Risk In Capital Markets

© Chartis Research Ltd 2008 Page 36

Extract from Chartis Research Report – #RR08022 Credit Risk Management Systems 2008 – Market analysis

See www.chartis-research.com for further details and to obtain the full report.

Risk in capital markets and trading

Algorithmics

“The modern trading book carries many risks: Issuer risk; Default risk; Migration risk; Spread risk; Interest rate risk. Each of these risks must be measured. Typically, the �rst step to measurement is classi�cation: is it market risk or credit risk? After outlining the standard classi�cation of risks using Basel II as a guide, this paper presents an integrated approach to modeling market and credit risks and illustrates its application to enhanced risk management. Using integrated risk measures e�ectively dissolves the arti�cial boundaries between risk types.”

Markets evolve quickly to address investment needs and risks in new and innovative ways. Derivatives allow sophisticated investors to create tailored risk-reward pro�les to serve their purposes and generate pro�ts. Ignoring or underestimating any of the risks of an investment creates a �ctitious risk-reward pro�le, preventing proper comparison of alternative investments and confounding mitigation strategies. However, markets don’t just evolve quickly, they also rebalance quickly. Risks can become losses – realized or unrealized – in a very short period. When those losses arise unexpectedly, due to risks that went unmonitored or unmeasured, investors raise questions concerning the competence of the entire �nancial community.

Clearly, measuring and disclosing risks is central to reputable investment management. However, this is more easily said than done, when all of those new products arising from the evolving markets must be quantitatively assessed. Traditionally, risks are managed, measured or mitigated individually, by categorizing them according to their nature: market risk, credit risk, operational risk, or other risks. Each risk is measured using detailed, often highly quantitative models. Various aspects of each risk are featured or ignored in particular models. For example, non-linearity is a di�erentiator for market risk models and concentration risk for credit risk models. Risks are also hedged or mitigated individually using separate strategies, in particular for market and credit risks.

Part of the recent evolution of products, however, is the ability to trade risks traditionally considered as credit risks. For example, a typical interest rate derivative has multiple sources of risk from the obvious, interest rate risk and counterparty credit risk, to the more obscure implied volatilities and possible risk arising from �uctuating exchange rates. As a further example, a credit default swap protects an investor who is buying protection from the default of the underlying name. The ability to trade CDS e�ectively turns the default and event risks of the underlying name into market risk. Should these be measured as market risks or as credit risks? Various risks also fall into this ever-expanding grey area between market and credit risks. To illustrate, consider how each of the following risks might be classi�ed: Issuer risk? Default risk? Migration risk? Spread risk? Interest rate risk?

Often the instinctual response to the question of categorization depends on the background of the individual risk manager. For example, those with market risk experience continually increase the scope of their models to address those risks falling into the grey area, leading to scope creep in the model. Credit risk practitioners also try to extend their models and mindset




to address a broader array of risks. It is worthwhile to examine current practice in the industry. While each investor and financial institution manages its risks in their own fashion, Basel II embodies a comprehensive review of current common practice. For example, specific risk treatments under Basel II fall into the market risk category. A Basel II example of such an extension is the use of expected positive exposure as a measure of counterparty credit risk.

To begin, one must define the scope of the problem. In fact, traditional risk management techniques are quite effective when applied to traditional products. As it is the traded products and their OTC counterparts that evolve most quickly, focusing new models and techniques on the trading book makes sense. In many cases, the trading book of a bank is the element the most similar to that of other types of financial institutions and to investors at large. Focusing on the trading book then, is likely to produce the greatest benefit.

