risk management and financial engineering

3.2. Credit Risk Management

3.3. JP Morgan Credit Metrics

(Applying VaR Principles toCredit Control)

3.4 The Basel Risk Charges for

Derivatives

TOPIC 3:

CREDIT RISK

MANAGEMENT

Topic 3

3 CREDIT RISK MANAGEMENT........................ 267-339 3.1 CREDIT RISK MEASUREMENT.......................... 272 - 291 3.1.1 Overview.................................................................................. 273 - 276 3.1.2 Assessing Default Risk........................................................ 276 - 278 3.1.3 Recovery Rates...................................................................... 279 3.1.4 Credit Exposure..................................................................... 279 - 291

3.2 CREDIT RISK MANAGEMENT........................... 292 - 299 3.2.1 Netting Arrangements......................................................... 293 - 294 3.2.2 Periodic Settlement............................................................. 295 3.2.3 Margin and Collateral Requirements................................ 296 - 297 3.2.4 Credit Guarantees................................................................. 297 3.2.5 Credit Triggers...................................................................... 298 3.2.6 Position Limits........................................................................ 299 3.3 JP MORGAN CREDITMETRICS (APPLYING VaR PRINCIPLES TO CREDIT CONTROL). 300 - 327 3.3.1 Measuring Credit Risk More Accurately........................ 301 - 315 3.3.2 Reducing Credit Risk - Overview...................................... 315 - 318 3.3.3 Using Credit Derivatives to Reduce Credit Risk......... 318 -327 3.3.4 Conclusions.............................................................................. 327

3.4 THE BASEL RISK CHARGES FOR DERIVATIVES...... 328 - 339 3.4.1 Introduction............................................................................ 328 3.4.2 Basic Information................................................................. 329 3.4.3 Counterparty Risk................................................................. 329 - 330 A. Customer Risk................................................................... 329 B. Country Risk....................................................................... 329 C. Transfer Risk..................................................................... 330

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3.4.4 Product Risk............................................................................ 330 - 331 A. Principal and Interest Rate Exposure....................... 330 B. Replacement Risk.............................................................. 331 C. Settlement Risk................................................................ 331 D. Collateral Risk................................................................... 331 3.4.5 Swap Credit Risk................................................................... 332 - 333 A. Introduction...................................................................... 332 B. Swap Risks.......................................................................... 332 - 333 C. Swap Credit Risk Assessment...................................... 333 3.4.6 Financial Futures Credit Risk............................................ 334 - 335 A. Introduction...................................................................... 334 B. Futures Risks..................................................................... 335 3.4.7 FRA Credit Risk..................................................................... 336 - 337 A. Introduction...................................................................... 336 B. FRA Risks............................................................................ 336 C. FRA Credit Risks.............................................................. 337 3.4.8 Options Credit Risk.............................................................. 337 - 339 A. Introduction...................................................................... 337 - 338 B. Exchange vs OTC Options.............................................. 338 C. Options Risks..................................................................... 339 D. Quantification of Credit Risks.................................... 339 Table 3.1 Probability of Credit Change.................................................... 306 Table 3.2 Probability of a Change in Credit Rating for Bond One... 308 Table 3.3 Rating Probability for First Issuer........................................ 309 Table 3.4 Spreadsheet Formulas to Calculate Standard Deviation for Table 3.2............................................................................. 309 Table 3.5 Rating Probability for Second Issuer................................... 310 Table 3.6 First Monte Carlo Simulation................................................... 310 Table 3.7 Discount Factors for Bond Ratings........................................ 312 Table 3.8 Bond Valuations for Different Credit Ratings................... 312 Table 3.9 Valuation of a Portfolio.............................................................. 313 Table 3.10 Specifications for a Total Swap............................................. 321 Table 3.11 Details of Bond Issuer............................................................... 321 Table 3.12 Default Swap Details.................................................................. 324 Table 3.13 Comparison Between Credit Instruments............................ 325

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Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6

Expected Credit Exposure and Credit at Risk..................... Credit Risk vs. Normal Market Risk......................................... Probability of Default.................................................................. Binomial Distribution.................................................................... Total Return Swap......................................................................... Default Swap................................................................................... 286 303 307 307 319 323

270

Time and again, lack of diversification of credit risk has been the primary culprit for bank failures. This topic will provide an extension of classical risk management methods to credit risk. It will explore the two major components of credit risk, default risk and exposures. Reference: John C. Hull, “Options, Futures and Other Derivatives”, 6th Edition, Prentice Hall, 2005, Chapters 20 Reading Materials: 1. Philippe Jorion, “Value at Risk The New Benchmark for Managing Financial Risk”, 2nd Edition, McGraw-Hill, 2000 2. John C. Hull, “Options, Futures and Other Derivatives”, 6th Edition, Prentice Hall, 2005. 271

TOPIC 3.1:

CREDIT RISK MANAGEMENT

3.1.1. Overview

3.1.2. Assessing Default Risk

3.1.3. Recovery Rates

3.1.4. Credit Exposure

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TOPIC 3: CREDIT RISK MANAGEMENT

3.1 CREDIT RISK MEASUREMENT

3.1.1 Overview

Credit risk can be defined as the risk of loss arising from the failure of a counterparty to make a contractual payment. Some examples are the risk that a bondholder bears from the possibility that the bond issuer will default and the risk that an option holder bears from the possibility that the option writer might not honor the contract if called upon to do so. Credit risk has three main components:

1.

Probability of default: the probability that the counterparty will fail to make a contractual payment.

2.

Recovery rate: the proportion of our claim that we recover if the counterparty default.

3. Credit exposure: credit exposure relates to the amount we stand to lose in default. This is usually interpreted as the replacement value of the contract in the event of default, net of whatever we expect to recover from the counterparty.

We now have two main tasks: to analyze and measure these three components of credit risk, and to investigate how institutions can influence these factors to reduce their credit risk.

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HISTORICAL CONTEXT

It is important to appreciate how credit risk has altered in recent years. Traditionally, credit risk was mainly the concern of bank lending managers, bondholders and specialist credit rating analysts. The basic question was whether to grant a loan or buy a bond, and the credit exposure from any transaction was readily related to the book value of the amount loaned plus any accumulated interest.

Credit risk has since become much more complex. Whilst loans and bonds are still significant, a great deal of credit risk now arises from derivatives transactions. Credit risk is therefore a major concern to many of the institutions that participate in derivative markets, many of whom bore little credit risk in the past except for the trade credit they extended to their customers. Moreover, the newer credit risks are often less transparent and more difficult to assess than traditional credit risks. They are more difficult to assess for three main reasons:

☛ Notional amounts often give us little idea about derivative credit

exposures. With a bank loan, we at least knew that the book value of the loan gave us an idea of the amount we could lose. We could then estimate our likely loss by applying some estimates of default probabilities and recovery rates to this notional amount. However, with derivatives contracts there is often no clear relation between a contract’s value and its credit exposure. For example, swap or forward contracts will usually have zero initial values, and yet both contracts can produce large losses if the underlying variables move strongly in the wrong direction. Hence, when an institution engages in a derivatives deal, it is often not immediately obvious how much credit risk it is really taking on.

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☛ The credit risks associated with derivatives positions can vary

enormously (e.g., as with leveraged structured notes) and in complicated ways (e.g., as with cylinder options), with movements in underlying prices. In some cases, maximum losses can also occur when the underlying price does not move at all (e.g., as with a long straddle).

☛ Derivatives credit risk is further complicated by portfolio effects. With

loans, we know that the total exposure is closely related to the total gross amount loaned. However, with derivatives there are no simple rules to relate total credit exposure to the gross size of a derivatives portfolio. If we have two zero-value FX forward contracts, say, and one contract gains in value when the underlying exchange rate rises but the other falls, then the credit exposures of the two contracts will move in opposite directions when the exchange rate changes. In general, we cannot get an accurate picture of overall credit exposure by adding up individual exposures, because the individual exposures may (and generally will) interact with each other.

Consequently, it is not surprising that institutions had difficulty when they first started to handle derivatives credit risks, and resorted instead to convenient rules of thumb. For example, when interest-rate swaps were first being used in the early 1980s, institutions tended to treat swaps as offsetting bond purchases because doing so implied that a swap had the same credit risk as a bond purchase from the same counterparty. Unfortunately, this procedure overlooks an important difference: while mutual bond purchases imply commitments to make both coupon and principal payments, an interest-rate swap involves no exchange of principal at maturity and only

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implies a commitment to make mutual coupon payments. Hence, an interest-rate swap involves a lower credit risk - typically, a much lower one - than a corresponding mutual bond purchase. The result was that companies tended to overstate the default risk of swaps. Yet, as time passed and defaults were seen to be relatively rare, there arose an opposite tendency to regard interest-rate swaps as having no default risk at all, and some of those who did so became unstuck in the early 1990s. Swap managers swung from one extreme to the other. The truth of the matter is that interest-rate swaps are risky, though not nearly as risky as bonds, but we can only assess their true credit risk if we abandon rules of thumb and resort to some decent credit risk analysis.

3.1.2 Assessing Default Risk

Traditionally, likely default rates were assessed by loan officers using information from financial statements, knowledge of the relevant firm’s history, a view of the quality of the firm’s management and an assessment of its prospects. More recently, Moody’s and Standard and Poor’s have published studies of bond defaults in the US that enable one to use current credit ratings to predict default rates over specified horizons. These exercises indicate that there is a strong negative correlation between credit ratings and default rates, and this finding allows us to use current credit ratings to predict bond default rates.

