risk, however, also includes losses caused by the deterioration of the counterparty’s credit quality, which, without defaulting on their obligations, do imply the adoption of an economic provision in view of the increasing probability of a default occurring. Likewise, delays in the payment date of the debt could be susceptible to qualify as credit risks, although it is not uncommon for them to be considered as another variant of risk, which, using the English term, is referred to as settlement risk. In any case, a delay is an occurrence close to the characteristic nature of credit risk, which is non-payment. What risks do we face? What level of risk do we face? How much risk can we take? How much risk do we want to take? How much risk are we taking? How much risk will we take? The organizational structure and the allocation of resources to the risk function are crucial for the proper development of the same. The independence of the business functions is a relevant aspect in the organizational structure in which the direct reporting of the risk function to the Presidency and/or Board of Directors of the entity is desirable. The involvement of the entire entity in the risk functions is necessary. In any case, the specific functions must be adequately localized for a fundamental matter of SEGREGATION OF FUNCTIONS. Certain functions must be framed within the risk area and others will be transversal to the entity. In capital markets, the risks are generated by financial sources. Financial risks are focused on credit, balance sheet and market risks, with some common elements that may even overlap. 1.1.2.1 Credit Credit risk usually has a structural character and represents one of the most relevant risks in banking activity, in which the central axis of the business revolves around the assumption of this type of risk. In fact, the essence of the banking business is focused on attracting financing at the lowest possible interest rates for credit investment that allows sufficient margins to cover the risks that this entails and the consequent consumption of capital. 14 PRINCIPLES OF RISK MANAGEMENT Credit risk is segmentable into 4 major groups: 1.1.2.2 Market Market risk is the exposure implicitly assumed in positions adopted in the financial markets inherent to changes in the values of four major groups of financial assets: Issuer Settlement Delivery Counterparty The metrics used for the quantification of credit risk are usually of a structural nature and will aim to measure the potential losses that may occur throughout the life of the contracted operations. It arises from the eventuality that losses are generated due to non-compliance with the payment obligations of the borrowers, as well as losses of value due to the simple deterioration of the economic situation and the solvency of their assets. Concentration risk is also considered, understood as exposures with a loss potential large enough to affect the Entity’s solvency, derived from both the individual concentration of borrowers and sectoral concentration. The establishment of limits in line with the entity’s risk appetite is one of the most important binding frameworks in the risk function. Limits should be easily implementable and measurable, and should be adapted to the type of risk to which they are associated. The main drivers to be considered are: -- The process of requesting approval of limits should be one of the initial steps in business activity. -- The proposal must come from the unit that will adopt them (with the support of the risk area) to facilitate their technical evaluation, before being submitted to higher levels for approval. The follow-up returns to the risk area and may coexist with a middle office within the business unit. -- Equities: stocks: indexes, derivatives on these, etc. -- Interest rates: deposits, bonds, derivatives on these, etc. -- Exchange rates: purchase/sale of currencies, derivatives on them, etc. -- Commodities: purchase/sale of commodities, gold, oil, etc. Market risk is induced by the positioning acquired in the different areas described above. It is fundamentally induced by the volatility that the prices of all variables quoted in these markets usually present when they are subject to the forces of demand and supply that concur in the free markets. The roles of each of these financial assets listed on the markets cause a great diversity in the levels of volatility, as well as relative causal behaviors that generate uncertainty about the future values of the positions adopted. We can say that the future evolution of the prices of these financial variables have a stochastic component that generates a potential risk of losses that depend on the levels of market volatility that, in turn, are a function of aspects as diverse as monetary policies, the macroeconomic situation, political events, market perception, expectations, etc. Market risk has a more conjunctural character because it depends fundamentally on the positions that are adopted at any given time in the various financial assets; it is for this reason that the metrics intended for the quantification of market risk usually have a shorter horizon than credit risk. 15 The market risk measurement methods are divided into two main groups: a) One in which we quantify the potential changes in the value of our instruments as a consequence of unit variations in market variables. An example will be presented for the case of fixed-income assets. b) The estimation of the probability of occurrence of certain losses in a given future time horizon through measures that will be framed within the scope of the value at risk and scenario analysis by virtue, to a large extent, of historical information. This analysis would be incomplete if we do not answer the other great unknown: the probability of occurrence of these variations. Knowing this and combining it with the estimated magnitude of loss, we will have a measure of risk that will give us a little more information. The answer to this second question will be answered with the metrics that we will see later on, in the area of what we will call value at risk and/or stress scenarios. In both cases, we will estimate potential losses that may occur over certain time horizons and with certain confidence levels. In some cases, we will refer to losses in extreme market situations while others will be in normal market conditions. The objectives to be achieved are: To identify the valuation criteria in the different types of financial instruments. To exemplify the sensitivity metrics for the case of fixed income assets. To outline additional metrics that will provide “probabilistic” market risk information. To answer the second question on the measurement of potential market risks (What is the probability or risk of occurrence of such variations?) we must resort to different metrics. In the previous points, the first fundamental aspect in the analysis of market risks has been identified: the one that allows estimating the impact of a variation in exogenous variables on the instrument held in a portfolio. It should be noted that, in the metrics previously discussed, only the valuation model and its derivatives were used to measure the price elasticity with respect to exogenous market variables. At no time was historical information on these variables used and only what we have come to call the sensitivity of the instrument was evaluated. It should be noted that, in order to achieve these objectives, the metrics we are going to use require, in one way or another, historical information on the evolution of the prices that determine the instruments whose risk we wish to quantify. This is a differential aspect of the metrics that will be discussed in the next topic. Having dealt with those market risk metrics that allow us to quantify sensitivities through the calculation of the first derivatives of their corresponding valuation functions, we will now deal with the metrics that will quantify losses and gains for certain confidence levels and for specified time horizons. If the previous metrics were independent of the behavior of market variables in the past and only dealt with the valuation models and variables that determined them, in these metrics, historical information will become especially relevant. Their treatment will take different forms and their application will respond to different methodological criteria that must be outlined by the analyst. 16 PRINCIPLES OF RISK MANAGEMENT The metrics around what we will call Value at Risk date back to the early 1990s. At that time, one of the world’s leading investment banks, JP Morgan, made a methodological proposal for calculating market risk under the name of Riskmetrics. Since then, this methodology, implemented by the investment bank, has been a benchmark in the field of market risk. It has also given rise to methodological developments that have been evolving the proposal and have brought with them at least three different methodological currents that will be studied throughout the course. 1.1.2.3 Balance sheet (structural) Balance sheet risk or Asset-Liabilities Management (ALM) is the strategic management of the balance sheet of financial institutions from the perspective of market and liquidity risks. The ALM function is complemented by the management or monitoring of trading positions, funding and equity planning. It affects all financial institutions that have a balance sheet subject to business risks as a result of credit operations, regardless of their trading activities. The fundamental objectives pursued are the measurement, analysis and management of the aforementioned risk factors by: Maximizing the profit between assets and liabilities. Modulating the exposure of these factors according to the future vision of: -- Market variables. -- New business opportunities. -- Customer behavior that could lead to transfers from one instrument to another. Also complying with banking regulations in terms of control, internal supervision, reporting and good capital management practices is part of ALM. 1.1.3 Fundamental Methodologies In order to address the measurement of the different risk factors that exist in the financial field, an approxima- tion must be made that covers at least 4 perspectives. The first aims to quantify the exposure to the risk being measured. That is, it is a question of estimating the basis on which losses can occur. As these apply to the present value as to the base future values of the exposure, the determination is not always immediate, especially when it comes to estimating potential exposures that may occur at future points in time. The second has to respond to sensitivity exercises, that is, metrics that allow us to know what would be the impact on the value of a portfolio in the face of certain movements of the exogenous market variables. The third approach will take into account a probabilistic component that, in the first instance, will quantify losses under normal market conditions. That will be covered by Value At Risk measures implemented through 3 main streams of methodologies: Historical simulation. The Monte Carlo Simulation. Parametric techniques. Finally, the estimation of losses that may occur under extreme conditions will be treated by what is called stress testing. 