One of the main risks faced in the trading book is market risk, which Basel II defines thus: “the risk of losses in on and off-balance-sheet positions arising from movements in market prices.” [Basel II, 683(i)] Given the generality of this definition, and the prevalence of issuer risks in defining market prices, it becomes clear that many of the risks delineated earlier are easily interpreted as market risks. To address this, Basel II goes further, providing more guidance that market risk includes specific risk: “Specific risk is defined as the risk of losses arising from an adverse movement in the price of an individual security owing to factors related to the individual issuer.” [Basel II, 709(iii)]

Beyond name-related basis risk and event risk, which are typically included in advanced VaR measures, there is also default risk to consider. Basel II, for example, extends the definition of market risk to include incremental default risk; a risk that must be measured separately from the VaR model and the result added on to that measure. Specifically, “the capital requirement for incremental default risk in the trading book equals the greater of zero or:

• The level of capital required to absorb losses that might occur to trading positions due to defaults of credit-sensitive instruments

• Less the capital requirement for default losses implicit in the bank’s VaR-based capital computation.” [Guidelines, 9]

The main reason for the separation is that while market risk is measured to a 99% standard over ten days, and then scaled to provide additional protection, “the incremental default risk capital charge is calibrated to and measured at a 99.9% confidence interval over a capital horizon of one year. Because default risk is so fat-tailed compared to market risk, incremental default risk would be measured directly at the 99.9th percentile, rather than measured at a lower percentile and scaled to approximate the 99.9th percentile.” [Guidelines, 16]

Here one encounters the fundamental flaw in models that segregate risks in order to measure them: the final addition. By adding, one assumes that a series of worst-case events converge into a single, super event that leads to simultaneous losses from each type of risk. While this would be a suitably conservative assumption, human nature automatically discounts the risk because of the perceived excess conservatism of the measure. Often, the discounting overcompensates for the conservatism, leading to an effective underestimation of the true risks. Measures that quantitatively, objectively combine all risks are therefore more desirable as they are less subject to this psychological interpretation. Basel II acknowledges the conservative nature of the current measures: “In theory, certain aspects of default risk in the trading book should diversify against other risks in the trading book. For this reason, this topic should be the subject of further discussion…” [Guidelines, 42]

© Chartis Research Ltd 2008 8



To summarize, market risks are generally pricing risks, but credit now plays a role in pricing: credit spreads are key factors for many instrument types. Specific risks arise from perceived or actual credit quality changes in the market place. The incremental default risk charge (IDRC) calculation is essentially a Credit VaR calculation, but for issuers rather than counterparties or obligors. And in the end, aspects of credit risk affect pricing through spreads and issuer ‘value’, infringing on the ‘purity’ of market risk estimation.

Approaching the issue from the other direction, one might consider credit risk. Although Basel II doesn’t define credit risk, earlier documents published by the Basel Committee on Banking Supervision define it as “the potential that a bank borrower or counterparty will fail to meet its obligations in accordance with agreed terms.” [Credit, 2] The most relevant form of credit risk in the trading book is typically counterparty credit risk, which Basel II does define as “the risk that the counterparty to a transaction could default before the final settlement of the transaction’s cash flows. An economic loss would occur if the transactions or portfolio of transactions with the counterparty has a positive economic value at the time of default.” [Basel II, Annex 4, 2A, 2G.]

Basel II further defines the key components of credit risk to “include measures of the probability of default (PD), loss given default (LGD), the exposure at default (EAD), and effective maturity (M).” [Basel II, 211] Each of these components bears further examination and definition.

PD represents the credit quality of the name, counterparty, or obligor. It may be expressed as an ordinal ranking (i.e. a credit rating) and then translated into a probability of default. Some models first calculate the probability of default and then use it to group obligors into classes. Closely related to default probabilities are transition matrices that describe not only default events, but also transitions in credit quality (upgrades and downgrades). Such transition matrices are typically derived from historical experience of rated names.

The process of recovering value from a defaulted obligation can be long and onerous. Increasingly, it is possible to sell off distressed debt and circumvent this process. In either case, the extent of the ultimate loss is heavily influenced by the ‘cents on the dollar’ recovered, or LGD. Various aspects of the transaction play a role in determining the most likely recovery amount, including its relative seniority, collateral, covenants, margining agreements, and specialized structuring.

