Freeing capital: swaps versus CLOs
The collapse of Japan’s tenth largest bank is a timely reminder that credit risk is the largest and most pervasive of all those which financial institutions face but the least rationally priced and least scientifically managed. New approaches to credit-risk modelling, applying modern mathematical, computational and database techniques, could revolutionize the way banks allocate economic capital and make provisions and could also create a new discipline of credit portfolio management.
Banks need to aggregate their credit exposures into portfolios, work out the possible losses then allocate capital to cover them. The large commercial banks, particularly Bank of America, Citibank and SBC Warburg Dillon Read, have spent heavily to develop proprietary systems. Two have gone public: JP Morgan has published its CreditMetrics data model, and its Credit Manager software is available for about $25,000 a year; Credit Suisse Financial Products has released CreditRisk+, which is free and can be downloaded from the Internet.
These are not pricing models though their results usually will modify banks’ demands for particular types of risk and so affect their price at that institution. They allow credit risk to be measured across portfolios of different instruments and enable institutions to measure changes in the value of their portfolios caused by upgrades, downgrades and defaults. This means that loan portfolio risks can now be aggregated and the marginal contribution of each credit to return on capital can be measured. This in turn means that banks can identify the usually small number of exposures whose risk/return contribution is unsatisfactory and then lay off those exposures using credit derivatives. JP Morgan and CSFP hope that when clients begin to use their models, demand for their credit-derivative expertise will grow.
But the models have a much more important function for their exponents. They allow banks to measure the amount of capital required to support each individual position in their credit portfolios. The world’s big banks – a number of whom have co-sponsored CreditMetrics – want a new regulatory framework which differentiates between high-quality and high-yield loan portfolios and which rewards those banks which seek to manage their credit exposures with lower regulatory capital charges. To achieve this new framework the banks will have to persuade the regulators, in much the same way they did with market risk. The models are their way of doing that.
“It’s in our interest to make our model public,” says Chris Goekjian, president and chief executive officer at CSFP in London. “I believe that in time the regulators will adopt a models-based approach but they will want those models to be road-tested. That means they need to be made public.”
Now is a good time to strike. The European Union’s second Capital Adequacy Directive is due next year. The present regulations are based on the 1988 Basle Capital Accord, whose guidelines do not recognize that diversification reduces risk, so does not penalize banks whose portfolios are dangerously concentrated in one sector, region or ratings band. Neither does the accord recognize that differences in obligor credit quality create different levels of default probability and different levels of expected loss variability. And it takes no account of the maturity of loans.
These shortcomings mean that, while on average the Basle guidelines may allocate the correct amount of capital across the banking system, they do not accurately reflect the amounts of economic capital that should be set against the individual loans in a portfolio.
This is distorting the lending market. Banks are lending to less-creditworthy counterparties to earn adequate returns on capital from overall lending activity. Spreads for lower-rated borrowers have collapsed and the average tenor of loans to high-yield and emerging-markets borrowers in the past five years has more than doubled from around four years to almost 10. At the same time, more highly rated borrowers have either been pushed into the bond markets or have strong-armed relationship banks into lending at rates so fine that those same relationships banks are securitizing their loan portfolios.
“The real injustice in the loan markets at the moment is that no one will lend to the high-quality credits,” says one loan officer. “No one is lending to the single-A and double-A credits and all those loans are being securitized into the bond markets.”
Banks whose main clients are highly rated say they are being forced to set aside too much capital, thereby depressing earnings, while institutions with poorer credit controls and lower quality portfolios are setting aside too little. The key function of the models they have made public is to calculate economic capital (the capital set aside to cover expected losses) more accurately to eliminate this competitive disadvantage.
How the models work
The models attempt to measure value at risk occasioned by credit risk. They do this by different means but the goal is the same: to generate a loss distribution for a portfolio of credit exposures to calculate, to any given confidence level, the expected loss on the portfolio, the volatility of those losses (also known as unexpected losses) and the amount of capital required to support the portfolio.
The models focus on default risk. Credit spread risk, changes in the excess return demanded by the market for assuming a certain credit exposure, is only exhibited when portfolios are marked-to-market. Since most loans are accounted for on an accruals basis, banks generally do not attempt to measure credit spread risk in loan portfolios. Where instruments are marked-to-market, such as in bond portfolios, credit spread risk is covered by existing market risk models.