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Predictions of default rates can also be improved by using other observable factors. The work of Edward Altman in particular has examined the predictive power of a range of financial variables and uses the results to discriminate between those firms likely to fail and those that are not. Altman’s procedures are reasonably good at discriminating between these types of firm, and can therefore be used to fine-tune predicted failure probabilities. However, they are not well suited to predicting the failure rates of highly rated firms. Since highly rated firms are very unlikely to default, we can expect only a very small number of such firms to fail in any given sample. Hence, even a good discriminant rule that correctly predicts their failure will also incorrectly predict the failure of a large number of other firms that do not subsequently fail. The cost of these errors is therefore likely to be high relative to the benefits of being able to identify the small number of highly rated firms that do fall. Accordingly, Wakeman (1996a. p. 316) recommends that we do not bother with such methods when trying to predict the failure rates of highly rated firms. We should therefore concentrate our credit evaluation procedures on firms with lower credit ratings or no credit ratings at all.

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Topic 3: Credit Risk Management BOX 3.1: DIFFERENCES BETWEEN CREDIT AND MARKET RISK Credit and market risks differ in a number of ways: (1) To handle credit risk we need to pay attention to default probabilities, recovery rates in default, and the identity of ourcounterparties - factors that are not directly relevant to market risks. (2) When dealing with market risk, we tend to focus on risk overone, often relatively short, time horizon; when dealing with credit risk, we often tend to be concerned about risks over a much longer horizon, until the credit risk is eliminated. (3) Assuming normality with credit risks is more problematic thanassuming normality for market price risks. There are two reasons for this. (a) Normality is harder to justify over the longer horizons often relevant for credit risk. (b) When dealing with credit-related risks, the underlying risk variable - the occurrence or otherwise of default - is not itself normally distributed, and this makes it harder to treat the resulting credit risks as normally distributed. (4) When trying to control market risk, we usually try to impose position limits on individual unitswithin our organization. When trying to control credit risk, we try to impose limits on the other party (i.e., the counterparty) taken as a whole. (5) While market risk issues are legally clear-cut, there are a number of major legal uncertainties surrounding credit risk (e.g., over the legal status of netting agreements and the ownership of collateral in default), and these uncertainties are a major source of concern for credit risk managers andcorporate lawyers. 278 Professor Malick Sy

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3.1.3 Recovery Rates

The second major factor affecting credit risk is the amount recoverable in default: the greater the amount we expect to recover, the lower the credit risk, other things being equal. Not surprisingly, evidence indicates that recovery rates vary considerably. They depend on the seniority ranking of the creditor: recovery rates typically vary from 10 - 50% for subordinated debt, 30 - 70% for senior unsecured debt, and 40 - 90% for secured debt, and derivatives claims generally rank equally with senior unsecured debt.

Recovery rates also depend on the terminal value and credit rating of the defaulted firm, the bargaining power of different groups, the arbitrariness of the legal process, and other relevant factors.

These figures also give a clear indication that courts tend not to apply absolute priority rules, so junior creditors often get some payment when senior ones are not paid off in full, despite absolute priority rules that should, in principle, require creditors to be paid off in strict order of seniority.

3.1.4 Credit Exposure

Credit Exposure as Replacement Cost

An institution faces credit exposure on a contract only if that contract has a positive market value to the institution. Its replacement cost is then equal to this positive value minus whatever is recovered from the defaulting counterparty (collateral, proceeds obtained through bankruptcy court, and so

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on). If a contract has a negative value, on the other hand, the institution is owed nothing and therefore has no current credit exposure. Hence, the replacement cost of a contract is the bigger of the market value of the contract minus its recovery value, or zero.

In practice, we will usually be interested in fours sorts of exposure: the expected credit exposure and expected default loss, and the maximum likely credit exposure and maximum likely default loss, at given levels of confidence. We now consider each of these in turn.

Expected Credit Exposure and Expected Default Loss

The expected credit exposure can be found by specifying a PDF for our net replacement cost - either a theoretical one such as a normal distribution, or an empirical one based on real-world data - and taking its mean. Let x be the estimated replacement value of a contract at some future date t. If x has a PDF f(x), the expected credit exposure (ECE) is.

∞

Expected credit exposure = ∫−∞Max(x,0)f(x)dx …Eqn (3.1)

This equation tells us that the ECE is the probability-weighted average of possible credit exposures, where each credit exposure is the maximum of the amount we are owed, if positive, and zero otherwise. If f(x) is normal with standard deviation σ, then Expected credit exposure = σ / √ 2π …Eqn (3.2)

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Topic 3: Credit Risk Management BOX 3.2: THE BIS ADD-ON APPROACH TOCREDIT RISK During the last decade many institutions have attempted to allow for credit risk by the add-on procedure used by the BIS to determine minimum capital requirements. As revised in 1995, this procedure allowsfor credit risk by classifying instruments into categories and giving each category a fixed weight. With on-balance-sheet positions, the credit exposure is held to be the nominal value of the position times the relevant credit weight. For off-balance-sheet positions, the credit exposure is held to be a credit equivalent amount (CEA) times a relevant credit weight, and this CEA is equal to the absolute value of the mark-to- market value plus an add-on factor, itself taken to be a certainpercentage of the effective notional amount. Different percentages are specified for different types of position, and positions are classified in terms of the type of contract (e.g., interest-rate, FX) and the time to maturity (e.g., less than one year). The total credit exposure is the sum of the credit exposures of the individual instruments, subject to some limited (and arbitrary) allowance for the netting of risks. This approach has the attraction of being simple to operate, but its drawbacks far outweigh any advantages. The most fundamental problemis that it does not tell us much about credit exposure at all, except for the most simple portfolios and only then if the weights just happen to be about right. More specifically: (1) The principle of allowing for credit risk by fixed ‘add-ons’ is intellectually indefensible, and makes no allowance for default risks, market volatilities, recovery rates, and so on. (2) The broad categories used - interest-rate contracts, and so forth -are far too broad to do any justice to the contracts involved. Two interest-rate derivatives can have very different risk exposures, andwe cannot do justice to them by imposing the same exposure weights on each. (3) The weights chosen are completely arbitrary and do not reflect the diversity and complexity of real-world credit exposures. (4) The add-on approach makes no genuine allowance for portfoliofactors, and the modifications used to allow for them do not really do so. This in turn usually leads to risk exposures beingoverestimated. These drawbacks have led many institutions to abandon the BIS model when assessing their credit risks and to develop their own modelsinstead. 281 Professor Malick Sy

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The expected credit exposure is therefore a multiple (i.e., 1 / √ 2π) of the standard deviation of the estimated replacement value.

We can also estimate the expected default loss. This is the loss in the event of default times the probability that the contract is in the money and the counterparty defaults, and this latter probability is usually the probability of default times one-half. Hence

Expected default loss = ECE . prob[default]/2

The expected default loss under a normal distribution is then found by substituting Eqn (3.2) into Eqn (3.3): Expected default loss = σ. prob[default]/ √ 8π …Eqn (3.4)

This expected default loss tells us how much we can expect to lose from our estimated credit exposure on a certain contract over a certain period. This is very useful cost information and should always be subtracted from the contract’s expected revenue if we are to arrive at an appropriate estimate of the project’s expected profit. Such information is not only useful for budgetary purposes, but can also be useful to set up default reserves, rank prospective contracts, and guide purchase and sale decisions.

…Eqn (3.3)

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CREDIT AT RISK AND DEFAULT VALUE AT RISK

We can also estimate the maximum credit exposure at some level of confidence. This maximum is not to be confused with the maximum credit exposure possible. Instead, the maximum credit exposure with which we are concerned is an upper bound on a confidence interval for the estimated replacement cost. If we chose the 95% confidence level, we would therefore have the maximum credit exposure that we could expect on 19 days out of 20. We can regard this estimate as a kind of credit exposure at risk, or Credit at Risk (CaR) for short, and can formalize it in the same way as the expected exposure. If we again assume that the replacement cost is normally distributed, the credit at risk at the 95% confidence level is:

Credit at risk = 1.65σ …Eqn (3.5)

This figure gives us an estimate of our maximum likely credit exposure by a certain future time. This can be very useful when making purchase and sale decisions, pricing contracts, setting and/or monitoring credit limits, evaluating performance and allocating capital.

We can also estimate the maximum default loss (as opposed to credit exposure) at the same confidence level. This tells us the maximum loss to expect from default in 95% of cases. It is therefore a measure of the value at risk arising from credit risk, as compared to the earlier VaR that arises from market-price risk. In other words, it is a measure of default-related value at risk, or default VaR for short. Assuming normality and an exogenous default probability, this default VaR is:

Default VaR = 1.65σ prob[default]

…Eqn (3.6)

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This default VaR is extremely useful, and has all the obvious uses of other VaR figures: it can be used to assist purchase/sale decisions, price contracts, allocate capital, and so forth. Since it gives us the maximum likely loss from counterparty defaults, but ignores market risks, it is a mirror image of, and in fact a natural complement to traditional VaR, which looks at market risks but ignores default-related risks.