Measuring exposure, or EAD, is conceptually straightforward: it is the amount outstanding on a loan. However, when dealing with OTC derivatives, exchange-traded instruments, credit derivatives, and even masses of retail obligors, quantifying and modelling exposure becomes a discipline unto itself. As a key determinant of credit risk, exposure is often managed in its own right. Depending on the manner in which EAD is estimated, a separate measure of maturity, M, may or may not be required.

Part of the measurement process for EAD in the trading book is a factor, alpha, defined only as “the ratio of economic capital from a full simulation of counterparty exposure across counterparties (numerator) and economic capital based on EPE (denominator)” [Basel II, Annex 4, 34] Alpha is multiplied by effective EPE to create EAD. This allows EAD to be interpreted as a loan equivalent amount, facilitating its incorporation into traditional credit risk model. Effectively, the trading book market risks are embodied in the EPE calculation, which then is related back to the more familiar credit risk environment through a scaling factor.




As credit markets expand and deepen, information, such as spreads and downgrades, increasingly contributes directly to the valuation of positions (e.g., CDS, CDO) and more broadly, influences a variety of traditional markets (e.g., corporate bonds). Thus, credit risk factors influence market risk. Similarly, because market rates drive the value of derivatives (for example), counterparty credit risk can only be properly assessed in such portfolios when exposures are evaluated under a variety of market conditions. Market risk factors are fundamental for a correct measure of credit risk.

Clearly, the quest for comprehensive risk measures for modern trading books quickly becomes a tangled, complex endeavour. The answer, of course, is not to create more standardized classification schemes or more complex models, but rather to create a model that encompasses all types of risks inherent in the investment. Only in this manner can appropriate risk-reward trade-offs be articulated clearly and concisely and more all-encompassing management and mitigation schemes be truly effective.

To be effective, an integrated model must address several key issues. An integrated risk model must:

• Capture all sources of risk – from interest rates to spreads, from downgrades to defaults, and the interactions between risks.

• Accurately assess the impact of risks on the portfolio. For example, interest rates may have a non-linear impact on the value of an options portfolio or a portfolio of structured credit assets may be sensitive to changes in the shape of credit spread curves. Conversely, margining, collateral or guarantees might serve to mitigate default risks, while themselves varying with market prices.

• Provide insight into the portfolio risks. Beyond the comprehensive impact assessment of all risk types, the identification of the key sources of risk for a particular portfolio is essential. Thus, the model must provide a coherent, usable measure of risk attribution by risk type and to portfolio subcomponents.

• Create suitable risk profiles. By providing risk measures at multiple time horizons mitigation and diversification strategies can be compared more effectively to projected returns, enabling effective investment decisions.

The most straightforward place to begin the quest for an integrated model is with a standard portfolio modelling approach to credit risk, and extend this beyond expected positive exposure and alpha, to create a truly integrated measure of market and credit risks. Once this integration is accomplished, one must still address important questions such as time horizons, levels of surety and mitigation strategies. The remainder of this paper, however, focuses on producing a comprehensive distribution in a manner that allows such extensions.

Beyond the factors of PD, LGD and EAD referenced in Basel II and detailed above, portfolio credit risk relies on a further critical component: correlation (RHO). Undoubtedly, the unique characteristic of portfolio credit risk is its treatment of correlations amongst names as they downgrade, upgrade, and default under systematic influences. In fact, it is correlation – and the associated name, sector, or other concentrations – that have the largest influence on the magnitude of portfolio credit risk measures. In general, other types of correlations may also be included: between EAD and PD, LGD and PD, and so on.

The typical model assumes that all inputs are known and constant: PD, LGD, EAD, RHO. This traditional model can be described in three essential steps, as follows:

1. Describe creditworthiness by creating credit models that relate obligor, sector, or account creditworthiness to both systematic and idiosyncratic factors. Default and/or




migration probabilities vary as a result of changing economic conditions, and these changes can be viewed as the drivers of default correlations. Thus, an obligor’s default/migration probabilities are conditioned on the scenario path up to each point in time. Correlations amongst obligor defaults and transitions are determined by their individual relationships to a set of common risk factors. This step combines PD and RHO.

