Interest rate risk. Each of these risks must be measured. Typically, the first step to measurement is
classification: is it market risk or credit risk? After outlining the standard classification 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
effectively dissolves the artificial 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 profiles to
serve their purposes and generate profits. Ignoring or underestimating any of the risks
of an investment creates a fictitious risk-reward profile, 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 financial 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 differentiator 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 fluctuating 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 effectively 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
classified: 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.”
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.”
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 percent 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.”
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…”
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 allencompassing
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 9, 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 experiencebased
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.
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.