1.1.3.1 Exposure The starting point for measuring market risk is the proper valuation of the different types of instruments. The exposure is defined by the current and potential value of the instruments. In this topic, we will address and identify the main criteria that must govern the valuation processes of instruments in the field of equities, fixed income, currencies, money markets and commodities. Each of them will have their own specificities, although the observation of market prices will be a common factor that will provide the necessary inputs for the valuation of the different types of finan- 17 cial instruments. The demand and supply of the various financial assets in the markets will determine the prices used for the valuation processes of the different instruments. As we have already seen, there are different activities that involve the assumption of market risks. The ways of measuring market risks fall into two large groups: -- One in which we quantify the potential changes in the value of our instruments as a consequence of unit variations in market variables. An example will be presented for the case of fixed income assets. -- The estimation of the probability of occurrence of certain losses in a given future time horizon through measures that will be framed within the scope of the value at risk and scenario analysis by virtue, to a large extent, of historical information. The objectives to be achieved are: -- To identify valuation criteria for different types of financial instruments. -- To exemplify the sensitivity metrics for the case of fixed income assets. -- To outline additional metrics that will provide “probabilistic” market risk information. Each financial instrument in a portfolio will have its own more or less simple or complex valuation model. The possible variations in the market prices of the variables (which serve as input for determining the value of each financial instrument) will ultimately determine the level of market risk of each one and of a portfolio as a whole. It is therefore essential to identify these models, since the determination of the potential risk will be given by the difference between the value of the instruments according to these models under market conditions and under adverse conditions for certain confidence levels. These activities are basically classified as follows: Equities. Foreign exchange. Fixed income. Money markets. Commodities. And, in all cases, there were different derivative instruments that could be traded. We will mainly identify futures, options and swaps. 1.1.3.2 Sensitivity One of the first questions we have to answer in risk measurement is: “What would be the impact on a portfolio if there were specific variations in the market variables (exogenous)? In order to answer this question (i.e., to quantify the impact that a portfolio would have if specific variations in the [exogenous] market variables were to occur), elasticity measures must be used. Those that quantify the variation in the value of the instrument, in the face of unit variations in the explanatory variables, will provide an answer to this question. For example, in fixed-income financial assets, risk measurement in terms of elasticity is immediate, given the dependence of the value of the asset on interest rate levels. In the following, we will approach the subject both from a mathematical point of view and from financial aspects that are useful for the understanding of risk management. We will develop this type of market risk analysis for fixed income assets, although its application can be extended to any other 18 PRINCIPLES OF RISK MANAGEMENT type of financial instrument. We will mainly deal with the calculation of sensitivities of the instrument’s value for a given variation of the exogenous variable. The price of a bond is the present value of the flows discounted at the market interest rate for that term. FIGURE 1 Bond valuation. Given the function relating the price and YTM (yield to maturity) of a bond, it is essential to quantify the impact on the value of a fixed-income asset of a unit change in interest rates (the fundamental variable of these instruments). To do this, we will derive the above function in first order and obtain: -- Absolute Sensitivity. -- Modified Duration. -- Duration. These measures refer to aspects related to: Risk: degree of exposure of the value of a bond to variations in the YTM. Time: average residual maturity weighted by the present value of the flows. 19 For example, for a security with a duration of 5 years, we can say of that bond that: Its price will fall by approximately 5% in the face of a percentage increase in the YTM of 1%. This is the definition from the risk side. The existence of three elasticity measures is justified simply by the different possibilities in which the variations of both price and YTM can be expressed. We will discuss the following: Price variations: Its weighted average remaining life is 5 years. This is the definition from the time side. The term “approximately” appears, since the three measures of price-YTM elasticity are an analytical approximation to the real function. In fact, the absolute sensitivity is the first derivative of the function, approximating it by a straight line even though it is a convex function. If we wanted a better approximation, we should perform the second derivative of the bond value with respect to the YTM, thus obtaining the second order elasticity measures, which are: -- Convexity. -- Modified convexity. -- Absolute convexity. Relative: Absolute: P1 - P0 YTM variations: Relative: Absolute: Y1 - Y0 Under the above assumptions, we have that: Duration represents the percentage or relative variation of the bond price in the face of a unit percentage variation of the YTM. Modified duration represents the percentage or relative change in the price of the bond in the face of a unit absolute change in the YTM. Sensitivity represents the absolute change in the bond price to a unit absolute change in the YTM. FIGURE 2 Price-YTM relationship of a bond. Financially, duration is very intuitive if we turn to that definition based on the time aspect of it, so that we have: 20 PRINCIPLES OF RISK MANAGEMENT FIGURE 3 Calculation of duration. Mathematically: Therefore, between the three expressions there is the following relationship: Duration: Convexity Modified duration: Sensitivity: where: P: price F: flow t: time in years N: number of flows D: duration MD: modified duration AS: absolute sensitivity The function that defines the YTM-price relationship in a fixed income asset with intermediate flows is not a straight line. It is a convex curve. This implies that the approximation obtained by the first family of elasticities (duration, modified duration or sensitivity) does not perfectly fit the real function. For further approximation, we will find the second derivative of the function: being the modified convexity: 21 Mathematically and generally: to know the effect of convexity for variations other than 1 %: Convexity has a number of properties that are worth mentioning: if we divide all by P: Convexity is asymmetric: price rises of an asset as a consequence of decreases in profitability by a given magnitude are usually greater than decreases in these in the face of an increase in YTM of a similar amount. This is due to the increasing, though not linear, relationship between duration and convexity. Convexity is positive: higher durations imply higher convexities. In general: Convexity is maximal at low coupons: in extreme cases, zero coupon bonds define higher convexity than securities with similar maturity. However, they are less convex than bonds of the same duration and with intermediate flows. Convexity is “desirable”: for the bondholder. It is always in his favor. This implies that we must now consider, for example, in terms of absolute sensitivity at first and second order: So it is practical to establish a correction coefficient for convexity: To the extent that duration and convexity are positively related, the causal relationships (which were between term, coupon, YTM with duration) are the same for convexity. While we have illustrated the sensitivity metrics in the field of fixed income assets, this risk quantification is applicable to any type of financial instrument. For example, within the field of derivative instruments we will find similar metrics for quantifying the risks of financial options. The main metrics that we have that quantify the elasticity of the value of the options to changes in the different market variables that affect their value are: 22 PRINCIPLES OF RISK MANAGEMENT Delta: measure of the elasticity of the value of an option against changes in the underlying asset in the first order. Gamma: measure of the elasticity of the value of an option in the face of changes in the underlying asset in the second order. Vega: measure of the elasticity of the value of an option in the face of changes in implied volatility. Theta: measure of the elasticity of the value of an option in the face of variations in time. Rho: measure of the elasticity of the value of an option in the face of changes in interest rates. Phi: measure of the elasticity of the value of an option against variations in dividends in the case of equity options. These are just other examples of measures of activity used in the financial field to quantify potential changes in value in the face of unit variations in exogenous variables. The analysis must be complemented with metrics that incorporate probability of occurrence of the shuffled variations because they alternately project probable variations based on different estimation criteria. 1.1.3.3 Value At Risk The Value at Risk (VaR) is the maximum likely loss of a portfolio for a given confidence level over a specified time horizon. The term “maximum probable quantity” implies normal market movements (excludes large financial crises). It does not calculate the maximum loss of the portfolio in absolute terms. Therefore, we are facing a measure that will quantify the potential loss of the portfolio but associated with a statistically defined level of confidence and within a specific time horizon. While the VaR reflects a potential loss, it is expressed as a positive figure in the same base currency (currency units) and summarizes all the risk of the portfo- lio, however complex it may be. Afterwards, it will be convenient to check the results of the portfolio at the end of the time horizon with the Figures of the VaR. In this sense, it should not be surprising that some of the losses that occur are higher than this VaR figure. In fact, statistically it must occur on a certain number of occasions. The important thing is that this number of occasions is within the confidence interval expected from a statistical point of view. Loss estimation can be conceived indistinctly in historical distributions or, for example, in normal distributions. 