2. Count idiosyncratic risks because, while the overall economy plays a role in corporate (sovereign or retail) defaults and transitions, there is also an element of individuality to be considered. In some cases, such as retail and SME exposures, the sheer number of obligors allows for ‘averaging’ and other statistical properties to take over from individual details. In other cases, such as large corporate lending or sovereign investment, the details of a name are important in determining portfolio-level risks. Conditional on a particular scenario, idiosyncratic risk for each obligor is independent of that for other obligors.

3. Aggregate loss distributions and measure risk by first estimating the unconditional distribution of portfolio credit losses by aggregating the conditional loss distributions (from the previous step) over all scenarios. Once such a distribution is available, it may be analyzed statistically. Note that this needs to happen both for the overall portfolio and for more granular sub-portfolios, usually down to the name level. It is this extra aggregation sequence that allows for capital allocation through measures of risk contribution.

To extend the model to support an integrated, comprehensive risk measurement, one must somehow include market risk elements. One option is to follow the Basel II approach: use market risk factors to estimate the exposure (EAD) and use it within the standard model. As the Basel II model indicates, however, an adjustment must be made to account for correlations between market and credit risks and to fully capture the co-variability of all factors. Ideally, one would capture these co-variations directly, rather than resorting to adjustment factors and approximations. By extending the three-step model to five steps, this can be accomplished. The five steps, illustrated in Figure 16, are as follows:

1. Generate Market Scenarios. Risk factors include primary market risk factors. Scenarios explicitly defining the joint evolution of all the relevant market risk factors over the analysis period are created in this step using historical data and a model. This step contributes to the estimation of EAD. As above, it can be omitted when measuring credit risk only for market invariant portfolios.

2. Evaluate net credit exposures, whether aggregated into buckets or obligor specific, capturing any mitigation (especially netting, margining & collateral). The amounts that will be lost in the event of a default or credit migration are computed under each scenario. Based on the level of the market factors in each scenario at each point in time, exposures for each obligor are obtained accounting for netting, mitigation and collateral. The results are stored for use in subsequent steps. In some instances, exposure may be independent of the scenario – or deterministic – in other words, it is calculated once for all scenarios. This step focuses on EAD, but includes many facets of LGD.

3. Generate Credit Scenarios. The fundamental credit model relates obligor, sector or account creditworthiness to both systematic and idiosyncratic factors. Default and/or migration probabilities vary as a result of changing economic conditions – and these changes can be viewed as the drivers of default correlations. Systematic factors are simulated consistently with each market scenario, typically according to an experience-based ratio. In the case where market risk factors are not simulated, one would generate only credit scenarios. It is common to use hundreds of thousands of credit scenarios to capture tail risks appropriately. This step embodies the macroscopic RHO and allows integration of market and credit risks.

Describe creditworthiness. Based on the credit scenarios, an obligor’s default/migration probabilities are conditioned on the scenario path up to each point in time. Correlations amongst obligor defaults & transitions are determined by their individual relationships




to this set of common risk factors. This step combines PD and RHO, translating them to the individual obligor level.

4. Count idiosyncratic risks. Proceed as described in the standard model.

5. Aggregate loss distributions and measures. Proceed as described in the standard model.

Figure 16: The five-step model

The efficacy of the framework can be seen in the context of a very simple example. Consider a typical fixed rate corporate bond with 5.25 years to maturity. Assume, for simplicity, that the bond is the only instrument held against its issuer, and is held without mitigation. The bond carries several risks, including general interest rate risks and issuer-specific spread, downgrade and default risks. In the first step, one would generate scenarios based on the interest rates and the spreads. For example, using a mean-reverting Monte Carlo model, one thousand scenarios are generated three months and one year into the future for the interbank interest rate curve and the sector spreads.

In the second step, the bond is evaluated three and twelve months forward for each of the one thousand scenarios. In the evaluation, independent, standard normal scenarios are used to represent the incremental, issuer-specific spread. Based on the assumption of a single, unmitigated exposure to this name, the (positive) value of the bond is equal to its exposure. In theory, the outcome of this second step is two vectors (one for each time step) of 1000 exposures. In fact, supposing a simple seven-grade rating system plus default, the total number of pre-processed exposures would be sixteen thousand, expressed as a grid of two time steps, by eight grades by 1000 scenarios.

