Stage I – establishment of reserves:

number of suppliers and their reliability;

capacity and quality of storage facilities;

appropriate means of transportation nature of the goods;

availability of raw material prices and transportation for the borrower;

number of intermediaries between buyers and manufacturers of raw materials and other tangible assets;

distance provider;

economic factors;

Fashion at the purchased raw materials and other valuables;

exchange rate risks;

risk of entry restrictions on exports and imports of imported raw materials.

Stage II – the stage production:

availability and qualifications of the workforce;

age and power equipment;

load of equipment;

state of industrial premises.

Stage III – the stage of marketing:

number of buyers and their ability to pay;

diversification of debtors;

degree of protection against non-payment buyers;

belonging to the borrower’s primary sector credited by the nature of the finished product;

the degree of competition in the industry;

impact on the price of finished goods credited social traditions and preferences, the political situation;

there is a problem of overproduction in the market of the product;

demographic factors;

exchange rate risks;

• Ability to provide restrictions on the export of and import into another country of production.

Moreover, risk factors at the stage of marketing can be combined with the factors of the first and second stage. Therefore, business risks at the stage of sales is higher than at the stage of establishing reserves or production.

In terms of economic instability analysis of business risk at the time the loan substantially complements the assessment of creditworthiness of the customer based on financial ratios that are calculated on the basis of secondary evidence of elapsed periods.

These factors of business risk must be taken into account in developing standard forms of bank loan applications, feasibility studies for the possibility of issuing a loan-

Assessment of business risk commercial bank could be formalized and carried out by a system of scoring, when every factor of the business risk is assessed in points (Table 9.3).

Table. Criteria of business risk

Points

I Number of suppliers

more than three

10

two

5

one

1

II. Reliability of suppliers

all suppliers have an excellent reputation

5

most reliable suppliers as business partners

3

bulk suppliers are unreliable

0

III. Cargo transportation

within the city limits, there is an insurance policy,

form of transportation conformity of the goods

10

provider remote from the buyer, there is an insurance policy,

Transportation conformity of the goods

8

provider remote from the buyer, transportation may

lead to a loss of product and reduce its quality

there is an insurance policy

6

supplier within the city, transportation does not meet the

cargo insurance policy is missing, etc.

4

IV. Storage of goods

the borrower has its own warehouse

satisfactory quality or warehouses

not required

5

warehouse leased

3

storage space required, but not at the moment

assessment of business risk

0

etc.

A similar model assessment of business risk and apply on the basis of other criteria. Points are tabulated for each criterion and summed. The greater the total score, the less risk and more likely the deal with the projected effect, allowing the borrower to repay term debt obligations.

The liquidity risk that does present a real challenge is the need for funding when and if a sudden crisis arises. In this case, the issues are very different from those addressed above. Standard reports on liquid assets and open lines of credit, which are germane to the first type of liquidity need, are substantially less relevant to the second. Rather, what is required is an analysis of funding demands under a series of “worst case” scenarios. These include the liquidity needs associated with a bank-specific shock, such as a severe loss, and a crisis that is system-wide. In each case, the bank examines the extent to which it can be self-supporting in the event of a crisis, and tries to estimate the speed with which the shock will result in a funding crisis.

Reports center on both features of the crisis with Table 11 illustrating one bank’s attempt to estimate the immediate funding shortfall associated with a downgrade. Other institutions attempt to measure the speed with which assets can be liquidated to respond to the situation using a report that indicates the speed with which the bank can acquire needed liquidity in a crisis. Response strategies considered include the extent to which the bank can accomplish substantial balance sheet shrinkage and estimates are made of the sources of funds that will remain available to the institution in a time of crisis. Results of such simulated crises are usually expressed in days of exposure, or days to funding crisis.

Such studies are, by their nature, imprecise but essential to efficient operation in the event of a substantial change in the financial conditions of the firm. As a result, regulatory authorities have increasingly mandated that a liquidity risk plan be developed by members of the industry. Yet, there is a clear distinction among institutions, as to the value of this type of exercise. Some attempt to develop careful funding plans and estimate their vulnerability to the crisis with considerable precision. They contend that, either from prior experience or attempts at verification, they could and would use the proposed plan in a time of crisis. Others view this planning document as little more than a regulatory hurdle. While some actually invest in backup lines without “material adverse conditions” clauses, others have little faith in their ability to access them in a time of need.

Nonetheless, the techniques employed by those that define the industry standard could use some improvement. By category, recommended areas where additional analytic work would be desirable are listed below.

A. CREDIT RISK

The evaluation of credit rating continues to be an imprecise process. Over time, this approach needs to be standardized across institutions and across borrowers. In addition, its rating procedures need to be made compatible with rating systems elsewhere in the capital market.

Credit losses, currently vaguely related to credit rating, need to be closely tracked. As in the bond market, credit pricing, credit rating and expected loss ought to be demonstrably closer. However, the industry currently does not have a sufficiently broad data base on which to perform the migration analysis that has been studied in the bond market.

The issue of optimal credit portfolio structure warrants further study. In short, analysis is needed to evaluate the diversification gains associated with careful portfolio design. At this time, banks appear to be too concentrated in idiosyncratic areas, and not sufficiently managing their credit concentrations by either industrial or geographic areas.