1.1.3.4 Stress testing VaR is a useful risk control tool in “normal” market environments. Using the VaR movements of the variables under control can be anticipated with a certain level of confidence. Because it is an estimate, a series of scenarios are left out, which are characterized by having a low probability of occurrence and a great impact if they occur. The VaR does not contribute anything about this type of situation, so it is necessary to complement it with a measure that fills this gap (Knop, Ordovás and Vidal, 2004). Stress testing is not a substitute for VaR, but a risk management tool. Its functions are as follows: 1. Identifying potential sources of risk. 2. Evaluating the impact of the risk factor on the portfolio. 3. Managing risk through limits. 4. Applying tools to mitigate risk. 23 FIGURE 4 Value At Risk Basel’s capital agreements require stress testing to be applied in the case of the implementation of internal models (Internal Model Approach) or in the case of advanced credit risk models (Internal Ratings-Based Approach). Stress testing is more intuitive and simple (a priori) for the analyst/risk manager. Work on possible scenarios and their impact on the income statement. The application of VaR methodologies involves the prior study of statistical distributions (movement analysis, estimation and backtesting) and their subsequent effect on the income statement. One of the weaknesses of stress testing is: not being able to predict structural impacts (e.g. shift from a fixed to a floating currency). Its impact goes beyond exchange rate products, as it affects interest rates and equities. Scenario analysis can be interpreted as a coherent measure of risk. Scenarios that remain above the VaR level can be considered extreme risk situations. In addition, under the distribution assumption on which the estimate has been made, they are associated with probabilities of occurrence. The mean of all extreme scenarios (Expected Shortfall) is a coherent measure of risk. Scenario analysis It was initially used as a tool for risk analysis before the development and implementation of VaR methodologies. It consists of selecting a group of 24 PRINCIPLES OF RISK MANAGEMENT scenarios and evaluating their impact on the portfolio (measured as loss in a given time horizon). There are no defined rules for the choice of scenarios: the judgment and experience of the risk analyst intervenes a lot. In general, you have to choose those that do not contain contradictory or impossible assumptions and that preferably include the relationships between variables. We must try to cover, in an ideal way, all the situations covered. A priori, a probability of occurrence is not associated with each scenario that, in many cases, is in the opinion of the analyst: thus, subjectivity appears. The generation of scenarios can be: 1. Event-driven: The impact on profit and loss comes from financial situations that could significantly affect. Examples: 11-Sep-2001 effect, Lehman’s Sept.-Dec. effect, 2008, etc. 2. Portfolio-driven, in which portfolio weaknesses are identified, and ad hoc scenarios are created to compute the impact. Example: portfolio of long positions in senior issues in which interest rates increase and credit spreads increase. According to the effects analyzed, the following can be distinguished: 1. Analysis of univariate sensitivity scenarios. 2. Analysis of multivariate sensitivity scenarios. First, in the analysis of univariate sensitivity scenarios, the impact on the total portfolio of extreme movements in a variable is analyzed. It does not take into account possible correlations between variables. These univariate sensitivity scenarios are: 1. Parallel movements of the curve. 2. Changes in the slope of the curve. 3. Combination of previous ones. 4. Changes in interest rate volatility. 5. Changes in stock market index values. 6. Changes in stock index volatilities. 7. Changes in the levels of exchange rates of quoted currencies. 8. Changes in exchange rate volatility. On the other hand, in the analysis of multivariate sensitivity scenarios, the impact on the total portfolio of extreme movements in several variables is simultaneously studied. It extends to other areas of risk management (balance sheet risk, etc.). These multivariate sensitivity scenarios are: 1. Historical: based on past crises. Not all crises affect all assets equally. Extreme movements occur over different time horizons. You have to find the one that really affects the portfolio under study (trading books, investment portfolios, liquidity buffers, etc.). 2. Prospective: based on possible future crises (e.g. an earthquake in New York, a drastic reduction in fuel production, armed conflicts, etc.). Factor push method: it is based on moving all the underlying risk factors of the portfolio. The movement is performed in a manner proportionate to your average jump: 3, 4, 5 standard deviations. The direction of the movements can be (1) the same for all or (2) the one in which it generates the greatest loss for each variable. Applying the above involves ignoring the correlations between the underlying variables (even in some cases, the greatest loss occurs if the underlying does not move). 25 Univariate Sensitivity Scenarios Advantages Disadvantages TABLE 1 Ease of implementation and explanation of results. Multivariate Sensitivity Scenarios It incorporates cross-effects of the underlying variables. Uncovers concentrations in certain positions (e.g. Equity + Credit Spread) by increasing the effects well above a VaR. It requires a detailed analysis of the prevalence of the variables according to the composition of the portfolio at It does not incorporate the any given time. correlation between variables. Problems with the probability allocation of those scenarios. Increase in the calculation time of the scenarios. Advantages and disadvantages of univariate and multivariate sensitivity scenarios. Conditional Scenario Method: includes correlation between the movements of risk factors. However, the correlation between factors is a parameter that depends on time. It can be a disadvantage if its variability or circumstances in times of crisis are not taken into account. Worst Case Scenario Measure (WCS Analysis): It consists of taking the set of possible results above the VaR/EaR and studying it as if it were an independent result vector. The WCS will be the 1% percentile of that new vector. This analysis is a complementary study to the VaR/EaR value of the original result vector. Principles of good practice (usefulness of stress testing) It does not matter to evaluate the impact of any extreme situation, but rather to detect weaknesses of the portfolio. Once the weakness or weaknesses are detected, actions can be carried out that limit their impact: Buy protection in the market: market risk is replaced by credit risk. Modify the position to reduce exposure to the risk factor or diversify. Restructure the business by allocating resources to other market niches. Have an updated contingency plan, with detailed actions and instruments to activate according to the severity of the crisis. In case of a liquidity crisis, it is paramount to have cushions that allow an adequate survival horizon. Weaknesses Lack of involvement on the part of Senior Management, from the implementation of a stress analysis program to the making of strategic decisions based on it. 26 PRINCIPLES OF RISK MANAGEMENT Lack of global vision of risk: do not apply stress analysis in separate businesses. Lack of a complete development of the stress testing program applicable to all areas of risk (operational, market, credit, legal, etc.). Lack of adequate tools to apply in times of crisis, mainly related to the treatment of information in an environment of high volatility. Recommendations Greater involvement of management in the stress analysis process. Senior Management: application of conclusions in strategic decisions. Management and intermediate managers: maintenance, development and review. Have an exhaustive stress program. It has to cover: -- Risk identification and management. -- Search for alternatives. -- Decisions on capital allocation and liquidity management. -- Internal information (audit, senior management...) and external information (supervision). Use a wide range of stress techniques (sensitivities, scenarios, simulation, etc.). Formalize the stress process through processes and documentation. Have adequate infrastructure: agile calculation tools, which allow to quickly incorporate new scenarios and BB. DD. with sufficient information. Subject the entire process to periodic reviews: more frequent in periods of greater volatility in the markets. 1.1.4 Capital implications Banks consider a major management priority to secure a sufficiently high level of capital resources in order to maintain and strengthen their financial position. Capital risk is the possibility that an entity will lose money from an investment of capital. Capital risk can manifest as market risk where the prices of assets move unfavorably, or when a business invests in a project that turns out to be a dud. The use of a portfolio approach enables us to define capital adequacy. We would like to be able to measure adequate capital in a way that could be used by managers, insurers, and regulators. Such a task is not simple; if it were, no special studies would be needed. Our experience shows that modern theories of finance enable us to define and model capital adequacy. The measurement problem, while not easy, does not appear more difficult than those solved elsewhere. Applications of known techniques allow us to clarify many problems and to arrive at preliminary estimates of the magnitude of some of the key parameters. What constitutes adequate capital depends upon the amount of risk assumed by a firm. Capital is adequate either when it reduces risk of future insolvency to some predetermined level or when the premium paid by the bank to an insurer is “fair”; that is, it covers the expected losses of the insurer, given the risk and capital of the firm and the terms of insurance with respect to when insolvency will be determined and what losses will be paid. Portfolio theory supplies the necessary tools for measuring the risks of insolvency. A bank selects a portfolio consisting of a variety of particular activities, including assets, liabilities, commitments, nonbalance-sheet operations, and net worth (capital and reserves). The expected changes in these activities, their rate of return, and the bank’s capital policy give an expected end-ofperiod net worth. However, expectations are unlikely to be realized exactly. Because of economic events, total income (including changes in capital values) will exceed or fall short of expected levels. (Markowitz, 1959; Sharpe, 1964; Lintner, 1965; Mossin, 1966; Merton, 1974, 1977). 