DYNAMIC PROFILE OF CREDIT EXPOSURES

These measures, however, give us information about prospective exposures or losses only over a specified future period, and this information is usually not enough for reliable credit analysis. Credit analysis is not like, say, VaR analysis, where we can usually assume that the VaR over one holding period is highly correlated with the VaR over some other holding period. The prospective credit exposures on a given portfolio often change dramatically as we look further into the future, so we cannot assume that our prospective exposure two years from now, say, is a simple ‘well-behaved’ function (e.g., a straightforward extrapolation) of our credit exposure six months from now. Depending on the position, our credit exposure may rise or fall over time, or move around in all sorts of convoluted ways.

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Topic 3: Credit Risk Management BOX 3.3: CREDIT at RISK AND DEFAULT VaR vs. VERSUS ‘TRADITIONAL’ VaR Whilst credit at risk and default VaR are analytically similar to‘traditional’ market-price VaR, there are nonetheless a number of important differences between them: (1) CaR and default VaR are more difficult to estimate thanmarket VaR, since they require estimates of recovery rates, collateral, guarantees and other variables. They therefore require more information and are more dependent on theassumptions that go with using such information. Default VaR also requires estimates of likely default rates, and these too are problematic. (2) The nature of credit risk compels us to consider the dynamic profiles of credit at risk and default VaR. Unlike traditional market-price VaR, we cannot usually get away with looking over only one horizon period, such as the next day. We need to consider credit exposures over a number of different periods. (3) CaR and default VaR require that we consider each counterparty separately. We therefore have to consider bothcounterparty and position type, not just the latter. (4) The very nature of credit risk means that we are dealing with losses that will not be realized in most instances, but will alsobe much bigger than expected ex antein those cases where they do occur. The distribution of losses will therefore exhibit potentially very fat tails. 285 Professor Malick Sy

Topic 3: Credit Risk Management (a) Expected Credit Exposure and Credit at Risk for Hypothetical Forward Contract Credit Exposure Credit at Risk Expected Credit Exposure (b) 2 4 6 8 10 Years after initiation Expected Credit Exposure and Credit at Risk for Hypothetical Five-Year Interest Rate Swap Credit Exposure Credit at Risk as Percentage of Notional Principal 12 24 36 48 60 Months after initiation Expected Value as Percentage of Notional Principal Expected Credit Exposure and Credit at Risk Figure 3.1. 286 Professor Malick Sy

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Some examples of typical credit exposures for simple positions are given in Figure 3.1. Figure 3.1(a) shows the mean and maximum exposure curves for a forward contract, while Figure 3.1(b) shows the same curves for an interest-rate swap. As we can see, in both cases the two curves begin at a zero exposure - reflecting the initial zero market value of each contract - and then rise as the horizon increases.

These increases in exposure reflect a diffusion effect: exposures rise because the underlying variable on which exposure depends is likely to move more over a longer horizon than over a shorter one. However, the exposures of the two contracts differ at medium and long horizons. With the forward contract, there is no offset to diffusion so the exposure continues to rise as the horizon increases. However, in the case of the swap contract, each set of regular payments reduces the value of outstanding obligations. The contract amortizes over time, and this amortization process serves initially to dampen the diffusion effect and then eventually to overcome it.

As the swap approaches maturity, most payments will have been made already and there will be relatively little credit still outstanding. The swap exposure therefore peaks somewhere in the mid-term of the contract and then gradually goes back towards zero as the swap approaches maturity.

However, these are only the credit exposures of uncomplicated positions, and even simple alterations of the contract terms can make a big difference to the exposure profile. Imagine, for example, that we introduce a mutual termination option in the swap contract that gives us the right to close out the contract after two years.

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Assume too that we expect this right to be exercised and a three-year swap to be initiated at that point to replace what is left of the terminated swap agreement.

The credit exposure in Figure 3.1(b) would then dip back down to zero after two years, only to rise again and show another hump over the two- to five-year period. This simple adjustment would therefore lead to two peak exposures, one occurring after about one year and the other after about four years, rather than one single peak exposure occurring mid-way over the five-year period.

Furthermore, the adjusted contract would show relatively little exposure at the very time when the exposure on the unadjusted one was peaking. This example illustrates the importance of looking at the whole profile and not just at the prospective exposure at one particular date. Naturally, the credit exposures of more sophisticated derivatives positions can be even more complicated.

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Topic 3: Credit Risk Management BOX 3.4: A SHORTCUT TO CREDIT at RISK AND DEFAULT VaR If we are prepared to make certain simplifying assumptions, we can estimate credit at risk and default VaR easily from existing estimates ofmarket-price VaR. Suppose we wish to estimate our credit exposure over the same period for which we estimate VaR (e.g., over a month). If we start with zero credit exposures, assume that the recovery value ofdefaulted contracts is zero and ignore non-credit-related profits (e.g., capital gains on equity holdings), then our credit exposure by the end of the next day will equal our accumulated profit. Our credit at risk will therefore beequal to the upper fifth percentile of our profit/loss distribution. If we now assume that the profit and lossdistribution is symmetric, with azero mean profit, the upper fifth percentile profit (i.e., the CaR) will be equal to the lower fifth percentile loss (i.e., the VaR itself), so the CaR is equal to the VaR. We can then estimate a shortcut default VaR by applyinga default rate to the CaR just estimated. (For example, if the estimated default rate is 1% and the CaR is $100 million, our default VaR would be $1 million.) We therefore have the following two shortcut formulas: Credit at risk (CaR) = VaR Default VaR = prob[default].VaR We can of course modify the formulas accordingly if we wish to relax the assumptions that the profit and loss distribution is symmetric and has zero mean. We can also relax other assumptions, such as that of zero recoveryvalue. For example, we could assume a certain average recovery value, which would lead to CaR being a known fraction of maximum likely profit. Alternatively - and this might be particularly appropriate if recovery value islow and/or recovery itself particularly uncertain -we could keep the zero recovery assumption and regard the CaR and default-VaR figures as conservative (i.e., upper-bound) estimates. This approach has the attraction of giving us a short cut to the estimation of credit and default risk without the need for ‘real’ credit data. However, it is also dependent on a number of obviously dubious assumptions. It is also limited by the requirement for a VaR figure predicated on the horizon periodin which we are interested. If we are interested in credit/default risk over the next year, we would want a VaR figure that was also based on an annual holding period, and so on. The only practical solution in thesecircumstances is to fall back on the assumption that the underlying profit and loss distribution is appropriately well behaved (e.g., normal). Only thencan we infer the VaR(s) for the relevant horizon period(s). Hence, this shortcut implicitly requires normality or some substitute distributionalassumption, and such an assumption will often not be appropriate. 289 Professor Malick Sy

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PORTFOLIO EFFECTS

We must also consider how individual credit exposures interact with each other when put together in a portfolio, and we cannot assume that a portfolio’s aggregate exposure is simply the sum of individual exposures taken on their own. If we had a portfolio of two similar contracts, a given change in the underlying price would have much the same effect on the values of both contracts. The credit exposures of both contracts would therefore change in the same way, and the change in portfolio exposure would be the sum of the changes in individual contract exposures. However, in general, a change in a risk factor will lead to changes in the credit exposures of individual assets that are less than perfectly correlated with each other. Indeed, where portfolios are hedged, changes in risk factors will have no major effects on the portfolio as a whole, and hence no major effects on overall exposure. Individual positions may be exposed to a given source of risk, but whether and to what extent the portfolio is exposed will depend on how the individual exposures interact. Everything comes down to the interaction of the exposures.

Perhaps the best way forward is to map our exposures onto core risk variables and use a variance-covariance approach to allow for these interactions. The resulting credit-at-risk estimate is analogous to our earlier portfolio VaR estimates: it estimates the relevant maximum likely exposure at a given level of confidence, taking into account interactions among the exposures of the individual positions.

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We would also want some idea of prospective losses and not just exposures. We would therefore want a default-VaR system as well. The simplest way to construct such a system is to assume that default probabilities and recovery rates are constant and translate expected exposures into expected default-related losses using Eqn (3.6). This default-VaR figure would then give us the maximum amount we are likely to lose from counterparty defaults, at some level of confidence, taking into account the interactions of different underlying risk variables.

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3.2. Credit Risk Management

3.2.1. Netting Arrangements

3.2.2. Periodic Settlement

3.2.3. Margin and Collateral

Requirements

3.2.4. Credit Guarantees

3.2.5 Credit Triggers

3.2.6 Position Limits

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3.2 CREDIT RISK MANAGEMENT

There are thus three elements of credit risk: default probability, recovery rate and risk exposure. Credit risk management can therefore be regarded as a set of techniques for reducing default probability and risk exposure, and increasing the recovery rate.

3.2.1 Netting Arrangements

There are a number of different ways institutions can achieve these ends. One way is to use netting arrangements. These help to reduce credit exposures and are widely used in derivatives contracts. Netting arrangements stipulate that each party should be liable for the net rather than the gross amount they owe the other party. If there are two contracts between A and B, and the first contract has positive value to A and the second one has positive value to B, a netting arrangement means that A owes B only the difference between the values of the two contracts, if that is positive, or zero otherwise. Without netting, A would still be liable to pay B the whole of what it owes on the second contract, even if B defaults on the first. A netting arrangement protects the non-defaulting party from a situation where its counterparty defaults on one contract and yet simultaneously insists on the payment due on the other.