B. INTEREST RATE RISK

While simulation studies have substantially improved upon gap management, the use of book value accounting measures and cash flow losses continues to be problematic. Movements to improve this methodology will require increased emphasis on market-based accounting. However, such a reporting mechanism must be employed on both sides of the balance sheet, not just the asset portfolio.

The simulations also need to incorporate the advances in dynamic hedging that are used in complex fixed income pricing models. As it stands, these simulations tend to be rather simplistic, and scenario testing rather limited.

C. FOREIGN EXCHANGE RISK

The VaR approach to market risk is a superior tool. Yet, much of the banking industry continues to use rather ad hoc approaches in setting foreign exchange and other trading limits. This approach can and should be used to a greater degree than it is currently.

D. LIQUIDITY RISK

Crisis models need to be better linked to operational details. In addition, the usefulness of such exercises is limited by the realism of the environment considered.

If liquidity risk is to be managed, the price of illiquidity must be defined and built into illiquid positions. While this logic has been adopted by some institutions, this pricing of liquidity is not commonplace.

E. OTHER RISKS

As banks move more off balance sheet, the implied risk of these activities must be better integrated into overall risk management and strategic decision making. Currently, they are ignored when bank risk management is considered.

F. AGGREGATION OF RISKS

There has been much discussion of the RAROC and VaR methodologies as an approach to capture total risk management. Yet, frequently, the decisions to accept risk and the pricing of the risky position are separated from risk analysis. If aggregate risk is to be controlled, these parts of the process need to be integrated better within the banking firm.

Both aggregate risk methodologies presume that the time dimensions of all risks can be viewed as equivalent. A trading risk is similar to a credit risk, for example. This appears problematic when market prices are not readily available for some assets and the time dimensions of different risks are dissimilar. Yet, thus far no one firm has tried to address this issue adequately.

Finally, operating such a complex management system requires a significant knowledge of the risks considered and the approaches used to measure them. It is inconceivable that Boards of Directors and even most senior managers have the level of expertise necessary to operate the evolving system. Yet government regulators seem to have no idea of the level of complexity, and attempt to increase accountability even as the requisite knowledge to control various parts of the firm increases.

A. Introduction

The purpose of this policy is to provide the basis for the bank to responsibly manage the investments in accordance with the philosophy and objectives stated below. Unless stated otherwise, the terms “investment” and “investment portfolio” will refer to both cash management activities and longer-term investment securities. The term “capital “ will refer to the sum of Undivided Earnings, Paid in Capital, Regular Reserve, and the Allowance for Loan Losses.

B. Investment Philosophy

The bank recognizes a fiduciary responsibility to customers to invest all funds prudently and in accordance with ethical and prevailing legal standards. It recognizes that the investment portfolio must complement the loan portfolio and together they must be matched with liabilities. In addition, the policy will support the overall business and asset/liability strategies of the institution.

Certain general tenets apply to the investment portfolio. Safety of assets is of primary concern. In all cases, only high quality investments will be purchased. The investment portfolio should provide adequate, but not excessive liquidity in meeting member demand for funds. Reasonable portfolio diversification should be pursued to ensure that the bank does not have excessive concentration of individual securities, security types or security characteristics. The investment portfolio will be managed on a “buy and hold” basis. However, periodic sales of investment securities are permissible to meet operational cash needs or to restructure the portfolio mix in accordance with changes in investment strategy. In all cases, investments must meet all criteria stated in the Federal Law, the Rules and Regulations of the Regulators, and all requirements of our bonding company. Investment performance in all classifications will be monitored on a frequent and regular basis to ensure that objectives are attained and guidelines adhered to.

C. Investment Authority

Authority for investments is the responsibility of the Board Directors. The Board shall designate the Chief Executive Officer and the Chief Financial Officer to act on its behalf and in accordance with this policy. The Chief Financial Officer, in conjunction with wither the Controller or the Financial Analysis Manager, shall oversee the day-to-day operations of the investment portfolio and have specific investment and transaction execution authority. Quarterly, the activity for safety and sound the Chief Executive Officer, Chief Financial Officer and the Financial Consultants will review the past quarter’s investment activity for safety and soundness.

D. Investment Objectives and Guidelines

Firm investments shall be managed at two levels: cash management needs and longer-term investment activities. In all cases, safety of funds shall take precedence over yield and its attendant risks, and the only financial instruments which may be purchased are those which in the opinion of the Chief Financial Officer pose no significant credit risk. All investment activity is to be guided by the criteria specified in this policy.

1. The funds of the bank can be invested in the following types of instruments with qualifications as provided:

a. United States Treasury obligations will have a maximum maturity of three years.

b. United States Agency Securities (excluding MBS) shall be limited to a maximum maturity of three years.

c. Mortgage Backed Securities issues by or fully guaranteed as to principal and interest by the Federal National Mortgage Association, Government National Mortgage Association, or the Federal Home Loan Mortgage Corporation.

These investments will primarily be one year ARMs and five year balloons, but three year ARMs and seven year balloons may be purchased. Individual issues shall not exceed $50 million in value at the time of purchase.

d. Private Issue Mortgage Back Securities. Before authorizing a purchase of this type, the Chief Financial Officer shall review a prospectus to determine whether the investment is permissible. Total private issue Mortgage Related Securities purchased shall not exceed $50 million. The minimum credit rating of these securities at the time of purchase must be AA or equivalent.