The problem with analyzing default risk is that, statistically speaking, public defaults are rare. In the case of emerging markets, the lack of data is almost complete. Moody’s has rated Thailand for all of four years – the Eurobonds that have defaulted there were not even rated. Information on the loan market is even more sketchy because loans are private contracts.
Therefore, the challenges for any model are to find a branch of mathematics that deals with events that are extremely unlikely – but will happen – and then to keep the number of inputs required to feed the model as low as possible and to base them, as far as possible, on observable data.
Prussian horses
CreditRisk+ uses an analytic approach based on the default rates associated with particular ratings levels, the volatility of those default rates and a sector analysis. The basic mathematics it uses are similar to those used in insurance. Instead of the normal probability distribution and random walk assumptions used by standard financial mathematics to describe asset price movements, CreditRisk+ uses the skewed Poisson distribution and the maths associated with it. Named after the French mathematician Siméon Denis Poisson, this describes the probability that a rare event will occur in a particular time period because, although that probability is very small, the number of trials is so large they ensure that it will. The first application for Poisson’s work was to calculate the number of deaths likely to be incurred by soldiers in the Prussian army being kicked by a horse in 1898. It turns out that it works just as well for calculating the number of blows a credit portfolio is expected to receive in any given time.
CreditMetrics, unlike CreditRisk+, is only a methodology and dataset (if you want to run the numbers you need additional software). It uses Monte Carlo simulation. This is because its loss distribution is calculated from the probabilities of credit migration – the risk that a rating will change – and the probabilities that ratings changes are correlated. Simulation is necessary because the statistical methods it uses to model the possible values of the credits in the portfolio create exponential jumps in the number of calculations necessary to compute the effect of adding one more credit. In a three-asset portfolio the model examines 512 possibilities. In a five-asset portfolio this number jumps to 32,768.
CreditRisk+ uses a piece of mathematics rather than running scenarios. Tom Wilde, quantitative analyst at CSFP in London explains: “In CreditRisk+ we don’t attempt to model the reasons for default. Instead we focus on the key portfolio aspect of default, namely that it is a rare event. We have applied and developed some of the mathematical techniques used to analyze portfolios of insurance risk. Technically our methodology is quite distinct from the continuous variable mathematics used in CreditMetrics and many market risk models. However, I believe that whichever model you used to study a portfolio – and McKinsey has one and so do KPMG and KMV – you would get pretty much the same relative risk ranking [by capital allocation].”
Both models rely on the data put into them and this is where dificulties arise. Just about the only simple, key variable is the credit exposure of the instruments in the portfolio. The rest are difficult because data is so scarce.
Recovery rates have to be put into the models because they measure how much of a defaulted bond or loan is likely to be repaid after workout. The ratings agencies publish data on recovery rates across ratings categories and obligations of differing levels of seniority. However, this data is based only on public securities. Most banks are interested in loan recovery rates as they are trying to analyze loan portfolios. Most loan defaults are not reported and most go into workout. Unless the problem is revealed in court, the workout plan is not made public and so information on expected recovery rates, essential for calculating expected losses, is also sketchy. However, loan recovery rates tend to be higher than those for bonds. This is because loans are better secured and also because default is a continuing process of renegotiation between lender and borrower. As difficulties arise, covenants are tightened and security is increased.
Shared experiences?
One answer to the problem of data paucity is data sharing. But can banks be persuaded to share their experiences of loan default and recovery rate by contributing anonymous data to a third party? Several groups are studying this, including Loan Pricing Corp, Robert Morris Associates and the European Loan Traders Association. However, banks are proving unwilling to expose their failures.
The most important input is the default rate: the likelihood of a default by any particular obligor. This can be treated as a continuous or a discrete variable.
As a continuous variable the possible default rate is described by a distribution which is specified by a default rate and a volatility of the default rate. A simplification is to treat the default rate as a discrete variable by assigning credit ratings to obligors and mapping default rates to credit ratings. This can be achieved by using a rating transition matrix that specifies probabilities for keeping the same credit rating and so the same value for the default rate and for moving to a different credit rating and so to a different value for the default rate.
These transition matrices are available from ratings agencies and other external data suppliers. For example, KMV Corporation, supplier of credit risk analysis systems that can cost more than $300,000 a year and which extrapolate credit information from the equity markets, provides buyers of its products with transition matrices.