Without netting, the loss in the event of counterparty default is the sum of the net market values of all contracts (i.e., the market values net of collateral and the expected recovery value of counterparty assets) in the agreement, if the sum is positive, or zero, if the sum is negative:

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n

Potential Loss = ∑Max (Vi, 0)

i=1

…Eqn (3.7)

where there are n contracts between the two parties and Vi is the net market value of the ith contract. With netting, the potential loss is the sum of all positive-value contracts, viz.:

Potential Loss = Max (∑Vi, 0)

i=1n

…Eqn (3.8)

This netted amount will usually be less than the gross amount given in Eqn (3.7). The only exception is where all replacement costs are perfectly correlated, in which case the two amounts will be the same - and often very much less. The total potential loss to any party is then the sum of the potential losses over all counterparties - the sum of the gross potential losses Eqn (3.7), if there is no netting, or the (usually) smaller sum of net potential losses Eqn (3.8), if there is netting. In general, the reduction in credit exposure created by netting will also be greater, the greater the number of deals outstanding with a counterparty and the more nearly aligned the individual contracts are (in terms of maturities, contract size, and so on).

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3.2.2 Periodic Settlement

We can also reduce credit risk by agreeing to the periodic settlement of outstanding obligations at certain points during the lifetime of the contract (e.g., every quarter). Credit exposures are therefore periodically eliminated. An extreme version of periodic settlement is the daily marking to market that takes place on futures exchanges: gains or losses are realized in full at the end of each business day. Periodic settlement arrangements can be useful where counterparties are restricted in their ability to pledge assets or where there is legal uncertainty about the rights of collateral holders in bankruptcy. Alternatively, parties can simply agree to give each other options to terminate the contract early provided outstanding obligations are settled. Creditor parties can then use such options to realize their profits and cut short the credit extended to the debtor party. Creditors’ potential exposures can also be limited by stipulating that positions will be closed out if settlement/margin demands are not met.

However, these periodic settlement arrangements can also create liquidity problems. Firms that suffer adverse market moves will need to settle their losses quickly, and there is the danger that the need to settle quickly will provoke a liquidity crisis. Ex ante, a firm is taking on a potential liquidity risk when agreeing to such clauses, and the management ought to take this risk into account and consider how they would meet these liquidity demands if called upon to do so.

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3.2.3

Margin and Collateral Requirements

Institutions can also reduce their exposure by means of margin or collateral requirement, (i.e., so the counterparty makes available some particular asset that it would forfeit to a creditor in the event of default). Collateral might be demanded upfront, for example, as with the margin requirements of organized exchanges and many derivatives brokers. This margin is usually set to cover a specified large adverse move in the underlying price over some horizon period (e.g., a day for an organized exchange, but longer for some dealers).

The size of the margin requirements can be determined by theoretical considerations (such as extreme value theory, as suggested by Longin (1994)) and/or by reference to past experience. The margins could also be tailored to reflect the size of the position and the credit ratings of counterparties. The contract could then be marked to market, with collateral being returned if the market moves in favor of a particular party, and more collateral being demanded if the market moves against. This marking to market ensures that gains or losses are realized quickly and so prevents the build-up of large credit exposures.

If these additional margin demands were not met, the creditor party would have the right to close out the contract and so stop its credit exposure from rising any further. In other cases, there may be no margin upfront, but margin would be required if a contract’s value reached a threshold level. For instance, two parties might agree on an interest-rate swap with an initial value of zero, but also agree that the losing party would give the other a stipulated amount of collateral if the contract value reached a certain level.

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We can think of this as a marking-to-market arrangement by which a losing party agrees to realize its loss on the contract whenever the loss hits a threshold level. Again, credit exposure is limited by providing for positions to be closed out if required margin payments are not made.

3.2.4 Credit Guarantees

Credit risk can also be reduced by seeking guarantees from third parties. Such guarantees mean that default on the contract can occur only if both the counterparty and its guarantor default, and can sometimes lead to a major reduction in credit risk. Suppose that our counterparty has an estimated probability of default of 10% over a horizontal period. Now suppose that that party gets a guarantee from a company with an estimated default probability of 1% over the horizon. The probability of default on our contract then fails to 1% or less, depending on how the default probabilities are correlated (e.g., the probability of default will be 0.10 times 0.01, or 0.1%, if the probabilities are uncorrelated, and less if they are negatively correlated). Guarantees from third parties can therefore reduce credit risks drastically.

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3.2.5 Credit Triggers

Credit triggers are clauses that allow a contract to be terminated on pre-agreed terms if the credit rating of a counterparty falls to some trigger level. These clauses are similar to the covenants often used in commercial lending that specify that the debtor must maintain minimum net worth or credit ratings. They are often used in long-term derivatives contracts and typically specify that a party has the right to have the contract immediately settled if the counterparty’s rating falls below investment grade. A credit trigger protects against the credit exposure that would arise from a deterioration in the counterparty’s rating: should the counterparty’s credit rating deteriorate, the contract is terminated and the creditor can (hopefully) escape with his profit. It therefore ensures that default can occur only while the counterparty still has a strong credit rating (i.e., default can occur only when it is least likely to), and simulation evidence suggests that the reduction in default probabilities can be very substantial.

However, as with periodic resettlement, credit triggers can put considerable liquidity pressure on the losing party to a derivatives transaction. In fact, credit triggers go even further in that they hit the losing firm at a vulnerable time (i.e., when its cost of credit has risen and its access to credit has become more restricted). A credit trigger can therefore precipitate a liquidity crisis when a firm is downgraded, particularly if the firm has a number of outstanding contracts each of which includes similar credit triggers. Credit triggers therefore have a potentially serious downside, and the parties concerned need to think carefully about this before they agree to them.

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3.2.6 Position Limits

Institutions can also limit credit risks by placing position limits on their counterparties. Such limits might be based on both notional amounts (i.e., counterparty x might be allowed up to $y credit) and credit-at-risk figures. The latter limits would reflect measures of the total exposure to any given counterparty (e.g., maximum total exposure), given other relevant factors (e.g., existing exposure to that industry, prospective risks and returns elsewhere). From what has already been said, it should be clear by now that this total exposure is not just the sum of the individual exposures associated with each contract with that counterparty, but an aggregate exposure that takes account of the way individual position exposures interact.

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3.3. JP Morgan Credit Metrics

(Applying VaR Principles toCredit Control)

3.3.1. Measuring Credit Risk

More accurately

3.3.2. Reducing Credit Risk

3.3.3. Using Credit Derivatives to

Reduce Credit Risk

3.3.4. Conclusions

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3.3 JP MORGAN CREDIT METRICS

(APPLYING VAR PRINCIPLES TO CREDIT CONTROL) 3.3.1

Measuring Credit Risk More Accurately

INTRODUCTION

For centuries, banks have built up considerable expertise in the evaluation and control of credit. Yet, it is only recently that banks have started to look at credit risk from a portfolio basis. At the present time, most banks manage credit risk by imposing limits on the amount of money that they lend to a counterparty. The procedure is analogous to the way that market risk was traditionally controlled, simply by putting limits on the amount of money that traders could put at risk. Today, the emphasis is on using the techniques developed by VaR systems to quantify the overall credit risk assessment on a portfolio basis which measures exposure to market, rating change, and default risk. The overall role and aim of this approach is to help portfolio managers to better identify those areas which are contributing most to credit risk and, like VaR, to examine possibilities for diversification.

In the past, risk managers relied heavily on their own intuitive feelings when making decisions on credit risk. Obviously, a credit portfolio model will not replace the quality of the decisions that experienced credit managers will make, but it will focus minds on the marginal credit risk that a bank is exposed to as opposed to the absolute risk.

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RISK CONCENTRATION

One dilemma facing banks is that while they want to build up expertise in lending to a particular sector, they do not want to overexpose themselves to that sector. For instance, a bank may concentrate its lending portfolio on the British building sector. The benefit of doing so is that by gathering up specialist knowledge it has a better understanding of the building industry and can, therefore, forecast troubled companies or troublesome loans more accurately. However, by overexposing itself to one particular sector, there is the risk that the bank itself will collapse if the industry faces a downturn. In the past, banks have simply imposed counterparty limits as well as industry sector limits. Although such tactics control risk, they are unsatisfactory in that they prevent banks from exploiting lucrative and profitable opportunities. The ideal situation is where banks can build up their specialist knowledge and then diversify their risk away. In the past this was not possible, but now, with the emergence of credit derivatives, banks can apply their expertise in one sector and then “swap” credit risk with another bank in order to reduce its exposure, thus achieving diversification. VaR techniques have an important role to play for credit managers. In the first place, loan managers can identify those loans that contribute most to risk. Second, the risk manager can identify areas where credit derivatives can reduce his bank’s exposure to risk.

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THE MONTE CARLO APPROACH TO ESTIMATION OF CREDIT RISK

Up to now, we have relied heavily on the normal distribution curve when measuring VaR. It features in the variance covariance method and in Monte Carlo simulation. However, with credit risk, the normal distribution curve may not be the most appropriate model. Most experts believe that market risk does not have an exact normal distribution profile, but the distribution is at least symmetric, and so is close to being normally distributed. Credit risk is not symmetrical, and, thus less suited to the normal distribution curve. This is shown in Figure 3.2.