Individual securities shall not exceed $10 million in value at the time of purchase.

e. Repurchase and Reverse Repurchase Agreements, but only with a Federally Insured Bank on the approved bank list, with both parties acting in the capacity of principal. Maturities will be no longer than 180 days and the securities will be delivered to a third-party safekeeping agent.

f. Fed Funds sold shall be conducted only with approved banks. Total Fed Funds sold to a single institution shall not exceed $50 million. Term Fed Funds shall not exceed one year in maturity.

g. Certificates of Deposit issued only by approved banks with a maximum maturities not to exceed one (1) year. Total certificates deposited in a single institution shall not exceed $50 million.

h. Bankers’Acceptances issues only by approved banks. Total Bankers’ Acceptances purchased from a single issuing institution shall not exceed $50 million.

i. Yankeedollar or Eurodollar deposits only in approved banks. Total Yankeedollar or Eurodollar deposits in a single institution shall not exceed $50 million.

j. Money Market mutual funds that invest in CDs, Repurchase Agreements, Banker’s Acceptances, Agency Notes, etc., and that which conform to Federal rules and regulations. Mortgage Backed Securities mutual funds that invest in agency and private issue MBS. The objective of the MBS fund must be current income, capital preservation, and minimal fund price volatility. Investments in the money market mutual fund will be limited to $100 million on and investments in the MBS mutual fund will be limited to $25 million.

Deliverable securities purchased will be delivered (either physically or via the Federal Reserve Bank wire system) simultaneously with the release of cash. Such delivery will be made to a third party for safekeeping, whether to a custodian or to a trust account maintained. At a minimum, the contracted safekeeping agent or trustee will provide written confirmation of each transaction to us and a monthly listing of all securities in its account.

The Chief Financial Officer shall maintain an approved list(s) of banks and other financial institutions with which the bank may conduct investment transactions. The list may include several of the largest domestic banks and U.S. domiciled subsidiaries of foreign institutions which are federally insured and carry a minimum credit rating of “B/C” by Keefe, Bruyette and Woods. The bank will minimize the risk associated with executing securities transactions by limiting the securities brokers/dealers with which it does business to those who are primary dealers recognized and approved by the Federal Reserve System. The Chief Financial Officer will make additions/deletions from the list(s) as appropriate.

2. Cash Management

a. The objective of the firm’s cash management policy is to provide sufficient liquidity each day to meet operating cash needs, member demand for funds, and minimum balance requirements for the Federal Reserve Account.

b. Cash management funds shall be maintained to meet the withdrawal and lending needs of the customers. The amount of funds will be continually evaluated depending upon lending trends and withdrawal experience, and other external factors deemed appropriate.

c. The Chief Financial Officer, Financial Analysis Manger, or Controller, or Accounting Supervisor shall execute these cash management activities and the Chief Financial Officer shall review these transactions.

3. Investment Portfolio

The management objective of the firm’s Investment Portfolio is to provide maximum return within the bounds of safety of principal and interest, liquidity, and asset liability management demand. Each specific investment decision will be evaluated with respect to such issues as expected return, credit risk, liquidity, effect on the investment portfolio, impact on asset/liability needs, and proper safekeeping. The Chief Financial Officer, Controller, or Financial Analysis manager will execute investment portfolio transactions.

4. Prohibited Activities

The following activities are prohibited:

a. Cash forward agreements to buy when the delivery date is in excess of ninety (90) days from the trade date.

b. Standby commitments to purchase or sell a security at a future date whereby the buyer is required to accept delivery of the security at the option of the seller.

c. Adjusted to trading, meaning any method or transaction used to defer a loss whereby the bank sells a security to a vendor at a price above its current market price and simultaneously purchases or commits to purchase from that vendor another security above its current market price.

d. Short sales of securities not owned by the bank.

e. Futures trading.

E. Maturity Structure

The maturity structure of the investment portfolio will be managed in accordance with asset liability management needs, market conditions, and the objectives of this Policy Statement. It is the responsibility of the Chief Financial Officer to constantly monitor the maturity structure of the investment portfolio and implement modifications in the average maturity and makeup of the portfolio. These modifications will be based on Asset/Liability Management concerns (i.e., price risk, liquidity risk, reinvestment risk) and changing market conditions.

F. FASB 115 Compliance

In order to comply with the FASB 115, the bank will classify its investments as Trading, Held-to-Maturity, and Available-for-Sale. All Fed Funds and mutual fund accounts will be classified as Trading Accounts. All balloon MBS securities, FHLB stock, and other fixed rate investments with a maturity of greater than one year at the time of purchase will be classified as Held-to-Maturity.

The remainder of the portfolio will be classified as Held-to-Maturity. The bank has the positive intent and ability to hold these to maturity. These securities will not be sold in response to changes in market interest rates. The bank normally has $20 million in Fed Funds and has a line of credit with the FHLB of over $50 million. Given our asset size, $200 million of instantly accessible cash is more than adequate liquidity for any possible scenario.

G. Sovereign and Exchange Rate Risk

The bank will not invest in any foreign banking institutions or securities denominated in currencies other that U.S. Dollar and therefore will not incur any Sovereign or Exchange Rate Risk.