27 Measuring the risk of a portfolio requires a calculation of its expected end-of-period net worth and of the probable distribution of possible net worth around this level. The bank will become insolvent if events cause its income to be so negative as to more than offset its initial capital, plus any contributions less any dividends paid during the period. Risk depends on both the probability of insolvency and the expected losses in case of such failure. A bank is theoretically insolvent either (a) when its liquidity is so low that it cannot pay its debts, i.e., a negative cash flow cannot be met, or (b) when the market value of its liabilities exceeds that of its assets reduced by the costs of bankruptcy. Because of gains and losses on intangibles not shown on a bank’s books, the determination of insolvency is complex. Not infrequently, regulators delay bankruptcy procedures beyond the economic occurrence of insolvency. In an attempt to avoid the costs of liquidation, regulators close banks only with reluctance. In the interim, the FDIC or debenture-holders or non-insured depositors bear the cost of future potential losses. Measuring Capital Adequacy in a Bank There are four steps to estimating the capital adequacy in an individual bank. 1. The first step is to estimate the risk in each activity. This calls for a basic examination of how risks vary for each activity in which a bank might engage. Ideally, a complete co-variance matrix covering all of the pertinent activities under possible future conditions should be developed. This is not feasible. Our study estimated risks in approximately 10 separate activities. It seems likely that an optimum number of classes of activities for analysis would be between 15 and 20. When an activity encompasses assets with a wide spread in duration, it should be further subdivided by maturity. 2. The next task is to apply the estimated risk matrix to the activities the bank is expected to engage in between now and the next evaluation. Since total risk depends on the proportion of each activity to the total, the estimates of variance by function must be applied to assets aggregated into the desired classes. Each aggregate must be corrected for possible changes in size. Where the bank ends up depends on how it has been changing and where the economy goes. The matrix of expected returns and variances must be applied to the estimates of the average and end-of-period portfolios to obtain an expected income for the period, together with a distribution function for expected income. 3. The risk of insolvency depends on how the initial economic net worth of the bank may be altered by. what happens to earnings. The initial capital is available to absorb potential losses. Thus, to measure risks, capital must be properly defined and estimated. Economic, rather than book or reported capital is required. Any exogenous (not dependent on income) capital changes must also be projected. Bank examiners have traditionally requested added capital if they believed it was weak. But they have not had proper measures of weakness. 4. Finally, the actual risk and measure of capital adequacy must be calculated. Several techniques are available for this purpose. Each uses a known relationship between initial net worth, expected income, and capital changes to give expected endof-period net worth, together with the variance of this expected net worth. Merton (1974, 1977) has shown that the pricing of deposit insurance as well as most other financial claims on a firm can be thought of as an application of generalized option pricing theory. This theory shows that the value of the fair insurance premium depends only on the risk-free interest rate, the value of the promises to pay, or liabilities at the date of the next examination, the time until the examination, the current value of the firm’s assets (the difference between the current value of its assets and liabilities being its 28 PRINCIPLES OF RISK MANAGEMENT net worth), and the variance rate per unit time for the logarithmic change in the value of assets. The fair insurance premium will differ depending on the distribution which expected events are thought to follow. The second approach to measuring risk is through simulations. They enable one to relate the risk in particular portfolios either to a forecast of exogenous variables available from other sources or to a distribution of probable events based on past relationships. A third approach models risk by use of regression techniques. It determines prediction rules for the systematic and residual risk experienced in the market for the bank’s common stock. It aims to measure the predictive significance of a large number of variables as indicators of risk and, hence, as potential targets for management or regulation. The capital-to-risk weighted assets ratio, also known as the capital adequacy ratio, is one of the most important financial ratios used by investors and analysts. The ratio measures a bank’s financial stability by measuring its available capital as a percentage of its riskweighted credit exposure. The purpose of the ratio is to help banks protect their depositors and promote financial health. The capital-to-risk-weighted assets ratio for a bank is usually expressed as a percentage. The current minimum requirement of the capital-to-risk weighted assets ratio, under Basel III, is 10.5%, including the conservation buffer 1. Having a global standard promotes the stability and efficiency of worldwide financial systems and banks. The Formula for the Capital-To-Risk Weighted Assets Ratio The formula to calculate a bank’s capital-to-risk weighted assets ratio is: Capital-To-Risk Weighted Assets = (Tier 1 Capital + Tier 2 Capital/Risk-Weighted Assets). Tier 1 capital is the core capital of a bank; the capital it needs to absorb losses without stopping operations. It includes equity and disclosed reserves. Tier 2 capital is supplementary capital that is less secure than Tier 1 capital. It includes undisclosed reserves and subordinated debt. A bank’s risk-weighted assets are its assets weighted by their riskiness used to determine the minimum amount of capital that must be held to reduce its risk of insolvency. These items can all be found on a bank’s financial statements. 1.2 Risk framework The financial institutions must define the risks they are willing to assume and the level of these risks in order to achieve their business/profitability objectives. The Chief Risk Officer is responsible for developing the risk appetite framework and principles to be approved by the Board of Directors; implementing appropriate independent control frameworks; developing risk measurement and reporting frameworks; authorizing exposures, limits, provisions. It is necessary to establish metrics to define the risk appetite and its monitoring. It is articulated on the basis of: Policies Metrics Limits 29 FIGURE 5 Credit risk calculation. 1.2.1 Risk appetite definition Principles for an effective risk appetite framework Risk appetite framework There are a number of questions that are essential to answer for any financial institution or risk management entity: Comprehensive approach, including policies, processes, controls and systems through which risk appetite is established. It includes the risk appetite statement, risk limits and roles and responsibilities. What risks do we face? What level of risk do we face? How much risk can we take? How much risk do we want to take? How much are we taking? How much risk will we take? It is the aggregate level of risks that an entity is willing to assume for each of them in order to achieve strategic profitability objectives. Risk appetite statement The written articulation of the aggregate level and types of risks that an institution is willing to accept or avoid in order to meet its business objectives. It includes qualitative and quantitative statements regarding income, capital, risk measures, liquidity and other relevant measures. 30 PRINCIPLES OF RISK MANAGEMENT FIGURE 6 Risk definition Risk capacity Limits Maximum level of risk that the institution can assume given its current levels of recourse and to break restrictions determined by regulatory capital and liquidity needs, operational framework and obligations with respect to stakeholders (e.g. depositors, shareholders, investors, etc.). Quantitative measures based on forward-looking hypotheses to distribute the entity’s risk appetite statement to business lines, subsidiaries, specific risk categories, concentrations, etc. Risk appetite Point-in-time assessment of aggregate gross and net (after mitigation) risk in each relevant risk category, based on forward-looking assumptions. Aggregate level and types of risk that an entity is willing to assume within its risk capacity to achieve its strategic objectives and business plan. Risk profile 31 1.2.2 Risk governance Key issues that can weaken risk functions are: The risk function in any entity is of strategic importance and must therefore be supported from the highest organizational hierarchy. Lack of support for senior management’s risk culture. Difficulties in the identification of potentially emerging risks. Lack of independence to ensure the effectiveness of the risk function. Lack of clarity on the responsibility of the risk function. Over- or under-estimation of risks. Unnecessary complexity in risk documentation and reporting. Only support from the top of the organization allows for the proper performance of the risk function. Any decision to assume risks must define tolerance thresholds in terms of IMPACT and PROBABILITY of occurrence of the consequence of the identified risks. The main elements that should characterize the risk function should be: Value creation. Integral part of the organization’s processes. Part of the decision-making process. Locate the uncertainty. Systematic, structured and recurrent. Based on the best information. Tailored to the entity. Considers human and cultural factors. Transparent and inclusive. Dynamic, iterative and responsive to change. It must facilitate the continuous improvement and evolution of the organization. The entity’s top management will define the STRATEGY, the implementation of which requires the definition of an execution PROGRAM. This program requires certain implementation decisions based on processes and OPERATIONS. All phases are subject to UNCERTAINTY, therefore to the risk function. The organizational structure and the allocation of resources to the risk function are crucial for the proper development of the same. The independence of the business functions is a relevant aspect in the orga- 32 PRINCIPLES OF RISK MANAGEMENT nizational structure in which the direct reporting of the risk function to the Presidency and/or Board of Directors of the entity is desirable. FIGURE 8 Risk Organization The involvement of the entire entity in risk functions is necessary. In any case, the specific functions must be adequately located for a fundamental question of SEGREGATION OF FUNCTIONS. Certain functions must be framed within the risk area while others will be transversal to the entity. The Asset Liabilities Committee (ALCO) is the body in charge of DEFINING and MANAGING the global risks of a financial institution: FIGURE 9 ALCO 33 1.2.3 Defenses lines Once the risk appetite and its framework have been defined, it is necessary to transfer it to the rest of the entity, ensuring the correct implementation of each of its elements. The structure that outlines the risk organization is the 3 lines of defense: FIGURE 10 Defense lines 1.2.4 Limits definition The establishment of limits in line with the entity’s risk appetite is one of the most important binding frameworks in the risk function. Limits should be easily implementable and measurable, and should be adapted to the type of risk to which they are associated. The main drivers to be considered are: Loss: Risk: Quantification of the maximum loss you are willing to assume in the development of risk assumption. Horizon: Definition of the nature and time horizon of the assumable loss. Frequency: Periodicity with which the limits will be reviewed, evaluated and sanctioned. Segmentation: Definition of the minimum units for the establishment of boundaries, as well as aggregation units subject to them. Triggers: Pre-limits that determine warning or alarm levels below the established official limits. 