Observed credit spreads from traded instruments can be used to provide market-assessed probabilities of default. Or credit ratings and mappings of credit ratings to default rates can be used to generate probabilities of default to obligors. Again there are serious difficulties with extrapolating meaningful data from publicly-rated instruments, and if banks plug their own ratings and default information into the models, they must ensure that their internal ratings system is sound.
“If there is a dollar of value to be extracted by better credit risk management, 90 cents of that is in better ratings and 10 cents in managing credit on a portfolio basis,” says Lea Carty, vice president at Moody’s in New York. He points out that incentivization packages for lending officers and banks’ own internal capital charging systems often distort the rating process. So if a bank’s internal capital charging system moves up a notch at BB+, then there are likely to be a surprising number of loans rated just above that. These factors will also significantly distort the credit migration process. Plug these ratings and migration analyses into the model and the single value-at-risk (VAR) number that results will not be a sensible basis for allocating capital although the indications of concentration risk will remain valid as long as the ratings have been misapplied consistently.
As JP Morgan emphasizes: “CreditMetrics is not another ratings service. We assume that exposures input into CreditMetrics will already have been labelled into discrete rating categories as to their credit quality by some outside provider.”
Assuming a satisfactory default rate input, the models then have to take into account the possible correlation between individual obligors’ credit behaviour and between credit events in general and background factors such as the state of the economy. Here CreditMetrics and CreditRisk+ take different approaches. CreditMetrics does attempt to compute correlation effects and suggests a number of ways to do this including the use of historical default data and calculation of bond spread correlations on the relevant assets. There are problems with both approaches. Historical data is not much use as there is too little data on multiple defaults with which to calculate correlations. Using bond spreads looks more promising, but requires additional assumptions on the relationship between asset prices and ratings changes or default.
CreditRisk+ takes a different view and does not attempt to model correlations explicitly. This is because CSFP believes that a positive correlation between default events does not necessarily imply a causal relationship. The near impossibility of analyzing every credit’s relationship with every other in a portfolio means that in practice the most important correlation observed is that between economic conditions and the level of defaults. Even here, since the level of defaults varies so much year to year and since different sectors will be affected to different degrees by the state of the economy, it is extremely difficult to tie specific economic variables to specific levels of default. In the absence of any stable relationship, CSFP uses default rate volatility as an input. As long as this volatility measure is taken over a long enough period to include times of recession as well as of boom, it should incorporate the effects of economic cycles.
Both sides argue that their approach is best. Greg Gupton, the CreditMetrics product manager at JP Morgan in New York, points out that default-rate volatility measures will be difficult to obtain because of the lack of default data. He also says that CreditMetrics is an attempt to look deeper into the data. “We want to look at the correlation in the fortunes of the assets of companies which is deeper than just the correlation of defaults.” And the lack of correlation analysis in CreditRisk+ does mean that the model would be most useful for creating an overall VAR number and less accurate in analyzing the marginal contribution of a sector or name to a portfolio – assuming that correlation effects are real and based on available data.
CSFP believes that defaults are so rare that default correlations are inaccurate and unstable, especially in difficult markets. “We have tried to keep data requirements low,” says CSFP managing director John Chrystal. “You can derive the correlations from the default rate and default-rate volatility. We give a methodology for doing that. However observed correlations are unstable. In addition, while correlation data is available for actively traded bonds, a correlation-based approach is not much use if you are looking at a retail loan portfolio with no price history.”
Fairer capital charges
Whatever the merits of these two public models, they both use inputs to calculate the frequency of defaults, the severity of losses and so a distribution of default losses. This enables banks to calculate the amounts of economic capital they should set aside, against their loan portfolios, in a way that they say better reflects the risks they are taking than do the Basle guidelines. The models rationalize obligor and tenor limits. The lower-rated the portfolio, the wider the distribution of possible losses, the higher the expected loss and so the more capital the models prescribe. The longer the average maturity of the portfolio the more capital the models say should be set aside. And the more concentrated the portfolio, the more capital has to be allocated.
To give an idea of the scale of the difference between the Basle guidelines and the VAR approach, CSFP uses its CreditRisk+ model to analyze the difference between regulatory capital and economic capital for three portfolios. Portfolio one contains 500 counterparties with a total exposure of US$12.3 billion. Portfolio two is the same except that it is less diversified, containing just 100 names with the same average credit quality. Portfolio three is the same as portfolio one except that the average credit quality is lower. For portfolio one the model gives an expected loss of US$212 million, an economic capital requirement of US$540 million and a regulatory capital requirement of US$982 million. Portfolio two is the same except that its lower diversity pushes the economic capital number up to US$834 million. But portfolio three, the lower quality portfolio, has an expected loss of US$535 million and its economic capital requirement is now US$1.225 billion, some US$243 million above the regulatory capital requirement.