MarketReturns Credit Returns

Figure 3.2. Credit Risk vs. Normal Market Risk

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Topic 3: Credit Risk Management The normal distribution curve is the more symmetric of the two curves. This simply means that the returns of a portfolio have as equal a chance of going up as they do of going down. The curve for credit risk is, however, skewed. This means that in the majority of cases a portfolio will have above average returns. However, there are a few cases when the portfolio will make a loss and, although the probabilities of these losses are quite small, when they do occur, they tend to be quite large. So, although the probability of making losses is below 50 percent for credit risk, the probability that a portfolio will make a large credit loss is quite high. We can see, therefore, that traditional VaR methods (which rely on the normal distribution curve) will underestimate the possibility of making huge losses. The Monte Carlo simulation approach overcomes this weakness. CREDIT EVENT In order to measure credit risk, we must first define a credit event. A credit loss is usually triggered by what is known as a credit event. Put simply, a credit event can take two forms. First the firm goes bankrupt, and second, the firm suffers a credit downgrading, in which case the value of the loan or bond declines. The value of a bond can be decomposed between interest rate changes and changes in credit quality. 304 Professor Malick Sy

There are two types of credit event: ☛ the borrower goes bankrupt ☛ the borrower suffers a credit downgrading froma credit agency. Topic 3: Credit Risk Management

To assess credit risk we are not interested in the fact that an increase in interest rates may bring the price of a bond down. We are simply concerned with the loss in value of a bond or loan because the issuer or borrower has either defaulted or has suffered a credit migration; in such cases the probability of a default will increase.

DOUBTFUL LOAN PROVISIONS

For profit and loss purposes, a more satisfactory approach to credit loss is to recognize when the quality of the loan has reduced and not to simply “book” the bad debt when it arises. This obviously creates less distortion in the profit and loss account and the actual profit or loss is measured with greater precision. Most banks now use VaR techniques when estimating the size of the loan provision. If over a year the quality of a loan suffered but did not reach default stage, then the loss in value, as a result of the greater risk, should be incorporated into the profit and loss account.

PROBABILITIES OF A CHANGE IN CREDIT RATING

We can illustrate the probabilities that a particular bond will suffer either a credit migration or default. Tables as illustrated in Table 3.1 are generally available from credit reference agencies.

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Topic 3: Credit Risk Management Rating First IssuerInitial Rating BBB AAA AA A BBB 0.03%0.32%5.94%87.00%Second Issuer CCC 0.22% 0.01% 0.23% 1.29% 2.39% 11.25% 68.00% 16.61% 100.00%100.00% BB 4.40%B 1.20%CCC 0.13%Default 0.98% Table 3.1. Probability of Credit Change Assume that a bank has a portfolio of two bonds as shown above. The first issuer is BBB rated and the second issuer is CCC rated. The probability that the portfolio makes a loss is the total of the probabilities in bold type. For the first issuer this is 6.71 percent and for the second 16.61 percent. The first issuer has a credit rating of BBB, while the second one has a credit rating of CCC and a high probability of going into default. Notice that if the bonds had a normal distribution, then the combined probability of making a loss for each bond would be 50 percent each. Figures 3.3 and 3.4 intuitively explain why the normal distribution curve is unsuited to measurement of credit risk. 306 Professor Malick Sy

Topic 3: Credit Risk Management 77.80%Bond Two15.50%Bond One 5.60% Bond Two 1.10% 100% Figure 3.3. Probability of Default In Figure 3.3, the probability of not making a credit loss is very high at 77.8 percent and the probability of making a credit loss is 22.2 percent. In Figure 3.4, the probability of avoiding a loss completely is only 25 percent. The probability of making a loss will depend on the weightings of the bonds but in cases two, three and four, it is possible that a market loss can occur. Figure 3.4. 25% 1 25% 25% 2 3 25% 4 Binomial Distribution 307 Professor Malick Sy

Topic 3: Credit Risk Management Before we generate random variables, we must adjust the figures in Table 3.1 to standard deviations. To do this, we simply assume that bond prices follow a normal distribution curve and calculate the number of standard deviations. Note that at this stage we are looking at the possibility that bond prices will change but are not, at this stage, trying to calculate the losses. Therefore, we can use the normal distribution curve to see how many standard deviations are necessary before an asset moves up or down to new credit ratings. B 114 115 116 117 118 Rating 119 AAA 120 AA 121 A 122 BBB 123 BB 124 B 125 CCC Table 3.2. C D E Cumulative Probability Number of Standard Deviation From F Bond A Probability 0.03% To 2.70 1.53 -1.50 -1.99 -2.29 -2.33 0.32% 99.97% 3.43 5.94% 99.65% 2.70 87.00% 93.71% 1.53 4.40% 6.71% -1.50 1.20% 2.31% -1.99 0.13% 1.11% -2.29 126 Default 0.98% 0.98% -2.33 Probability of a Change in Credit Rating for Bond One Table 3.2 can be interpreted as follows. If the return of the asset moves, say, 2.5 standard deviations below the mean, its credit rating will be B (between -2.18 and –2.75). Alternatively, if the new return is two standard deviations above the mean, its new rating will be A. 308 Professor Malick Sy

Topic 3: Credit Risk Management =====The next step is to do simulation tables as follows: ====== === C ==D ====98 Probability 99 100 AAA 101 AA 102 A 103 BBB 104 BB 105 B 106 CCC 107 Default Table 3.3. 0.03% 0.32% 5.94% 87.00% 4.40% 1.20% 0.13% 0.98% Rating Probability for First Issuer B 114 115 116 117 118 Rating 119 AAA 120 AA 121 A 122 BBB 123 BB 124 B 125 CCC Table 3.4. C D E Number of Standard Deviation From F Bond A Probability Cumulative Probability 0.0003 To 0.0032 C120+D121 NORMSINV(D120) E121 0.0594 C121+D122 NORMSINV(D121) E122 0.8693 C122+D123 NORMSINV(D122) E123 0.0440 C123+D124 NORMSINV(D123) E124 0.0120 C124+D125 NORMSINV(D124) E125 0.0013 C125+D126 NORMSINV(D125) E126 NORMSINV(D126) 126 Default 0.0098 C126 Spreadsheet Formulas to Calculate Standard Deviation for Table 3.2 309 Professor Malick Sy

Topic 3: Credit Risk Management For Bond B the relevant table is as follows: B 128 129 130 131 132 Rating 133 AAA 134 AA 135 A 136 BBB 137 BB 138 B 139 CCC Table 3.5. C D E Cumulative Probability Number of Standard Deviation From F Bond B Probability 0.22% To 2.83 2.60 2.11 1.73 1.02 -0.97 0.01% 99.78% 2.85 0.23% 99.77% 2.83 1.29% 99.54% 2.60 2.39% 98.25% 2.11 11.25% 95.86% 1.73 68.00% 84.61% 1.02 140 Default 16.61% 16.61% -0.97 Probability Statistics for Second Issuer The first step in risk estimation, using Monte Carlo simulation, is to generate random variables. This is the equivalent to using the random function on Excel, but because bonds are correlated with each other, we must “adjust” the randomness of the numbers to reflect this. Let’s assume that the bonds have a correlation of 1. Then we can use the calculations in Table 3.6. Random numbers Standard deviations Cholesky adjustment Table 3.6. Asset One 0.1042 -1.2580 -1.2580 Asset Two 0.7845 0.7875 -1.2580 Rating BBB Default First Monte Carlo Simulation 310 Professor Malick Sy

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Table 3.6 can be intuitively interpreted as follows. Assume that the correlation between both assets is one. Asset One is a bond issued from Company X and Asset Two from Company Y. Both are in the same industry, and this explains the strong correlation between them. The second company is clearly the weaker because the asset starts off with a credit rating of CCC, which is close to default. The random number for Asset One is only 0.1042 and is well below the mean point of 0.50 (this is the point where the normal distribution curve is split in two). Therefore, the random generator has picked a scenario where the building industry has suffered. The random number for Asset Two looks brighter, but the Cholesky adjustment recognizes the fact that both assets move together. In other words, they have a correlation of 1; therefore, the random figure for Asset Two can be ignored. The figure -1.2580 applies to both bonds. This means that the returns of both assets have gone 1.2580 standard deviations below the mean. We then look up the tables for Bond A and Bond B. Bond A stays at credit rating BBB. From Table 3.2, we see that the movement -1.2580 falls between 1.50 and -1.53, and Bond B moves from CCC to default (i.e., -1.2580 is below -0.97 in Table 3.5).

The final step is to calculate the market value of each of these bonds after the simulation.

Services like JP Morgan’s CreditMetrics and other credit reference agencies are able to produce tables similar to Table 3.7.