34 PRINCIPLES OF RISK MANAGEMENT The process of requesting approval of limits should be one of the initial steps in business activity. The proposal should come from the unit that will adopt them (with the support of the risk area) to facilitate their technical evaluation, before being submitted to higher levels for approval. The follow-up returns to the risk area and may coexist with a middle office within the business unit. FIGURE 11 Limits procedure 1.3 Credit risk 1.3.1 Definition Credit risk arises from the eventuality of losses arising from non-compliance with the payment obligations of borrowers, as well as losses in value due to the simple deterioration of the economic situation and solvency of the borrowers. Lax lending criteria, poor portfolio risk-management or lack of attention to economic changes causing a deterioration in the credit-worthiness of counterparties have historically been the main causes of serious problems in financial institutions. 35 The assets with which institutions assume credit risk are the following: FIGURE 12 Credit risk sources The expected loss should be estimated: FIGURE 13 Expected losses 36 PRINCIPLES OF RISK MANAGEMENT Lenders will look at the borrowers credit-worthiness. One way to do this is by checking what’s called the five C’s of credit: character, capacity, capital, collateral and conditions. payment. The Consumer Financial Protection Bureau recommends keeping your DTI ratio for all debts at 36% or less for homeowners and 15%-20% or less for renters. 1. Character 3. Capital Character refers to the credit history. Everyone starts developing that credit history when taking out credit cards and loans. Those lenders may report your account history to credit bureaus, which capture it in documents called credit reports. Capital includes savings, investments, and assets that the borrower will be willing to put toward your loan. One example is the down payment to buy a home. Typically, the larger the down payment, the better the interest rate and loan terms. That’s because down payments can show the lender’s level of seriousness and ability to pay back the loan. Lenders use credit scores and credit reports to determine whether someone qualifies for a loan or credit. But each lender has different criteria for assessing the credit history. When pulling the credit reports, they’ll look at the details of the payment history and how much was borrowed. They’ll also check for things like late payments, foreclosures and bankruptcies. Lenders may also set minimum credit score requirements. Generally, a higher credit score signifies less risk for the lender. So, maintaining good credit scores or improving your credit scores may help qualify for credit in the future. 2. Capacity Capacity refers to the ability to repay loans. Lenders can check the capacity by looking at how much debt someone has acquired and comparing it to how much income has been earned. This is known as the debtto-income (DTI) ratio. It can be calculated by adding up all the monthly debt payments and dividing that by the pre-taxed monthly income; then, multiply that number by 100. Generally, a low DTI ratio signifies less risk for the lender because it indicates that someone may have the capacity to take on an additional monthly debt The household income is often the primary source for paying off the loans. But if anything unexpected happens that could affect the ability to pay them off, like a job loss, capital provides the lender with additional security. 4. Collateral Collateral is something the borrower can provide as security, typically for a secured loan or secured credit card. If the borrower can’t make payments, the lender or credit card issuer can take the collateral. Providing collateral may help to secure a loan or credit card if the borrower doesn’t qualify, based on the creditworthiness. The asset is provided as collateral, and whether it is needed depends on the type of credit it is applying for. For automobile loans, the car usually acts as collateral. On a secured credit card, the borrowers put down a cash deposit to open the account. Secured loans and secured credit cards are considered less risky for lenders, and they could be useful for people who are establishing, building or rebuilding their credit. 37 5. Conditions 1.3.2.2 Counterparty Conditions include other information that helps determine whether someone qualifies for credit and the terms received. For instance, lenders may consider these factors before lending you money: Counterparty risk: Associated with all the other types of credit risk not included in any of the above. Includes all other credit risks not included in the above. Also called “pre-settlement”. It exists when the instrument has a positive market value. In general, it is defined as: How you plan to use the money: A lender may be more willing to lend money for a specific purpose, as opposed to a personal loan that can be used for anything. External factors: Lenders may also look at conditions outside your control—like how the economy is doing, federal interest rates and industry trends—before providing you with credit. While you can’t control these, they allow lenders to evaluate their risk. Replacement cost (current/future) - warranties + pending settlements. 1.3.2.3 Delivery risk The types of credit risks are established according to time to default, circumstance in which the defaults occur. Delivery risk: Associated with the counterparty’s failure to pay or deliver after delivery or payment by us. It is analogous to liquidation risk. It appears in the purchase and sale of securities. It is incurred when one party has satisfied its obligations to pay/deliver securities and the counterparty has failed to deliver/pay. It disappears when it is done through clearing houses (organized markets, clearing agencies, etc.) or when Delivery versus Payment (DVP) systems are adopted. 1.3.2.1 Issuer 1.3.2.4 Settlement Issuer risk: Associated with an adverse change in the value of a security due to a change in the market perception of the issuer’s credit-worthiness. Settlement risk: Associated with the counterparty’s default after the fulfillment of our contractual obligations in a transaction. The main determinants of issuer risk are: It is characteristic of foreign currency purchase and sale transactions on the maturity date of the transaction. 1.3.2 Types Situation of the issuing country. Issuer credit-rating. Type of security issued. Sector of the issuer’s activity. Current/future results of the issuer. Economic/financial strength of the issuer. It appears for very short periods of time: 24-48 hours. Settlement risk does not only have a credit component. It is also affected by liquidity, market and operational risk. 38 PRINCIPLES OF RISK MANAGEMENT 1.3.3 Measurements and indicators In order to carry out credit risk analysis, the following relevant factors shall be taken into account in order to verify, for example, in an individual the borrowercapacity to comply with the obligations deriving from the loan, amongst others: 1. Employment status. 2. Present income. 3. Foreseeable income over the life of the loan. 4. Assets in property. 5. Savings. 6. Fixed costs. 7. Commitments already made. 8. The foreseeable level of income to be received after retirement, if a substantial part of the credit or loan is expected to continue to be repaid after the end of working life. As mentioned previously, the expected loss depends on probability of default, exposure at default and lossgiven default. 1.3.3.1 Probability of default Probability of default is a characteristic of each borrower or counterparty and depends on their creditworthiness. For that purpose, ratings and scoring should be put in place. Estimating a probability of default implies assigning a score to each borrower. Behaviour analysis should be calculated periodically, based on historical financial performance data coming from statistic models using variables and weights. The results of a statistical study are based on a database of operations. Also socio-demographic indicators are supposed to be calculated at the time of admission, based on objective information about the client and the transaction (age, marital status, transaction amount). Expert models can be used in order to define the result of their judgment and experience. These do not require databases. 1.3.3.2 Exposure The exposure of default (EAD) is value of the receivables at the time of default. The EAD is seen as an estimation of the extent to which a bank may be exposed to a counterparty in the event of, and at the time of, that counterparty’s default. EAD is equal to the current amount outstanding in case of fixed exposures, such as term loans. For revolving exposures like lines of credit, EAD can be divided into drawn and undrawn commitments; typically, the drawn commitment is known, whereas the undrawn commitment needs to be estimated in order to arrive at a value of EAD. Based on the Basel Guidelines, EAD for commitments measures the amount of the facility that is likely to be drawn further if a default occurs. Calculation of EAD is different under foundation and advanced approach. While under the foundation approach (F-IRB) calculation of EAD is guided by the regulators; while under the advanced approach (AIRB), banks enjoy greater flexibility on how they calculate EAD. EAD = Max (Current Market Value; 0) + Potential Future Exposure Where: -- Potential Future Exposure (PFE) reflects the potential change in the instrument’s market value when the contract is replaced or closed out in the case of a counterparty default. PFE at trade level = Notional Amount × Supervisory add-on factor (based on asset class and remaining maturity). 