H. Modifications to Policy

The Chief Financial Officer is responsible for recommending changes to this policy. Approved by the Board of Directors

Collateral Risks

The existence of collateral minimizes credit risk if the collateral can easily be taken over and sold at some significant value. Collateralization is a widespread and common way to mitigate credit risk. There are many types of collaterals:

• Real assets, from houses for mortgages to aircraft and commodities in other business lines.

• Securities, mainly for market transactions, the most common example being that of repos.

• Commodities, when a cargo is financed, or in oil and gas financing.

• Receivables from a pool of assets in securitization, when credit card or mortgage receivables are securitized. Pools of assets include bonds and loans as well as structures used to sell these types of assets in the market.

• Margin borrowing.

Specialized finance makes wide usage of collaterals. In some cases, these are tangible assets. Assets financing is collateral-based, whether assets are ships, aircraft or assets of a corporation. In many other cases, there are intangible collaterals. Corporate acquisitions (Leveraged Buy-Outs, LBOs) or project finance pledge the cash flows from assets. Nevertheless, future cash flows are uncertain. Covenants help in structuring the transactions to minimize the risks. The collateralized assets are subject to a number of risks:

• Accessibility risk, since it might be difficult to effectively seize the collateral.

• Integrity risk, the risk of damage to the collateral.

• Legal risk, which is the risk of disputes arising from the various laws at play in international transactions.

• Valuation risk, since the liquidation value of a collateral depends on the existence of a secondary market and the price volatility of such a market.

Legal Risk

Legal risk results from the risk of dispute to access the collateral. In addition, the collateral in international transactions is subject to a number of laws, such as that of the lender, of the borrower, of the place where the collateral is located and the law of the contract.

The Ability to Physically Access the Collateral

Legal access to the collateral is one issue. Physical access might be another, since accessing the collateral might be straightforward or very difficult. With cash collateral or securities, the collateral is posted with a custodian, or the lender, and access is not an issue. When physical collateral is planes or ships, access might be an issue, because these assets can be moved away from their usual location. The case of aircraft is the best illustration. Aircrafts can be seized in airports where legal procedures can be enforced. When planes fly only within a foreign country using local airports, they might be impossible to find and seize. Flying through international airports is an important aspect of risk in such a case. Real estate is the opposite case. By definition, it stays where it is built and there is no physical access issue. Also, it is common to hide away collateralized inventories and equipment in distressed firms since everyone knows that these assets will be taken away. Although this is illegal, the risk always exists.

Integrity Risk

Collateral might be damaged, either through normal deterioration because of a lack of maintenance, or deliberately. Whenever equipment has valuable parts, there is an incentive to move them away once it is known that all equipment will be seized.

Price Risk

The collateral has a liquidation value, which is subject to price risk. Price risk for liquid assets is market-driven, since there are various periods to consider before liquidation can be effective:

• The grace period allowed for lenders before recognizing default of payment.

• The time to work out legal procedures as they are needed. With market transactions, the securities posted as collateral are readily available once a breach in the obligations of the lender has occurred.

• The time to liquidate the collateral depends on market liquidity. It is more difficult to sell large blocks of securities than small quantities. For large blocks, there might be an additional delay because it is worthwhile to sell slowly rather than selling fast and triggering a significant price decline.

The level of posted collateral depends on these factors. Whenever there is a secondary market, the time required to sell allows the price to deviate adversely because of market movements. Even after a worst-case adverse move of liquidation value, the collateral should still absorb the loss under default. Both market liquidity and price volatility are important parameters to define the adequate amount of securities pledged as collateral. Cash liquidation value is risk-free, at least in the local currency. Typical assets subject to measurable price risk include: securities, commodities, oil and gas, aircraft and ships, real estate, standardized equipment.

Market Collateral Transactions

Many transactions use market instruments as collateral, since they are liquid assets easy to sell and since their price is continuously observed. Individuals holding portfolios of securities have margin accounts, which they can use to borrow a fraction of their holdings. Financial institutions or funds can pledge the securities that they hold. Inter-bank transactions require pledging liquid collaterals. Broker financing and margin calls in futures markets are also collateral-based. Brokers pledge their securities. Margin calls in organized futures markets are set to absorb 1-day market volatility, 1 day being the minimum period between two successive adjustments.

The main collateral risk in such cases is price risk, since only liquid assets are generally eligible for collateralization. The principle is to set up a collateral, whose value is higher than the borrowers debt. In the event where the collateral value falls below a preset threshold, the lender can sell the securities to reduce the debt or to get repaid in the event of default.

In order to maintain a safety cushion between collateral and debt value, given that the collateral value moves constantly, there are rules triggering the sale of securities. In some cases, the collateral value is much higher than the debt value at inception. It is typical to borrow no more than 50% of the value of securities held by individuals. In other cases, the collateral value to debt value ratio is smaller. Various rules serve to keep collateral above debt when its value changes. A common rule is to post an additional amount of collateral when the existing security value falls below a threshold level. The excess of collateral value over debt value depends on the delay between the collateral deficiency event and all necessary corrective actions. This delay includes the minimum time required to notify deficiency to the borrower, plus some time to post additional collateral, plus the delay for selling the pledged securities under no corrective action. The difference between collateral and debt value (haircut in percentage terms) also depends on the securities price volatilities. The longer the delay and the larger the volatility, the larger the potential downside move of the collateral value under adverse conditions. Since the final value of the collateral at the time of the sale of securities should be above the debt, the required collateral increases with both delay and securities volatilities. The next chapter expands this simple model, determining the minimum value of pledged securities given volatilities and total period before sale.