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Topic 3: Credit Risk Management Category Year One Year Two Year Three AAA 4.00% 4.30% 4.70% AA 4.35% 4.65% 5.05% A 4.36% 4.66% 5.06% BBB 4.71% 5.01% 5.41% BB 4.72% 5.02% 5.42% B 5.07% 5.37% 5.77% CCC 15.42% 15.72% 16.12% Default Table 3.7. Discount Factors for Bond Ratings This table simply tells us that investors require a higher risk premium if they are going to buy a risky asset. The table also reveals that the yield curve is upward sloping, that is, in the long term, interest rates are expected to rise. In fact, it could be an indication that trouble might lie ahead for the building industry or other similar types of industries. For our Purposes, we need this information to value our bond. Assume that the first bond has three years left to maturity; we can use the grid in Table 3.8 to value it for each of the credit categories. AAA AA A BBB BB B CCC Default Table 3.8. $ 10 $ 10 $ 110 MV 0.9615 0.9192 0.8713 $ 114.65 0.9583 0.9131 0.8626 $ 113.60 0.9582 0.9129 0.8624 $ 113.57 0.9550 0.9069 0.8538 $ 112.54 0.9549 0.9067 0.8536 $ 112.51 0.9517 0.9007 0.8451 $ 111.49 0.8664 0.7468 0.6387 $ 86.39 Bond Valuations for Different Credit Ratings 312 Professor Malick Sy

Topic 3: Credit Risk Management To get the figure 0.9131 we take 4.65 percent for two years, that is 1/(1+r)^n = 0.9131. To calculate the market value, we simply discount each of the cash flows to their present value, that is for Bond AA $10 x 0.9583 = $9.583 and $9.583+ $9.131+$94.89 = $113.60. A default bond is a little bit more difficult to deal with simply because there would be uncertainty about the recovery rate. Again, credit reference agencies provide details of possible recovery rates in the event of default. For the sake of completing our table, we will assume a default recovery rate of 60 percent, giving Bond B a future value of $60. Time Period Random numbers Standard deviations Cholesky adjustment MV Nominal value holding Future market value Value of portfolio Table 3.9. Valuation of a Portfolio Asset One 1 0.1042 -1.2580 -1.2580 $ 112.54 $ 7,000,000 $ 7,877,800 $ 13,877,800 Asset Two 1 0.7845 0.7875 -1.2580 $ 60 $ 10,000,000 $ 6,000,000 Rating BBB Default 313 Professor Malick Sy

Topic 3: Credit Risk Management

This simulation could be done, say, 10,000 times and then we would take the five-hundredth lowest result to get the 95 percent confidence level. The difference between the current value of the portfolio and the “simulated” value of the portfolio would then be the credit at risk.

SUMMARY

This section illustrates how we can apply VaR techniques in estimating the amount of losses we could make due to a credit event, namely a reduction in the value of the loan or a default by the issuer. As with VaR, diversification is important. A bank could reduce risk if it diversified its portfolio across a broad range of issuers instead of concentrating on just a few areas. There is a conflict, of course, in doing this. Banks can reduce risk if they concentrate on once specific sector and build up expertise in that sector. The side effect of such a policy is that the bank is over-concentrated. We will see later how a bank can attain both objectives: specialize and diversify. This could be achieved, first, by using a portfolio approach to credit risk in order to estimate exposure and second, using credit derivatives in order to reduce specific exposure levels.

Unfortunately, credit risk does not follow a normal distribution, so we must alter the VaR methodology in order to measure the amount of credit at risk. Unlike market risk, VaR cannot assume that a portfolio of bonds follows a normal distribution. Therefore, we must look at each of the bonds separately but still apply normal distribution methodology to measure the risk that a bond will default. Once this is achieved, we calculate the value of the bond.

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Finally, we use Cholesky’s decomposition method to capture any correlation between bonds.

JP Morgan, the architect behind RiskMetrics, has introduced a new product - CreditMetrics - which is a framework for quantifying credit in portfolios of traditional credit products. As with VaR, the aim is to promote greater transparency of credit risk, and to provide a benchmark for credit-risk measurement.

3.3.2 Reducing Credit Risk - Overview

In the previous section I outlined the importance of measuring risk on a portfolio basis. In this section, I consider how we can use such measurements to reduce risk. Traditionally, banks set controls in two areas: 1. 2.

Banks would, of course, have restricted the amount of money they lent to customers with a poor credit rating. The worst fear naturally is that banks lend large amounts of money to companies, only to find that they have suffered a credit migration.

They considered the largest absolute size of the risk.

They considered the probability that a company would go into default.

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Calculating risk on a portfolio basis allows us to measure how much an individual instrument contributes to the overall risk of the portfolio. This allows for better decision making. We can, for instance, identify those types of loans that contribute most to risk. With this knowledge, a bank can make better quality decisions on resource allocation, performance measurement, and regulatory requirements.

REGULATORY REQUIREMENTS

Bank regulators have developed capital adequacy rules designed to penalize those banks which expose themselves to credit risk without implementing an appropriate hedge or control procedure. As with VaR, the purpose of portfolio risk management is to reassure the regulators that a particular bank is very aware of its credit exposures and has control procedures in place, thus reducing the possibility of closure. Obviously, it is in the interest of regulators to make sure that the portfolio risk management system is one that identifies not only the type of credit risk that a bank is exposed to, but also the effectiveness of the hedges used.

IDENTIFYING PRIME RISK EXPOSURES

Advanced portfolio credit risk management techniques can reveal important risk drivers. For instance, a bank may be exposed to an economic downturn in Belgium, and may also be heavily exposed to the electronics industry across the world. In these circumstances, it might be worthwhile to identify those clients that contribute most to risk within the electronics industry and which are based in Belgium and reduce that risk using credit derivatives.

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SUMMARY

The rationale for assessing risk on a portfolio basis is broadly similar to the rationale for measuring market VaR. To recap, we calculate VaR for four reasons:

1. regulatory requirements 2. setting market-risk limits 3. 4.

Although credit-risk measurements have some fundamental differences, VaR techniques can be incorporated for measuring and reducing exposure to credit risk.

TOOLS TO REDUCE CREDIT RISK

identifying the risk-reward relationship

identifying those areas of risk that need to be monitored more closely.

The growth in the market for credit derivatives provides an incentive for banks to pay closer attention to portfolio risk assessment. In the past, measuring risk on a country-by-country or industry-by-industry basis was useful for the setting of limits. However, as with market risk, setting credit limits involved more individual intuitive decision making than a scientific or rigorous approach. Most credit experts would still argue in favor of this approach. Portfolio risk management techniques can, however, like VaR, enhance the quality of decision making, as well as coordinate the activities of various lending officers. Without this coordination, banks could unwittingly become overexposed to the same risk drivers and, without realizing it, place all their eggs in one basket. Portfolio risk assessment can

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Topic 3: Credit Risk Management highlight this. More importantly, banks can now use credit derivatives to reduce domestic exposure and reduce concentration risk. Today, credit experts in major banks can identify economies with different cycles and characteristics and then, using credit derivatives, make sure that they are not overexposed to one particular type of economy. DISTINGUISHING CREDIT RISK FROM MARKET RISK One important contribution that credit derivatives have made is that they can distinguish credit risk from market risk. Consider a portfolio that has used interest rate futures to neutralize interest rate risk (which is market risk), and is left with a credit risk exposure. It is now possible to reduce this credit risk exclusively. In the past, banks were faced with a situation where they might have had to take on market risk alongside credit risk, by either buying or selling corporate bonds. Now this is no longer necessary. 3.3.3 Using Credit Derivatives To Reduce Credit Risk TOTAL RETURN SWAPS Total return swap – a total return swap transferscredit risk by swapping the returns of one particularasset from one party to another. The party whichreceives the returns pays the current interest rate tocompensate the party which pays the asset return. 318 Professor Malick Sy

Topic 3: Credit Risk Management LIBOR + spread Seller of protection A Asset return Buyer of protection B Corporate bond XYZ Figure 3.5. Total Return Swap Bank B has purchased a corporate bond in Company XYZ and seeks protection in case the company defaults. Bank B, therefore, enters into a total return swap with Bank A whereby B pays over the coupon plus any capital gain less any capital loss, and in return receives the current floating rate of interest (LIBOR plus spread). An alternative is, of course, for Bank B simply to sell the corporate bond and put the proceeds into a bank to earn the current floating rate of interest. However, the transaction costs of selling the bond might be high. Also, if the bond is illiquid and Bank B holds a large quantity, its price could come tumbling down. Third, if instead of purchasing a corporate bond, Bank B gave a loan to XYZ, banking relations might suffer if XYZ knew that its loan was being sold on. The solution then is effectively to “lend” the asset to Bank A and in return receive LIBOR plus a spread. 319 Professor Malick Sy

Topic 3: Credit Risk Management The total return swap also offers benefits to the seller of protection, Bank A. Bank A may, for instance, believe that XYZ’s credit rating is too high and that an upgrade is possible. To take a position on this, Bank A could simply buy the bond. However, transaction costs may be high, the bond may be illiquid, also, by buying the corporate bond, Bank A takes on an interest rate risk. A sensible solution to this, therefore, is to gain exposure to the credit change only, and this is what a total return swap allows the bank to do. If the underlying asset moves to a higher credit rating, Bank B gains from the increase in the economic value. If the bond suffers a credit downgrading or possibly a default, this will influence the asset return that Bank A receives. • ADVANTAGES OF A TOTAL RETURN SWAP OVER PURCHASE/OR SALE OF A RISKY BOND OR LOAN transaction costs are reduced illiquid nature of corporate bond could influencepurchase price confidentiality –client is not aware that lender ispurchasing protection. • • 320 Professor Malick Sy

Topic 3: Credit Risk Management ILLUSTRATION OF A TOTAL RETURN SWAP Table 3.10 illustrates a term sheet for a total return swap. Bank A pays Bank B pays Total return on asset with time adjustments on coupon where appropriate 6 month LIBOR + 80 basis points LIBOR USD LIBOR Principal $5,000,000 Initial price of asset Early termination Termination payment Capital Profit or loss Market price Business day convention Table 3.10. $102 Credit event as determined by independent party Capital profit or capital loss Market value at termination date less initial price of $102 To be established by the calculation agent 30/360 Maturity 5 years Documentation ISDA Specifications for a Total Return Swap Reference asset Name XYZ Corporation Grade BBB bond Type Senior bank loan Coupon 10% Maturity 5 years Payment Day count convention Table 3.11. Coupon paid per annum 30/360 Details of Bond Issuer 321 Professor Malick Sy

Topic 3: Credit Risk Management

The above is fairly straightforward. Bank B is the protection seller and so assumes any capital profit or loss on the reference asset. In return, Bank B pays A LIBOR plus the spread. In effect, Bank B is borrowing the asset from A and paying LIBOR plus the spread to compensate. Each year Bank B will receive the coupon and pay Bank A the floating rate of interest, until either the total return swap terminates or a credit event occurs. A credit event might be either a significant downgrading of the reference bond or an actual default. When this happens, an independent party, “the calculating agent”, decides the market value and Bank B pays over the difference. If, for instance, the calculating agent decides the market value to be $60, Bank B must pay to Bank A the capital loss $5,000,000/$100*($60-$102) = $2,100,000. Sometimes it makes sense to avoid having to calculate the market value and simply deliver the asset. Disputes in such cases are minimized.