39 PFE at netting set level = (0.4 x Agross) + (0.6 x NGR x Agross) -- where Agross = sum of the individual PFE addons for each trade. -- NGR = net to gross ratio which reflects the current level of hedging and netting benefits. Foundation approach Under F-IRB, EAD is calculated by taking into account the underlying asset, forward valuation, facility type and commitment details. This value does not take into account guarantees, collateral or security (i.e. ignores Credit Risk Mitigation Techniques with the exception of on-balance sheet netting where the effect of netting is included in Exposure At Default). For on-balance sheet transactions, EAD is identical to the nominal amount of exposure. On-balance sheet netting of loans and deposits of a bank to a corporate counterparty is permitted in order to reduce the estimate of EAD under certain conditions. For off-balance sheet items, there are two broad types which the IRB approach needs to address: transactions with uncertain future drawdown, such as commitments and revolving credits, and OTC foreign exchange, interest rate and equity derivative contracts. tegrity and reliability of these estimates. All estimates of EAD should be calculated net of any specific provisions a bank may have raised against an exposure. In some cases we may not know the EAD. It is absolutely key to have at each moment the pending debt and expected interests. The Basel Committee has replaced both the CEM and the SM with a single standardized method (SA-CCR) for measuring EAD for counterparty credit risk. The SA-CCR will apply only to OTC derivatives, exchangetraded derivatives and long settlement transactions. The SA-CCR method, while retaining the structure of CEM, is calibrated to a stress period. It recognizes the benefit of collateral and is more reflective of legal netting arrangements. SA-CCR covers a wide variety of derivatives transactions (margined and un-margined, as well as bilateral and cleared), minimizes discretion used by national authorities and banks, and improves significantly the risk sensitivity of the capital framework. Under this approach, the exposure is calculated as follows: EAD = alpha × (RC + PFE) Where: Advanced approach Under A-IRB, the bank itself determines how the appropriate EAD is to be applied to each exposure. A bank using internal EAD estimates for capital purposes might be able to differentiate EAD values on the basis of a wider set of transaction characteristics (e.g. product type) as well as borrower characteristics. These values would be expected to represent a conservative view of long-run averages, although banks would be free to use more conservative estimates. A bank wishing to use its own estimates of EAD will need to demonstrate to its supervisor that it can meet additional minimum requirements pertinent to the in- -- alpha =1.4 (scaling multiplier as used under IMM approach). -- RC = replacement cost (for margined / un-margined trades) -- PFE = multiplier (partial recognition of excess collateral) × Add-on agg (aggregate of asset class add-ons). RC and PFE are calculated differently for margined and un-margined netting sets. EAD for a margined netting set is capped at the EAD of the same netting set calculated on an un-margined basis. 40 PRINCIPLES OF RISK MANAGEMENT -- For un-margined transactions, RC captures the loss due to the default of the counterparty, assuming immediate closure of transactions. The PFE add-on represents any potential increase in exposure from the present up to one year into the future. -- For margined trades, RC captures the loss due to the default of the counterparty, assuming immediate closure and replacement of transactions. However, closeout of a trade upon a counterparty default may not be instantaneous and there may be a period between closeout and replacement of the trades in the market. The PFE add-on represents the potential change in value of the trades during this period. -- When determining the RC component of a netting set, banks may net transactions with a counterparty in a currency and value date when meeting specific conditions as specified by Basel. asset class level. Depending on the asset class, partial or full offsetting benefits are recognized for long and short positions within a hedging set. The Basel Committee proposes the following methodologies for calculating the add-ons and forming hedging sets: » Interest rate derivatives: The hedging set consists of all interest rate derivatives in the same currency. Long and short offsetting are allowed within the same maturity. By default, partial offsetting is allowed across maturities. However, banks may choose to not offset positions across maturities. » Foreign exchange derivatives: The hedging set consists of foreign exchange derivatives that reference the same currency pair, such as EURUSD. Long and short positions in the same currency pair are allowed to fully offset, but no offset is recognized across currency pairs. 1.3.3.3 Add-ons Similarly to the Current Exposure Method, the exposure at default (EAD) is calculated as the sum of (i) replacement cost (RC), which reflects the current value of the exposure adjusted for the effects of net collateral including thresholds, minimum transfer amounts, and independent amounts; and (ii) potential future exposure (PFE), which reflects the potential increase in exposure until the closure or replacement of the transactions. The PFE portion consists of a multiplier that accounts for over-collateralization and the aggregate add-on derived from the summation of add-ons for each asset class (interest rate, foreign exchange, credit, equity, and commodity), in turn calculated at hedging set level. SA-CCR defines a “hedging set” as a set of transactions within a single netting set which can be partially or fully offset for the purpose of calculating the PFE add-on. Add-on calculations for each asset class are performed first at the hedging set level and then at the Credit derivatives: All credit derivatives are considered as a single hedging set. Long and short positions referencing the same entity are allowed to fully offset. Partial offsetting is allowed between long and short derivatives that reference different entities, depending upon a supervisory correlation parameter. Equity derivatives: All equity derivatives are considered as a single hedging set. Long and short positions referencing the same entity are allowed to fully offset. Partial offsetting is allowed between long and short derivatives that reference different entities, depending upon a supervisory correlation parameter. Commodity derivatives: Four hedging sets will be used (one each for energy, metals, agriculture, and other commodities). Full offsetting is allowed for long and short derivative positions of the same commodity type within a hedging set. Partial offsetting is allowed for derivative positions of different commodity types within a hedging set, depending upon 41 a supervisory correlation parameter. No offsetting is allowed between derivative positions of different hedging sets. Unlike CEM, SA-CCR does not treat gold derivatives similarly to foreign exchange derivatives. Instead, they are treated as commodity derivatives and placed in the metals hedging set. Hedging sets for basis and volatility transactions: For each asset class, basis transactions and volatility transactions will form separate hedging sets in their respective asset classes. These hedging sets will be assigned specific supervisory factors and will follow the hedging set aggregation rules defined for the relevant asset class. -- All basis transactions denominated in a single currency that belong to the same asset class and reference the same pair of risk factors form a single hedging set. For example, all three-month Libor versus six-month Libor swaps in the same currency form a single basis hedging set. -- Volatility transactions form hedging sets according to the rules of their respective asset classes. For example, all equity volatility transactions form a single volatility hedging set. The steps for calculating the add-ons are: Trade Classification: For each transaction, the primary risk factor is determined and attributed to one of the five asset classes: interest rate, foreign exchange, credit, equity, or commodity. More complex trades that may have more than one risk factor (such as cross-currency swaps) may be allocated to one or more asset classes. Trade-level adjusted notional calculation: The adjusted notional amount based on actual notional or price is calculated at the trade level. When the trade notional amount is not stated clearly or not fixed until maturity, the same has to be determined, based on the specific rules specified by Basel. For interest rate and credit derivatives, the adjusted notional amount incorporates supervisory measures of duration. -- For interest rate and credit derivatives, the adjusted notional amount is the product of the trade notional amount in domestic currency, and the supervisory duration SDi: where Si and Ei are start and end dates, respectively. SDi is floored by 10 business days. -- For foreign exchange derivatives, the adjusted notional amount is the domestic currency value of the foreign currency leg of the contract. If both legs of a foreign exchange derivative are denominated in currencies other than the domestic currency, the leg with the larger domestic currency value is the adjusted notional amount. -- For equity and commodity derivatives, the adjusted notional amount is the product of the current price of one unit of the stock or commodity and the number of units referenced by the trade. Maturity Adjustment: Maturity factor for margined transactions (MFt (margined)) and for un-margined transactions (MFt (un-margined)), reflecting the type of transaction, are applied to the trade-level adjusted notional. where Mi is the remaining maturity of transaction i floored by 10 business days 42 PRINCIPLES OF RISK MANAGEMENT where MPORi is the margin period of risk for the margin agreement containing the transaction i. MPOR must be: -- At least 10 business days for non-centrally-cleared derivative transactions subject to daily margin agreements, 5 business days for centrally cleared derivative transactions subject to daily margin agreements between clearing members and their clients. -- 20 business days for netting sets consisting of 5,000 transactions that are not with a central counterparty -- Doubled for netting sets with outstanding disputes consistent with specific conditions. Supervisory delta adjustment: Applied to the trade-level adjusted notional amount based on the position (long or short) and non-linearity (option, CDO trance or neither), resulting in an effective notional amount that is aggregated at the hedging set level. See Appendix A for supervisory delta-adjustment values. Supervisory Factor: A factor specific to each asset class is used to convert the effective notional amount into Effective Expected Positive Exposure (EPE), based on the measured volatility of the asset class. Each factor is calibrated to reflect the Effective EPE of a single at-the-money linear trade of unit notional and one-year maturity. Supervisory correlation parameters: Applied only to equity, credit, and commodity derivatives asset classes. The parameters are derived from a single-factor model and specify the weight between systematic and idiosyncratic components. Aggregation method: Applied to aggregate the trade-level add-ons to hedging set level and subsequently to asset-class level. For credit, equity, and commodity derivatives, a supervisory correlation parameter is applied to capture important basis risks and diversification. 