Calculation of Joint Default and Conditional Probabilities

The process for calculating all the joint probabilities uses the conditional probabilities of Bs credit state given As credit state. In compact notation, P(A = D) = a designates the unconditional probability that A defaults and P(A = ND) = 1 — a the unconditional probability that A does not default, with similar notation for B [P(B = D) = b and P(B = ND) = 1 - b].

Three inputs determine all others: the unconditional default probabilities of A and B plus either the conditional probability that B defaults given A defaults, or alternatively the joint probability of default of A and B (using the simple formula applicable to two obligors as in Chapter 41). Table 46.6 shows the detailed calculations. The joint default probability P(A, B) results from the general formula:

Loss Distribution

The process above results in the matrix of Table 46.7 cross-tabulating both entities credit states showing the joint probabilities, with the margins summarizing the column probabilities and the row probabilities, which equal the unconditional probabilities. This provides the loss distribution.

The same observation on single defaults applies to the independent and correlation cases. The single probabilities of default in a portfolio context differ from the unconditional probabilities of default. For instance, the default of A alone has a probability of

6.094%, whereas its unconditional default probability is 7%. How can we explain the paradox of differing single default probabilities of A out of a portfolio and within a portfolio? The explanation is that A defaulting alone, in a portfolio context, is conditional on others not defaulting and is no longer an unconditional probability of default. It is the joint probability of default of A and of others not defaulting.

The standard presentations of the loss distribution, with cumulated probabilities, and the related graph are shown in Table 46.8 and Figure 46.2, respectively.

The Loss Statistics

The calculations show that the EL remains the same as with the independent case, as expected since expectation is not dependent on correlation. The LV and loss percentiles increase with the correlation (Table 46.9). These calculations allow us to relate the portfolio loss statistics to standalone risk measures, such as expected loss and loss volatility, and measure the effect of diversification.

The gain in LV quantifies the diversification effect: 36.412 — 27.744 = 8.668. Since risks do not add arithmetically, allocating the overall portfolio risk to each obligor is an issue. The risk contributions are risk allocations, dealt with in Chapters 51 and 52.

Comparisons of the Correlation and the Independent Cases

Correlation implies the following changes:

• The joint default probability is now higher than the product of the unconditional (standalone) default probabilities of A and B.

• The conditional default probabilities now differ from the unconditional (standalone) default probabilities.

As a result, the distributions fat tails gets thicker and the distribution mode shifts to the left-hand side. This results from the higher probability of big losses (150). Table 46.10 shows that the portfolio EL remains the same while the LV increases with correlation. In addition, the probabilities of larger losses are larger, as expected, than in the independent case.

Analytical Loss Distributions

This chapter describes some analytical loss distributions when single defaults correlate with each other. The most developed model of analytical distributions is CreditRisk+. Other simple techniques allow us to simulate and visualize the effect of correlation on portfolio risk, measured by loss volatility and loss percentiles, under restrictive assumptions.

The starting point is the simple case of independent losses. The portfolio distribution of the number of defaults is the well-known binomial distribution. This is also a loss distribution applying to uniform (equal) exposures only, since the binomial distribution does not accommodate size discrepancies. The binomial distribution over a uniform portfolio serves as a benchmark for measuring the effect of correlations on the portfolio risk. It also illustrates how the increase in loss volatility, as a percentage of the total portfolio exposure, tends rapidly towards zero when increasing the number of obligors.

The limit distribution corresponds to another simple case with a uniform correlation between uniform exposures, building on a simplified version of the Merton model. To obtain closed-form formulas, we assume that the standardized asset values of firms follow normal distributions with a uniform correlation across firms. The uniform correlation results from the common dependence of all individual asset values on a single factor, representing the state of the economy. This single factor conditions the normal distributions of asset values. When conditions improve, all asset distributions shift upwards, resulting in a lower portfolio default probability than its unconditional long-term value. Conversely, when conditions worsen, the default probability of the portfolio becomes higher than its long-term value. In essence, the technique relies on conditioning the asset value distributions on a single factor. Additional simplifying assumptions allow us to obtain an analytical form of the portfolio value distribution, called the limit distribution. The limit distribution ignores specific risk. An important finding of such distributions, confirmed empirically by full-blown models, is that the fat tail of the loss distribution is highly sensitive to the correlation between defaults.

The next chapters (48 and 49) illustrating Monte Carlo simulations use a similar one-factor model to generate correlated defaults, accommodating unequal exposures and unequal default probabilities of individual obligors.

CreditRisk+ uses actuarial techniques to find the shape of the loss distribution in a more accomplished manner, using the Poisson distribution to model the number of defaults. Starting from independent defaults, CreditRisk+ models defaults using a mixed Poisson distribution. The critical parameter of this distribution is the default intensity per unit of time, analogous to a default probability. It applies only to independent defaults. The mixed Poisson distribution uses as default intensity the product of the long-term (unconditional) default intensity with a multiple called the mixing parameter. The technique accommodates mixing parameters dependent on common factors, resulting in correlated default intensities of the various banks portfolio segments.