There are two tasks in the third step. First, one must generate credit risk scenarios conditionally on the market scenarios from the first step. In this limited example, suppose




the economy is represented by a single factor, namely the S&P500 index. Suppose that five hundred credit risk scenarios (i.e., scenarios on the value of the S&P 500) are generated conditionally on each market scenario, consistently at each time step. This brings the total number of credit risk scenarios to 500,000. The second part of step three relates the value of the S&P 500 to the creditworthiness of the bond issuer, by association correlating the downgrades and defaults of the issuer to the spreads in the market scenarios. This relationship might be quantified by regressing the monthly average share price of the issuer (assuming it is a traded firm) against the corresponding average S&P 500 values over the last ten years.

In the fourth step, suppose simple 200 random draws from an assumed independent standard normal distribution of idiosyncratic risk are used to assess the actual credit state of the issuer under each credit risk scenario. In this example, the total number of scenarios is one hundred million, ensuring a sufficient number of scenarios for accurate tail measures. For each of the one hundred million draws, the exposure – consistent with the associated market scenario at the simulated rating – is looked up in the pre-calculated table.

The final phase is to aggregate across names – whether issuers, obligors or counterparties – to produce a portfolio distribution which can then be decomposed using additive contributions or marginal measures in order to attribute capital to (for example) each name.

Four areas of the framework are particularly interesting in the context of an integrated risk measure. Firstly, the ability to condition systemic credit factors on market risk scenarios, across multiple future time horizons, allows market and credit risks to be measured consistently with each other and to support various types of mission-critical decisions. Secondly, the analytical tools available to model idiosyncratic risks more efficiently allow the selection of models for each group of risks, as appropriate for each part of the book facilitating enterprise-wide risk measurement, in conjunction with drill-down capabilities. Thirdly, the potential to use additive measures of risk enhancing the usability of risk measures for management purposes. Finally, the framework itself enables future extensions and additional options as markets and common practices evolve, effectively future-proofing the methodology.

The true innovation in the five step framework occurs partly in the segregation of decisions into the logical groupings described herein, and partly in the details of its implementation. For example, how does one aggregate individual name distributions to the portfolio level in step five having used non-simulation analytic techniques to model the idiosyncratic risks in the fourth step? The implementation details can then be determined on an individual basis.

References

[Credit] – Basel Committee on Banking Supervision: Principles for the Management of Credit Risk, July 1999.

[Basel II] – Basel Committee on Banking Supervision: Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework – Comprehensive Version, June 2006.

[Guidelines] – Basel Committee on Banking Supervision: Guidelines for Computing Capital for Incremental Default Risk in the Trading Book, October 2007.




About the Author

Diane Reynolds

Sr. Director, Economic Capital Solutions, Algorithmics Inc.Diane Reynolds is Director of Economic Capital at Algorithmics, leading the team dedicated to economic capital and portfolio credit risk solutions. Since 1997, Diane has worked in various areas of Algorithmics including professional services, development, product management, research, and marketing, spanning market, credit, and operational risks. She has authored several papers in scenario generation and operational risk. Previously, Diane worked for various firms including a large pension fund and a financial software provider. Diane holds an M.Math, Statistics-Finance and a B.Math Computer and Actuarial Sciences, both from the University of Waterloo.

About AlgorithmicsAlgorithmics is the world’s leading provider of enterprise risk solutions. Financial organizations from around the world use Algorithmics’ software, analytics and advisory services to help them make risk-aware business decisions, maximize shareholder value, and meet regulatory requirements. Supported by a global team of risk experts based in all major financial centers, Algorithmics offers proven, award-winning solutions for market, credit and operational risk, as well as collateral and capital management. Algorithmics is a member of the Fitch Group.

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Risk In Capital Markets

Economy & Finance

Transcript of Risk In Capital Markets