The theory works in practice. At Credit Suisse, whose overhaul of its internal credit risk management systems led to the development of the CreditRisk+ model, use of these concepts at lending officer level is leading to increased as well as decreased capital allocations. “If a loan officer wants to make a loan now he has to provide against the expected loss,” says CSFP’s Goekjian. So if the loan is priced below the level of expected loss – lending at Libor+10bp to a single-A counterparty where the expected loss is 20-30bp, for example – the provision will be higher and the loan’s poor economics exposed.
Pre-emptive provisioning
Using VAR-type models has other benefits. Most banks still provision only after they have experienced deterioration in their loan portfolio. VAR models based on the probability of default and the expected recovery rate after default of each of its exposures can be used to forecast future losses on a portfolio basis. The models allow banks to calculate the average expected losses on the portfolio and also the level of unexpected losses (the volatility of the level of losses). A bank can then set its provisions in advance, in the expectation that its provisions will more accurately match losses with earnings, and smooth earnings volatility.
Swiss banks have been most open in declaring their switch to pre-emptive provisioning based on VAR models. This is because they have lost almost $30 billion on domestic loans in the last six years. Robert Scanlon, managing director, credit risk management, at SBC Warburg Dillon Reed in London, saw his institution take a $2.9 billion charge last year. The bank now provisions in advance and measures credit risk on a client-by-client basis across all products. So a request to increase a credit line to a client by the swaps group will be analyzed in terms of all the other credit exposures the bank has to that client in foreign exchange, lending and other activities.
Portfolio management
But the biggest advance made possible by the models, at least according to their proponents, is that they allow banks to manage credit exposures on a portfolio basis. Traditionally banks have managed credit risk using individual counterparty limits, tenor limits, limits on the amount of exposure to counterparties of a particular credit rating and concentration limits. To analyze the risk of a particular exposure the bank would therefore look at the size of the exposure, its maturity, its probability of default and the concentration risk of that counterparty.
The models allow a bank to calculate the incremental effect on a chosen percentile level of the loss distribution when one exposure is removed from the existing portfolio. Since most risk managers set aside an amount of capital that covers losses up to 99% of the distribution, setting this percentile to 99 means that the risk contribution of a particular exposure is the incremental effect on the amount of economic capital required to support the portfolio. So, using the models, banks can calculate the marginal contribution to earnings of any one credit.
This paves the way for the active management of credit portfolios. Banks can rank exposures in their portfolios according to the amount of economic capital they eat up. They know the returns from each exposure and they can model the effects of removing or adding particular types of exposure.
In practice banks are finding that a relatively small number of borrowers hold a disproportionate amount of influence over a portfolio’s performance. These may be extremely large exposures to a relationship client, mispriced loans to a group concentrated in one sector, or two or three large exposures to lower-quality borrowers.
Again, using its CreditRisk+ model, CSFP takes the original portfolio of 500 exposures described above and removes the 25 exposures (5% of counterparties and 8.4% of the total exposure) from it. Running the economic capital calculation on the new portfolio reveals a fall in the economic capital requirement of 35%. Assuming that default swaps are used to remove the 25 exposures and assuming a market price for those instruments, the return on economic capital of the portfolio jumps from 8.00% to 8.11%.
This is the kind of analysis that is driving the boom in collateralized loan obligation issuance and that will lead to an explosion in the use of credit derivatives. Banks increasingly will use asset securitization, the secondary loan market and credit derivatives to offload exposures that do not meet their return on capital hurdles. They will identify hitherto hidden concentration risk and use these markets to lay off exposure to particular counterparties, sectors or regions.
And, in their search for assets with the required return and risk characteristics, banks will at the same time use these markets to buy new assets. Where the cash markets do not provide them, these will be created synthetically using CLOs and credit derivatives. Where there are funding cost or balance-sheet constraints, banks either will use unfunded instruments such as default swaps and total-return swaps or rent cheap balance sheet from other institutions or from new vehicles such as one being developed by Dresdner Kleinwort Benson.
The link between taking credit risk and originating lending transactions will be broken. The winners will be those institutions willing and able to make use of the new technology.