USES IN PORTFOLIO RISK MANAGEMENT

Consider a situation where Bank A is exposed to a lot of companies within the electronics sector in Belgium. The bank could suffer huge losses if there is an economic downturn in Belgium, together with a fall in demand for electronic products. A sensible strategy for Bank A, therefore, is to obtain credit protection on the bulk of those customers who fall within these risk criteria.

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Topic 3: Credit Risk Management DEFAULT SWAPS While a total return swap is the equivalent to a future or forward, a default swap is the equivalent of an option. In return for a premium, the protection seller undertakes to compensate the protection buyer in the event of a credit default. We saw earlier that in VaR models those derivative products that have “optionality” have a nonlinear relationship with the underlying asset. For writers of default swaps, risk measurement is more difficult and normally Monte Carlo simulation techniques would be used. NO DEFAULTSeller of protection Bank A Fee or premium Bank B Coupon + capital gains – capital loss Corporate bond XYZ DEFAULTSeller of protection Bank A Fee Bank B (Coupon + nominal – recovery rate)Recovery rate Corporate bond XYZ Figure 3.6. Default Swap 323 Professor Malick Sy

Topic 3: Credit Risk Management Figure 3.6 illustrates the cash flow of a default swap. Bank B in this case benefits if there is an improvement in the credit rating of corporate bond XYZ. However, if there is a credit default, then Bank A must pay over the difference. Whatever happens, Bank B is perfectly hedged. In the case of Bank A, the maximum profit that can be earned is the premium paid while losses are unlimited (although technically linked to the current value of the bond). Bank B is effectively granting an option to purchase the asset if it falls below a certain value. The specifications of a default swap appear below. The protection buyer pays Early termination Termination payment Final Price Materiality Business days Table 3.12. Default Swap Details Premium of 800 basis points semi-annually Credit event or in 4 years’ time Notional x (market price at inception – final value) Prevailing market price at date of payment Price falls below 90% of today’s value subject to interest rate movements 30/360 Notional amount of reference asset $ 8,000,000 XYZ Corporation Documentation International Swaps and Derivatives Association The buyer of protection undertakes to pay a premium that in this case is calculated at 800 basis points. The reference asset in question is XYZ Corporation. In return for paying a premium, the protection buyer receives four years’ protection from a credit default or a material reduction in the value of the bond because of a credit migration. 324 Professor Malick Sy

Topic 3: Credit Risk Management If no default or credit migration takes place, the seller of protection makes no payments over to the protection buyer. However, if, as a result of default or a credit migration, the asset suffers a fall in value of greater than 90 percent then a credit event is deemed to take place. Note that the fall in the price of the bond must be due to a credit deterioration and not due to a change in interest rates. Normally the calculation agent responsible for coming up with the final price will refer to government bonds and price the corporate bond on the assumption that throughout the period of the default swap, the risk free interest rates have remained constant. Table 3.13 illustrates how a default swap differs from a total return swap. Instrument Corporate Bond (for party long the asset) Total return swap (protection seller) Credit default swap (protection seller) Table 3.13. Interest rate increase Credit spread increase Market loss (VaR) Credit loss Credit loss Credit loss less premium received Interest rate reduction Credit spread increase Market gain Credit gain Credit gain Premium Comparison Between Credit Instruments 325 Professor Malick Sy

Topic 3: Credit Risk Management

CREDIT LINKED NOTES

Credit linked notes are simply bonds whose performance is related to the credit exposure of an underlying asset. They are normally used by investors as a convenient way of gaining access to credit exposure either to a single issuer or to a combination of issuers. The procedure operates as follows:

• •

A special purpose vehicle (SPV), the equivalent to a trust, is set up and investors are invited to subscribe for medium-term notes. The funds generated from the issue are then used to enter into total return swaps, default swaps, or a combination of the two, depending on the risk profile that the SPV wants to assume.

• If there is no credit event, the investors, in addition to receiving the risk free rate of interest, will also receive the premium (if a default swap is used) and capital gain (if a total return swap is used).

• If there is a default, the investor’s return is net of any protection payments made.

ROLE OF DIVERSIFICAITON IN CREDIT LINKED NOTES

VaR calculations are very important in credit linked note structures. Investors, who want to gain credit exposure will pay very close attention to two factors - the level of diversification and the level of gearing. As with banks, SPVs will set limits on certain concentrations, such as industrial sectors, geographical location, product type, etc. In the past banks used subjective judgments to decide on the limits. SPVs will more than likely combine subjective judgment with statistical packages that are designed to exploit diversification. If they succeed, then their simulations will reveal

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relatively low volatility in their earnings. Investors will therefore not demand so high a credit risk premium. In addition, if diversification can be exploited to the full, then the managers of the SPV can consider alternative means of enhancing earnings. A popular technique for instance is to use geared pool structures. This effectively provides greater leveraged access to the return on a pool of assets. For the investor who wants exclusive credit exposure, the benefit of an SPV is that he can obtain relatively high earnings (through gearing) coupled with diversification. Of course, there is a high correlation between the losses due to high gearing and credit default. An increase in interest rates, for instance, will have a significant impact on the building industry, and if an SPV is both highly geared and has a high concentration within the building industry then a VaR calculation will reveal a relatively high exposure.

3.3.4 Conclusion

The growth in the use of credit derivatives has given banks more resources with which they can influence the level of exposure to credit risk that they are prepared to tolerate. Credit managers can thus achieve better control over their portfolios if they understand the areas of risk that they are exposed to. Once this is known, banks can use specific derivatives to control that exposure. The growing use of market derivatives and the substantial losses that banks have made in the past from using such derivatives, means that credit control, even among top-ranking rate financial institutions, is of growing concern to banks. Portfolio risk measures can identify the overall exposure and can provide valuable information to lenders when deciding to invest in new securities, or credit derivatives they should use.

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3.4 THE BASEL RISK CHARGES FOR DERIVATIVES

3.4.1 Introduction

When a bank undertakes a business transaction with a client, it is involved in a financial risk. This is the risk that the bank itself may be:

) exposed to currency fluctuations, ) changes in its own funding costs, or ) changes in market liquidity

There is a further risk to be managed and this is credit risk. This is the risk that a counterparty to a financial transaction will fail to perform according to the terms and conditions of the contract, thus causing the bank to suffer a financial loss.

A central part of most banks' traditional business is to lend money to clients; the exceptions are the recently established derivatives houses. These are banks whose sole aim is to provide clients with a complete service in structured and derivative products. However, most banks earn a significant proportion of their income from lending to clients and investing. Consequently they must evaluate the potential returns against the possibility of default. This module focuses on credit risk as it relates to derivatives, but first: some basic information.

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3.4.2 Basic Information

When a bank lends, say, £1,000,000 to a client, and for some reason the client is unable to repay the loan, the bank is exposed to a loss of 100 per cent of the amount lent plus interest. Transactions like these are known as 'on-balance sheet', and will include general banking business such as:

) Money market transactions ) Trading and investing ) Trade and project finance ) Loans and commitments ) Accrued interest

3.4.3 Counterparty Risk

This is the risk that the client will default, and is an estimate of the probability that a loss will be incurred. The estimate must include an assessment of a number of independent variables.

A. Customer Risk

The risk that the client is unable or unwilling to meet his obligations to the bank.

B. Country Risk

The risk that some or all economic agents in a country (including the government) will for some common reason be unable to fulfill their international obligations. In Latin America, some governments were unable to service their debt in the 1980s.