The three sections of this chapter detail respectively: the binomial distribution; the limit distribution; the CreditRisk+ analytical framework.

Using marginal risk contributions makes pricing sensitive to the entrance order in the portfolio. The same facility entering first and second requires a different pricing to obtain a given target overall portfolio return, as explained when discussing risk contributions. However, whatever the entrance rank, risk-based pricing achieves the target overall rate of return over the entire portfolio. The same simple example of a two-obligor portfolio used for illustrating risk contribution properties now illustrates RaRoC calculations, with and without a new facility. After a reminder of the example data, we proceed with the calculations of the ex post risk-based performance and the ex ante risk-based pricing using a target required return on capital.

TheSamplePortfolio

The portfolio of two obligors of Chapter 46 (with 10% correlation) is as shown in Table 54.5. We now add revenues as annualized AISs, or interest margins plus any fee averaged over the life of the transaction in Table 54.6.

We conducted all detailed calculations to obtain the loss statistics of the portfolio and allocate the capital and loss volatility to each of the two obligors. A summary is given in Table 54.7. There are two cases for economic capital, using the confidence levels 2%

and 0.5%.

To conduct risk-adjusted performance analysis, we need existing revenues. To conduct a risk-based pricing calculation, we need to calculate the required revenues. The first case considers revenues as given (ex post view), while the second case determines the required revenues in line with target profitability (ex ante view).

Risk-based Performance

Risk-based performance is an ex post measure showing, given past pricing decisions, what are the relative performances of business lines, facilities and so on. All that remains to do is

Risk-based Pricing

Risk-based pricing implies pricing according to risk. The starting point becomes the required hurdle rate, set at 20% pre-operating expenses and pre-tax. Then we move to the required revenues that meet this target. The difference with the previous RAPM calculation is that we use the marginal risk contribution to capital, or MRC(K), rather than the absolute risk contribution. We show numerically here several implications: the pricing is not the same, using the unique 20% hurdle rate, when we use absolute or marginal contributions; the pricing depends on the order of entrance into the portfolio; the ex post portfolio RaRoC is in line with the target rate. In order to do so, we need to make a distinction between the events A first-in and B first-in.

Tables 54.9 and 54.10 show two calculations, the first with a capital of 90.5 (2% confidence level) and the second with a capital of 140.5 (0.5% confidence level).

Table 54.9 presents the absolute and the marginal risk contributions of A and B, both when A is first-in and when B is first-in. It shows the values of the required AIS based on both absolute and marginal risk contributions.

The obvious observation are: the target AIS differs when using absolute and marginal risk contributions; the target AIS of A and B also depend, when using marginal risk contributions, on which facility is the first-in the portfolio. Nevertheless, in all cases, the RaRoC is always equal to the target rate 20%, simply because the AIS are derived under this constraint. Calculations differ by their meaning. For risk-based pricing, only marginal risk contributions combined with the hurdle rate count. Note that the absolute risk contributions are unknown before a new transaction is selected, since this new facility changes all of them.

However, it is useful to check that the overall return on capital remains 20%. It is also necessary to see what are the absolute risk contributions after entrance of both exposures into the portfolio. The table summarizes all information.

From an ex ante view, we have to consider a first entrant and then a second one to build up the portfolio. When A enters first and then B, we require a high AIS on A (25.60) and a low AIS on B (2.00) to get the overall 20% return, because of diversification. The example shows that the entrance order changes the marginal contribution of A, or of B, as well as the target AIS. The same transaction, A, requires a different pricing depending on the order of entrance. If transaction A is first-in, it requires a 25.60 AIS and if the same transaction A is second-in requires only 11.10. Still, in both cases we always end up with the overall 20%. All marginal risk contributions to capital sum to the portfolio capital, 90.5, after all transactions are in, by construction. Therefore, necessarily, the sum of the excess spread over expected loss remains 20% of that capital, or 20% x 90.5 = 18.10. The sum of the gross AIS is 27.60. The difference between the sum of the excess spreads and the sum of the AIS is the sum of the EL, or 9.50.

The AIS that would be required using the absolute risk contributions is in the top section. It differs from the AIS required based on marginal risk contributions, because absolute and marginal risk contributions differ radically. However, the AIS values sum to 27.60. This is necessary, since absolute risk contributions sum to capital. Even though they comply with this overall ex post constraint, the required AIS on absolute risk contributions would not guarantee that the portfolio return remains at 20% during its build-up, while the marginal contributions do so.

Note that simple relationships would not hold when using marginal contributions to portfolio loss volatility rather than marginal contributions to portfolio capital. The reason is that the ratio of capital to loss volatility differs substantially when the first-in enters and when the second-in enters.

The second calculation (Table 54.10) uses the 0.5% confidence level, with a capital of 140.5. This calculation illustrates the case where all marginal risk contributions are positive. In this case, the marginal risk contributions to capital are identical for the first-in transaction (93.0), independent of whether it is A or B. Nevertheless, the marginal risk contributions between first-in and second-in always differ. Consequently, the required AIS for A and B changes, depending on which one is first-in. Of course, the overall portfolio RaRoC remains at 20% during the build-up period and after.