1.3.4 Limits definition Credit risk management should address the entity’s material risks under both normal and stress conditions. Forward-looking by understanding what events may take the entity outside its risk appetite and/or risk capacity. For this purpose, clear limits and quantitative expectations of losses or negative results that can be aggregated or disaggregated (in terms of profits, capital, liquidity at risk...) should be established. Limits or indicators (non-quantitative) should allow other types of risks to be 43 monitored. They should include a summary statement that is simple for all stakeholders to understand and address the levels and types of risk that the entity is willing to accept in order to achieve its objectives. The following is a brief description of the most common limits. Credit Risk Type of Risk Typical Metrics Remarks Issuer Maximum nominal per name PD-based analysis, LGD Liquidation Maximum nominal per name Analysis based on PD, LGD, deadlines. - Amount Deadlines. Delivery - Nomial Counterparty Market value Potential exposure TABLE 2 PD-based analysis. LGD Estimated volatility of the underlying reference instruments. Concentration limits. Credit risk metrics The main factors linked to credit risk are as follows: Total available liquidity. Each entity’s own resources. Rating. CDS quotes (probabilities of default). Position of the entity among its competitors. Country risk assessment: reserve level statements, possible devaluations, economic environment. Analysis of the banking system: -- Structure. -- Regulation. -- Government. Legal existence: bank incorporation document. Priorities in the event of liquidation. Sources of information. -- The accreditor’s own: audited annual accounts, annual report, economic publications, etc. -- Others: Boards of Directors, Central Banks, Chamber of Commerce. -- Rating agencies. -- Share price, etc. 44 PRINCIPLES OF RISK MANAGEMENT Capital Measure of the degree of compensation of the portfolio and risk with the equity available to absorb potential losses. Primary reference for the financial health regulatory body. Assets Asset quality is the most important and most difficult element to measure, mainly because it is highly subjective. The most important indicators are: -- Credit risk measurement culture: reporting, internal rating, etc. -- Overall loan portfolio valuation: sector concentration, recovery rates, growth rates. Management -- Evaluation: subjective. -- Loan approval culture. -- Information to senior management. -- Strategies implemented. -- Internal control systems. -- Decision-making procedure. Profitability -- Measure of the ability to create shareholder value. -- Quantitative measure of the management of its executives. -- Quality of benefits and sources. Liquidity -- Balance sheet management. -- Interest rate sensitivity analysis. Solvency ratios -- Leverage/Debt: Total debts/equity. -- Interest Coverage: BAIT/Financial Expense. Liquidity ratios -- Current: Current Assets/Current Liabilities. Profitability ratios -- ROA: of total assets = Net Income/Total Assets. -- ROI: of investment= BAIDT/ Net Operating Assets. -- ROE: on shareholders’ equity= Net income/ Shareholders’ equity. Limitations -- The degree of openness is small in some countries. -- They do not always reveal the true causes of the crises. -- Accounting techniques may be unorthodox compared to standards. -- The information is obsolete by the time it is received. -- In troubled banks it is not very representative. -- To be completed with qualitative analysis. 1.3.5 Key Risk indicators for the credit portfolio A definition of key risk metrics and indicators to analyze the evolution of credit quality versus appetite is very relevant. Indicators included in RAF (risk appetite framework): NPLs, coverage ratio, concentrations, etc. Indicators defined to achieve RAF objectives related to lending policies: minimum ratings/scorings, LTVs, funding ratio, maturities, etc. Indicators to detect changes in the trend of the portfolio profile and risk factors with impact on provisions: portfolio concentration by worst rating and scoring levels, alerted clients, use of limits, refinancing, opening by sectors, geographical areas, evolution of collateral value, etc. 45 FIGURE 14 Internal ratings Monographic reports with indicators of the evolution of provisions: distribution by stages, transition matrixes, analysis of the causes of entry into stages, etc., aimed at defining management measures with a direct impact on provisions. Specific indicators of policy compliance: overdue revisions, out-of-policy concessions, etc. 1.4 Market risk Market risk is induced by exposure to price variations in financial variables that may adversely affect the value of our portfolios. Its estimate aims to obtain potential losses under normal market conditions largely based on historical information or, in some cases, scenarios with a stochastic component. Achievement of objectives 1.4.1 Definition It is essential to conceptualize the portfolio monitoring process as an analysis exercise against target values of metrics and KRIs. This drives management decision-making in the face of quantitative triggers in the event of deterioration. As already mentioned, the Value at Risk is the maximum likely loss of a portfolio for a given confidence level over a specified time horizon. The term “maximum probable quantity” implies normal market movements (excludes large financial crises). 46 PRINCIPLES OF RISK MANAGEMENT There are certain concepts that we must specify: correlations and assuming a perfectly positive correlation structure (100%). Confidence levels Historical data The level of probability that the actual losses of the portfolio will exceed the estimated VaR figure for a pre-defined time horizon depends on the confidence level selected. Virtually all market risk measurement methodologies use historical data (prices, interest rates, volatilities, etc.). The final result will depend on the size and historical period (time window) chosen. Time horizon A time horizon must be established to calculate the VaR and be able to contrast the result. It is the period for which the maximum likely loss is estimated, from the present moment to the future. It is usually associated with the period necessary to be able to undo the position or cover the portfolio if it is not possible to close it. This means acting in the market without the variables, which affect the value of the portfolio, being altered and harmfully affecting the value of the portfolio itself as a result of the action. By virtue of this, short time horizons should be assigned to shortterm and long-term trading or speculative portfolios to more structural portfolios whose philosophy and dimension are not consistent with their liquidation in short periods of time. The VaR for a portfolio of assets The correlated net VaR is that VaR figure of a portfolio of financial instruments that reflects their risk considering the correlation structure between them. The un-correlated gross VaR is that figure of VaR obtained as the sum of the individual VaRs of the financial instruments that compose it and that reflects their risk considering a correlation structure of 100% between them. Therefore, it overestimates the real risk. The correlation effect is the difference between the correlated net VaR and the uncorrelated gross VaR. It reflects the difference in risks inherent in considering The use of historical data far removed in time may not reflect the current situation of market risk. Therefore, in certain measurement techniques, the choice of the time window is crucial, since it can, depending on its length, incorporate particularly binding historical facts. The following suggestions may be used for guidance: -- Minimum dimension: 252 days. -- Optimal dimension: around 504 days. -- Dimension in time: constant. The size of historical samples should not be arbitrarily altered over time. The entry and exit of events that are relevant in terms of price variation must occur naturally and according to the size of the sale that has been chosen at a given time. Example Suppose a portfolio of 5,000,000 shares of a company listed at 4.83 EUR (24,155,000 EUR market value) whose daily VaR is 932,890 EUR, considering a confidence level of 95%. Interpretation: It is estimated that the losses should be higher than the VaR figure of 932,890 EUR in only 5% of the next sessions. In the others, losses below that figure, zero results or profits will take place. 47 VaR Properties The VaR is proportional to the market value of the position. An excess of VaR consumed over the limit can be normalized by reducing the position proportionally. VaR varies by market value, by changes in asset volatility, and by substitutions in the vector of historical price data. VaR varies daily, even while keeping the positions stable, due to changes in revaluation prices and in the vector of historical data. The VaR of a portfolio of assets is not the sum of its VaRs because of the correlation that exists between them. VaRs from different business units are also not summable due to their relationship. Earnings At Risk (EaR): It is the maximum likely benefit of a portfolio for a given confidence level over a specified time horizon. It is the antonym of VaR, insofar as it expresses the likely profit rather than the corresponding loss. Under assumptions of normality, in the variations of the value of the portfolio whose average is zero, the EaR will be the same as the VaR. Under any other premise, this will not happen. FIGURE 15 EaR and VaR. The EaR will relate the current market value of a portfolio of financial instruments and the potential gain generated by it for a given confidence level. 48 PRINCIPLES OF RISK MANAGEMENT The EaR/VaR ratio can be of great help in portfolio management to the extent that it will be an indicator of symmetry of results for a given level of confidence, especially when calculating the VaR with simulation techniques. Instruments or portfolios that show the highest possible EaR/VaR ratio will be preferred, as they will potentially generate positive results greater than negative ones in absolute value for the specified confidence level. Example Suppose a portfolio of 5,000,000 EUR shares of a company listed at €4.83 (24,155,000 EUR market value) and the daily EaR is 992,637 EUR, considering a confidence level of 95%. Interpretation: it is estimated that the benefits should be higher than the EaR figure of 992,637 EUR in only 5% of the next sessions. In the others, profits below this figure, zero results or losses will take place. Given the portfolio of shares in this example, whose VaR is €932,890 and whose EaR is 992,637 EUR, the EaR/VaR ratio is 106.40%. This means that, for the same level of confidence (in this case 95%), the expected profits are greater than the losses. Therefore, it is recommended that the portfolio only caters for this indicator. However, in the measurement of risk and management, this indicator is one more factor to take into account within a wide range of decision tools. Profit estimation can be conceived indistinctly in historical distributions or, for example, normal distributions (i.e. Gauss bell-shaped). FIGURE 16 Earnings at risk 49 Obviously, the selection of the distribution with which we have projected the profit and loss account will have implications for the results obtained, both for the calculation of the VaR and for the calculation of the EaR. The methodologies that we will address