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Topic 3: Credit Risk Management C. Transfer Risk The risk that a country will find itself unwilling or unable to service all of their international obligations owing to a shortage of foreign exchange. This can occur even though most organizations in the country are still solvent, for example, the Philippines, in the early 1980s. It is also possible that a bank may have too much business in one particular area, this is known as concentration risk. It is the risk that, owing to inadequate diversification of the bank's portfolio, a high level of exposure may be encountered in one particular sector. The bank may have too much exposure to, say, the motor industry, where different customers would all be subject to the same troubles or influences. Establishing the amount and the extent of credit risk has become increasingly complex, with many banks currently fine-tuning their credit risk assessments on derivative products. 3.4.4 Product Risk This is the element which gives rise to the amount of the credit exposure and can arise from some or all of the following factors. A. Principal and Interest Rate Exposure This relates to the interest and principal amounts owing at their due date. It will apply to term loans made by the bank and also to overdrafts, but also includes instances where the bank has agreed to guarantee the obligations to a third party. 330 Professor Malick Sy

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B. Replacement Risk

This is the measure used to quantify the risk in most capital market and derivative transactions. Only a fraction of the amount is at risk as these are 'off-balance sheet' instruments where the principal is not exchanged and is therefore not at risk. Replacement risk can arise when the client fails to perform under the contract and the bank seeks to recreate the defaulting party’s payment streams. This can sometimes involve a substantial cost.

C. Settlement Risk

This is the risk at the end of a transaction when parties pay over their principal amounts, sometimes at different times. It can arise when the bank's counterparty fails to discharge its obligations or is late paying them. For example, a spot foreign exchange deal involves a settlement risk two business days later, when both the bank and the client pay over their side of the transaction, though possibly at different times of the day. If the bank has paid over its side of the spot deal, but the client has not, the client is long of both currencies, and the bank is exposed 100 per cent to the customer.

D. Collateral Risk

On some occasions a bank will ask a client to support a transaction by means of collateral. This could be in the form of securities, bullion or a cash deposit. It may be to complement an existing credit line, or as a stand-alone facility. The bank will be exposed if the collateral declines in value, for example the gold price falls. The bank may then have to call for further security to 'top up', the position.

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3.4.5 Swap Credit Risk

A. Introduction

As previously seen, a swap is an agreement between two counterparties to exchange sets of cash flows that can be linked to an oil index, a stock market index a currency rate or an interest rate or to a combination of these. A bank may enter into a swap transaction for one of three reasons:

) as an intermediary ) for trading purposes ) for hedging purposes

B. Swap Risks

The amount at risk on any given swap is a function of the following variables:

The type of swap

Currency swaps (fixed/fixed or fixed/floating) are generally more risky than a straightforward single currency interest rate swap, as they have the added complication of currency movements to consider and the risk of the 100 per cent principal movement at maturity.

Term to maturity

A long swap has a greater potential credit risk than a short swap, as there is a greater potential for interest rate, currency and equity movements.

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Payment mismatches

Many swaps result in one party making payments to another, prior to receiving payments (e.g., a party may make quarterly payments but receive them semi-annually).

Settlement risk

That settlement amounts may be agreed but payable at a later date.

C. Swap Credit Risk Assessment

It used to be the case that the credit exposure on an interest rate swap was generally accepted to be equivalent to between 3 per cent and 5 per cent of notional amount per annum. If a swap had a three-year maturity, the maximum risk would be 15 per cent of principal and the minimum risk would be 9 per cent of principal. Currency swaps obviously carry a much higher risk to the bank, as exchange rates are more volatile than interest rates. And a cross-currency interest rate swap will also have exposure to interest rate movements as well as movements in foreign exchange.

Establishing the amount and the extent of credit risk on swaps has become increasingly complex, with many banks currently fine-tuning their credit risk assessments on derivative products. It is very difficult to say categorically what the risk on a particular product is. If in doubt, it is always advisable to consult one of the banks direct and discuss the matter.

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3.4.6 Financial Futures Credit Risk

A. Introduction

An exchange-traded futures contract whether on an interest rate, a currency, a bond, equity or oil product will carry a substantially lower credit risk than OTC derivative instruments. This is because exchange-traded products are subject to margin requirements.

When a futures contract is opened, both buyers and sellers of the contracts, bankers, other financial institutions and corporates must put up collateral. This is known as initial margin and it represents a deposit placed in good faith. It is quoted in terms of so many pounds (or dollars) per contract. This is held by the exchange Clearing House, and is intended to provide the exchange with cover against all but the most extreme market movements.

At the close of business, each individual position is marked-to-market and profits and losses are crystallized against the daily settlement rate posted by the exchange. The losses must be paid daily. This is supposed to counteract a large part of the credit exposure, and does not allow market players to run loss-making positions without funding them daily. The trader is not able to say 'the position is £30,000 down at the moment but it will all come good next week, so I do not need to worry about it'. Good or not, the £30,000 must be paid today; profits, if they occur, will also be paid daily by the Clearing House to the trader.

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B. Futures Risks

The credit risk associates with the Clearing House of an exchange is taken by many to be insignificant. So the credit risk on exchange-traded futures it limited to the margin amounts paid to or due from the client's brokers who place the business for him on the floor of the exchange. This risk can be categorized under two headings, replacement risk and credit risk on margin deposits.

Replacement risk

The risk that the counterparty (the broker) will be unable to deliver the contract or meet the required margin call. In this case the contract may have to be covered in the market at current rates, perhaps resulting in a loss.

Credit risk on margin deposits

Once futures trades have been registered, each counterparty has a contractual arrangement with the Clearing House, so all risk lies with them, not the other side of the trade in the pit. Far more relevant to credit risk is the practice of futures trading, where the company or institution is not a member of the exchange and relies on brokers to execute the transactions. Here the client's transaction is not with the Clearing House but with the broker.

It is advisable for clients and banks to limit their transactions with one particular broker up to the level of credit risk that is comfortable. Likewise a bank should not be too exposed to one particular client. Both broker and client should examine each other's credit standing before they deal.

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3.4.7 FRA Credit Risk

A. Introduction

A forward rate agreement (FRA) is a contract between two parties to fix the interest rate earned or paid on a notional amount for a specific future period. It is a contract for differences (CFD), and the settlement amount is the difference between the fixed rate on the FRA and the market rate. These are also common in the energy market where they can also be called single settlement swaps.

The following points are worth noting:

) FRAs are used by corporates and banks to both hedge positions and to

speculate. )

Most FRAs are transacted under standard terms and conditions, FRABBA (FRA-British Bankers Association) or ISDA (International Swaps and Derivatives Association).

The notional principal amount on the FRA does not change hands, and is not at risk. Only the settlement amount is exchanged.

)

) FRAs are similar to tailor-made or OTC futures contracts.

B. FRA Risks

FRAs can be transacted in both domestic or in foreign currency, in which case a currency risk will exist, although the currency risk will be attached only to the settlement amount.

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C. FRA Credit Risks

As the credit risk is applied only to the settlement amount, the measurement of this risk requires the replacement cost of the FRA i.e., the current market value of the FRA, to be calculated.

The replacement cost represents the movement in interest rates since the deal was struck. It is therefore measured in terms of future interest rate volatility which can only be guessed at. A typical measure of credit risk used to be 5 per cent per annum of the notional amount. If a bank had transacted a 3s-6s FRA with a client, the risk would be assessed at 5 per cent ÷ 4 or 1.25 per cent. More banks are now using sophisticated models taking into account the volatility of the currency concerned and the time to maturity, giving them generally lower risk figures.

3.4.8 Options Credit Risk

A. Introduction

There are two different types of options: those that are bought and sold on a regulated exchange, and those that are traded Over the Counter (OTC). Options are available on a wide range of underlying commodities:

) currencies ) interest rates ) futures ) equities

) commodities - energy, metals etc.

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Topic 3: Credit Risk Management Options confer asymmetrical rights and obligations on the buyer and seller of the options. The buyer (or holder) of the option, who has the right not the obligation to do something, must pay the premium. This is the extent of his costs. If he does not pay the premium he has no option. He will still, however, have a credit risk exposure based on the performance of the seller regarding the options under the contract. The seller (or writer) of the option receives the premium and has an obligation to perform under the contract. In effect, if the option holder chooses to exercise the option, the option writer must deliver the 'underlying'. If for any reason, the option writer has not hedged the position, he himself could be open to considerable losses. Credit risk for options purchased on an exchange is effectively limited to margin amounts, and is regarded as much lower (effectively risk-free) than their OTC counterparts. B. Exchange vs OTC Options Exchange-traded options must conform to standard terms set by the various exchanges, and are subject to daily margin requirements with only rarely physical exercise into the underlying commodity. OTC options are more flexible, traded without formal margin requirements, and often result in physical delivery of the underlying product. 338 Professor Malick Sy

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C. Option Risks

Options generally possess elements of market, interest rate and currency risk, in addition to credit risk. Credit risk for options purchased on an exchange is effectively limited to margin amounts, and is regarded as much lower (effectively risk-free) than their OTC counterparts. Where a bank sells an option, the only risk to the customer involves the receipt of the premium. Where the bank purchases an option from a customer the risk is very different.

D. Quantification of Credit Risks

Where a bank buys an OTC option from a client, the risk is usually based on the following method.

Mark to market + buffer

This method quantifies credit risk by reference to a direct assessment of the market price of the bought option plus a margin for likely future rate movements over the life of the option. The margin is calculated by reference to changes in the underlying market price and also by reference to changes in volatility. A bank may recommend that the physical underlying price be altered by (say) 3 cents and volatility of 3 per cent.

Example

If the bank had purchased a sterling call, US$ put currency option for £750,000, and the spot rate at time of purchase was US$1.57 with volatility at 10 per cent, its credit risk would be calculated by revaluing the option using a spot rate of US$1.60 and volatility of 13 per cent.

Similarly for all other types of option, margins would be established by reference to estimated movements on physical underlying prices and volatility.

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