Portfolio Reporting

Three chapters address portfolio credit risk reporting. This first chapter details the specifics of a sample portfolio and provides an overall reporting on its risk-return profile. This is the top management view of the banks portfolio. The second chapter slices the portfolio along various risk and business dimensions. The risk dimensions are the various credit risk components, such as exposures, default probabilities and recoveries. The business dimensions refer to the usual product families, market segments and business lines. Reporting requires breaking down the portfolio along these dimensions, to provide the various management views of the portfolio as an aid to business decisions. The third chapter goes beyond these descriptions towards more analytical reports, such as sensitivity and what if analyses.

This chapter provides the portfolio overview using a sample portfolio. The portfolio description is given in the appendices. The major characteristics are: 50 obligors, uniform loss correlation of assets of obligors, two risk classes of default probability, two business units and two industries, unequal exposures and various loss given default percentages. Monte Carlo simulation generates the loss distribution using the simplified asset value model.

The portfolio overview through portfolio models provides a number of portfolio characteristics of interest. They include notably: the expected loss, the portfolio capital, the overall portfolio Risk-adjusted Return on Capital (RaRoC) and Shareholders Value Added (SVA), plus measures of correlation risk and concentration risk. The correlation risk measure is simply the ratio of a measure of overall risk, such as the loss volatility, to the sum of standalone risks of individual transactions, a percentage lower than 1 showing the overall gain from diversification. The size concentration risk addresses pure size discrepancies, summarized in adequate indexes, or with curves showing the percentage of the overall portfolio risk resulting from the largest exposures.

The first section describes the portfolio. The second section summarizes the portfolio overview, with overall statistics such as expected loss, capital and the aggregated portfolio RaRoC. The third section provides additional measures of portfolio concentration risk. The last section is a short transition towards the detailed views of individual facilities of the next chapters.

Diversification and Correlation Effects

In general, when the risks of two obligors correlate, the risk is higher if they have large exposures. There is an interaction between size and correlation. A simple measure combining these effects is the ratio of the portfolio loss volatility, 221.1, to the sum of individual standalone loss volatilities, 750.17 or 29.47% in our example. The portfolio diversifies away close to 70.53% of the standalone loss volatilities.

Concentration Risk: Diversity Score

Concentration characterizes size discrepancies. The individual loss given default weights, ratios of the individual loss given default to the total loss given default of 6000, measure exposure sizes. Synthetic views of portfolio size concentration, other than reporting the largest individual weights, include such measures as the diversity score and concentration curves.

The diversity score is an index synthesizing the discrepancies of exposure of individual facilities. There are as many concentration indices as there are metrics for risk. Alternative metrics include exposure weights, loss given default weights or capital allocation weights, each of them being the ratio of the individual measure to the total portfolio measure. There is a concentration index, or diversity score, for each metric. The diversity score is a number that is always lower than the actual number of facilities, here 50. The lower the ratio, the higher the risk concentration along the selected dimensions. The diversity score is the number of equal size exposures equivalent to the weight profile of individual exposures. The diversity score DS is the following ratio:

The w are the weights of facilities, using one risk metric, for instance exposure or loss given default of individual facilities. If all weights were equal to 1/n, with n the number of obligors, the ratio would be 1/(J^ⁿ_{= 1} 1/n²),or 1/(n/n²) = n. The diversity score is commonly interpreted as the number of uniform exposures equivalent to the number of actual unequal exposures. It is a convenient measure to capture pure size concentration effects, as opposed to correlation effects. The ratio of the diversity score to the actual number of exposures is always lower than 1 whenever there are size discrepancies, and the gap measures pure concentration risk.

Table 55.2 provides the diversity scores for exposure and capital allocation, respectively equal to 35.02 and 33.22. Both numbers are lower than the actual number of exposures, 50. The ratios of these diversity scores to this actual number of exposures, 50, measure the level of concentration in terms of weight discrepancies. Note that the capital diversity score combines both effects, concentration and diversification, since capital allocations capture the retained risk post-diversification effect.

Concentration Curves

A second measure of concentration risk is the concentration curve, or Gini curve. The curve shows the cumulated exposure, or any alternative risk metric, such as capital, as

a function of the number of exposures. The curve cumulates the risk metric (exposure) sorted by descending values. A uniform exposure portfolio would have a straight-line concentration curve. The higher the curve above the straight line, the higher the concentration risk.

In the exposure concentration curve of Figure 55.3, the first five biggest obligors represent 21% of the total portfolio exposure, the first 10 biggest obligors represent 40% of the total portfolio exposure, and so on. The curve hits 100% when all 50 exposures cumulate. The slope is steeper at the beginning of the curve because the largest exposures are the first along the X-axis. Steepest slopes also characterize concentration because they imply that a lower number of the largest risks concentrates a larger fraction of the total risk.

• Exposure, either in value or as a percentage of total portfolio exposure.

• Capital in excess of expected loss, either in value or as a percentage of total portfolio capital.

• Edf as a percentage.

• Lgd as a percentage of exposure.

• Expected loss and unexpected loss.

• Income measures, either as spreads or risk-adjusted performance measures, namely the RaRoC ratio and SVA.

All dots in the sample charts of this chapter represent individual facilities. Subsequent sections provide sample reporting examples.