later differ fundamentally in the type of distribution they assume. It is one of the main methodological hypotheses that will condition the VaR figure. However, while there will be differences in the results obtained, these should not be materially relevant in relative terms. In any case, we will use that hypothesis about the distribution of the income statement that is best able to predict the behavior of these in the future. This is the big goal of market risk metrics in the context of Value at Risk. The Expected Shortfall (ES) If with the VaR we try to predict, under a certain probability, the risk that is assumed, the average excess (Expected Shortfall) predicts, for that probability, the average loss once the VaR has been overcome. This analysis is what is known as Expected Shortfall and should be included in the backtesting analysis. Profit and loss estimation can be conceived indistinctly in historical distributions or, for example, in normal distributions, i.e. in the shape of a Gauss bell. FIGURE 17 Expected Shortfall 50 PRINCIPLES OF RISK MANAGEMENT VaR and ESF are two risk measures Both are useful for measuring capital requirements, for quantifying and for regulating the risk taken by market participants. In a bank, the first utility is to ensure that the risk incurred remains within the forecast. In addition, for the management of that risk to be acceptable over time, any corrective action must be possible. The VaR does not tell us the magnitude of the potential losses that exceed the level of VaR; on the other hand, the Shortfall does. Not in vain, the guidelines outlined from Basel have reinforced this measure as a reference of growing prominence, especially after noting in the financial crisis of 2008 or in 2020, the limitations of the VaR despite all its virtues. In addition, it is necessary to know that the ES (Expected Shortfall) is always higher in absolute value than the VaR. 1.4.2 VaR metholologies The calculation of the VaR can be carried out through various methodologies. The starting assumptions in the various parameters that are used will mark the differences between methodologies. The most relevant differential element between them is the form of the distribution of the expected profit and loss account. There are three different methodological currents for the calculation of VaR: 1. Parametric VaR. 2. VaR for historical simulation. 3. VaR by Monte Carlo simulation. As we will see, the parametric VaR is characterized by assuming a predefined functional form of the profit and loss account to be projected. Quite often, this assumed functional form is a normal distribution, as long as the variable or variables that we are going to project are within the financial field. The two simulation methodologies, that is, the historical and MonteCarlo, will differ in the genesis of the simulation scenarios. 51 In the case of historical simulation, the scenarios will come from the distribution historically defined by changes in the prices of the variables that determine the value of the portfolio. In the case of MonteCarlo simulation, the scenarios will come from a stochastic simulation process. In any case, a predefined functional form will be attributed (in the financial field, it will most often be a normal distribution). In an introductory way, let’s define the three methodologies that will be developed later: 1.4.2.1 Parametric VaR It applies to the current value of the portfolio volatilities and correlations of market variables considering a calculation model and assuming the form of the function of distribution of the rates of variation (results) of the assets. αVaR = -μP&L + σP&Lzα zα = normal distribution of the variable α μP&L = P&Laverage σP&L = P&L standard deviation FIGURE 18 Normal VaR 1.4.2.2 Historical simulation VaR It applies to the current portfolio historical price variations of the variables to generate possible verifiable scenarios against that current position, generating simulated results from which the VaR will be obtained. It does not assume any form of the function of distribution of the rates of variation (results) of the assets. αVaR = -μP&L + σP&L hα μP&L = P&L average σP&L = P&L standard deviation hα = historical distribution of the α 52 PRINCIPLES OF RISK MANAGEMENT FIGURE 20 FIGURE 19 MonteCarlo Simulation VaR Historical Simulation VaR 1.4.2.3 MonteCarlo simulation VaR It applies to the current portfolio random price variations of the variables to generate possible verifiable scenarios against that current position, generating simulated results from which the VaR will be obtained. αVaR =-μP&L+σP&L εα μP&L = P&L average Case study; equity portfolio risk measurement with different methodologies Calculate the Value At Risk of a portfolio of shares of TELEFÓNICA, BBVA, worth 100,000 Euros distributed in equal proportions, using: Historical simulation methodology MonteCarlo simulation methodology Parametric normal methodology σP&L = P&L standard deviation A dataset is provided in Excel containing the historical 1000 prices for both shares εα = random distribution of the variable α Historical Simulation With the calculations made in Excel file: -- Returns: for each of the two stocks held in the portfolio and for each pair of consecutive price observations, the rates of relative variation are calculated. 53 -- Simulated values: from the last available prices of both shares, the simulated values are calculated by applying on them the variation rates obtained in the previous step. -- Value of the portfolio: once the prices of the simulated securities of each of the shares have been obtained, they are multiplied by the number of securities that each of them has in such a way that in this way the value in monetary terms of the portfolio is obtained for each of the simulations generated. -- Profit and loss: simply comparing each of the simulations generated both at the individual level of the two shares and for the total portfolio proceeds to calculate the difference with respect to the securities originally invested on the day on which the risk is being calculated, thus obtaining a profit and loss vector on which the VaR will be extracted. -- Finally, on the vector of total losses and gains obtained in the previous step, the percentile corresponding to the confidence level is calculated: 100%-95%, thus obtaining a Value At Risk of 2,776.48 Euros. Montecarlo Simulation With the calculations made in Excel file: -- Returns: for each of the two stocks held in the portfolio and for each pair of consecutive price observations, the rates of relative variation are calculated. -- Volatility and correlations: volatility for each series is calculated and the correlation matrix as well. -- Cholesky matrix: the Choslesky matrix is obtained from volatilities and correlations in order to generate random correlated scenarios. -- Simulated values (5000 simulations): from the last available prices of both shares, the simulated values are calculated by applying on them the random variation rates obtained in the previous step. 54 PRINCIPLES OF RISK MANAGEMENT -- Value of the portfolio: once the prices of the simulated securities of each of the shares have been obtained, they are multiplied by the number of securities that each of them has in such a way that the value in monetary terms of the portfolio is obtained for each of the simulations generated. -- Profit and loss: simply comparing each of the simulations generated both at the individual level of the two shares and for the total portfolio proceeds to calculate the difference with respect to the securities originally invested on the day on which the risk is being calculated, thus obtaining a profit and loss vector on which the VaR will be extracted. -- Finally, on the vector of total losses and gains obtained in the previous step, the percentile corresponding to the confidence level is calculated: 100%-95%, thus obtaining a Value At Risk of 3,090 Euros. 55 Parametric Normal With the calculations made in the Excel file: -- Returns: for each of the two stocks held in the portfolio and for each pair of consecutive price observations, the rates of relative variation are calculated. -- Volatility (σ) and correlations: volatility for each series is calculated and for the correlation matrix as well. -- Application of these volatilities to the individual nominal values of the positions, considering the time horizon for which the VaR estimate will be made. Thus, individually, the VaR has to be: 56 PRINCIPLES OF RISK MANAGEMENT If we consider together all the j assets of a portfolio, given the matrix of correlations, we have: 1. Maximizing the profit between assets and liabilities. 2. Modulating the exposure of these factors according to the future vision of: We obtain a correlated VaR of 3179 Euros. -- Market variables. -- New business opportunities. -- Customer behavior that could lead to transfers from one instrument to another. In summary, we have: Volatility Multiplier (95%) 1.91% 2.34% 1.64485363 1.64485363 1.593 € 1.963 € 100.00 % 59.30% 59.30% 100.00% VaR Correlation Correlated VaR -3,179 EUR 1 day VaR, 95% confidence level Historical Simulation -2.776 EUR MonteCarlo Simulation -3.042 EUR (5000 simulations) Parametric Normal -3.179 EUR 1.5 Asset liability risk 1.5.1 Definition Asset-Liabilities Management (ALM) is the strategic management of the balance sheet of financial institutions from the perspective of market and liquidity risks. The ALM function is complemented by the management or monitoring of trading positions, funding and equity planning. It affects all financial institutions that have a balance sheet subject to business risks as a result of credit operations, regardless of their trading activities. The fundamental objectives pursued are the measurement, analysis and management of the aforementioned risk factors by seeking: Also complying with banking regulations in terms of control, internal supervision, reporting and good capital management practices is part of ALM. 1.5.2 Types The banking business is based on three fundamental pillars, which are: Clients Margins Risk management. This last aspect interrelates numerous levers of the banking business, since in its field traditional banking activities are interrelated, with the most innovative in both commercial and wholesale banking. Depending on the type of banking business of each entity, the quantitative weight of these pillars may be different in the final income statement. In general, the financial risks that the balance sheet of the financial institution will face will be fundamentally: Credit risk. Interest rate risk. Liquidity risk. Exchange rate risk, if it has activity in various currencies. Operational risk. Legal risk. 57 Specifically, the risks that are understood as structural in the balance sheet of an institution are those of interest rates and liquidity. These risks will be addressed below. 1.5.3 Interest rate risk Interest rate risk is the risk that changes in interest rates will adversely affect an institution’s net interest margin or economic value. BIS definition: “IRRBB refers to the current or prospective risk to the bank’s capital and

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