Facility Exposures and Risk Components (Edf and Lgd)

Two basic underlying components of credit risk, besides exposure, are the default probability (Edf) and the severity of loss under default, or loss given default (Lgd). They are basic ingredients of the expected loss EL, since Edf x Lgd measures the loss rate. In this sample portfolio, the default probabilities do not correlate with exposures. However, there are more small exposures in the area of high loss under default (low recovery rate). This is in line with expectations (Figure 56.4).

Setting Up Limits: EL and LV

Expected loss EL as a percentage of exposure is a relevant measure for risk quality, for assigning ratings or setting up limits and delegations. Loss volatility LV, both as a percentage of exposure and in value, synthesizes several risk dimensions, risk quantity, risk quality and capital allocation. Charts visualize the trade-off between risk quality and exposure.

Risk Quality versus Exposure

The EL-exposure graph (Figure 56.5) shows what happens when capping either EL or exposure. There are four quadrants, and points spread over all of them. The best measure of risk quality is EL as a percentage of exposure, while exposure (in value or as a percentage of total) measures the volume of risk. In addition, EL as a percentage is a frequent basis for rating risk because it combines both default probability and severity of loss. The EL in value serves better for economic provisioning. The EL as a percentage possibly serves for setting delegations and limits in terms of risk class. The graph shows EL as a percentage of exposure.

Capping exposure does not eliminate high EL, since there are many high ELs in the small exposure area of the chart. Conversely, capping percentage EL does not eliminate high exposures in general. The graph shows a tendency to take on more exposure for a small EL risk. It also shows that it is not equivalent to set a limit in EL and in exposure. Since exposure is not risk, because it does not embed all relevant risk dimensions, it is worth considering setting limits in EL.

The LV(%)-exposure chart shows a similar picture (Figure 56.6). Since LV is the basis of capital allocation, capping LV is another option to up economic risk limits rather than exposure. Note, however, that EL and LV depend on the same risk components—EaD, DP and Lgd—although LV is closer to capital than EL.

The graph of LV(%)-exposure value also shows the trade-off between risk quality (EL% or LV%) and risk quantity (exposure). The product LV(%) x exposure is the LV in value. Bounding this product is similar to bounding LV in value. The various levels of LV value in the LV(%)-exposure graphs are hyperboles, each one corresponding to an LV value. Pushing the curve towards the centre limits both quality and quantity of risk. Lets assume that the lower curve shown in the graph is the limit. There are still several points above this curve. The implication is that the subjective trade-off between risk quality and risk quantity does not filter high LV values.

Risk-based limits in LV eliminate some small and large exposures that appear less risky than they are. In order to push the LV value under a preset limit, we have to decrease either the risk quality (EL% or LV%) or the risk quantity (exposure), or both, to move below the risk limit curve. Since LV relates to capital allocation, bounding the LV is a proxy for bounding economic capital allocation.

Risk-adjusted Performance and Mispricing Reports

The performance measures relate revenues to exposure or economic risk measures. Revenues are All-In Spreads (AISs), including interest margins and fees annualized over the life of the facility, either in value or as a percentage of exposure. The percentage measure is the accounting Return On Assets (ROA), which is not risk-adjusted because it relates revenues to the volume on risk only, ignoring risk quality.

The risk-adjusted return is the RaRoC, or Sharpe ratio, of the facility, based on the allocated capital: RaRoC = (AIS — EL)/(allocated capital — EL). The RaRoC should be above the hurdle rate k, representing the target pre-tax and pre-operating expenses return on economic capital. RaRoC can be negative since it is the ratio of a difference in spreads and expected loss to allocated capital. The SVA is AIS — EL — kK. The SVA measure combines both size of transactions and risk-adjusted return. It shows the relative richness of transactions in value: positive SVA indicates creation of value. Unlike negative RaRoC, negative SVA has an interpretation, since it means destruction of value. The SVA minimum line is therefore the zero value horizontal line, a function of the 25% hurdle rate. The average SVA is the ratio of total SVA by the number of exposures, 50, or 1.24.

Risk-return profiles are also mispricing reports since they show gaps between target and effective pricing. Mispricing reports serve to identify which facilities contribute to the richness of the portfolio and which do not. There are two mispricing reports:

• The first mispricing is the gap between the target minimum return and the effective return. For RaRoC, the benchmark is the hurdle rate 25%. For SVA, it is the zero value showing that a facility breaks even on the cost of risk.

• The second mispricing is relative to portfolio average. It shows whether a facility is more or less profitable, after risk adjustment, to the average portfolio risk-adjusted return. For the RaRoC, the reference value is 38%.

For SVA, it is possible to use the average SVA as a benchmark, or 1.24. However, the SVA depends on size, so that the actual reference value for the portfolio should be the SVA per unit of exposure, or 61.82/11 000 = 0.56%. Mispricing would become the gap between the SVA per unit of exposure for each facility and the portfolio average unit exposure SVA.

We provide below representative reports for our sample portfolio (for illustration only).

RaRoC Reports

Figure 56.7 shows that accounting measures of profitability (ROA%) and risk-adjusted measures (RaRoC%) have no relationship. This is the primary reason for risk-adjusting performance measures. Negative RaRoCs appear in real portfolios whenever the spread does not compensate the EL plus allocated costs. When isolating a transaction, the AIS might not exceed EL because market spreads might not compensate risk. The phenomenon often disappears when extending revenues to all transactions and services to a client, because fees and other profitable transactions might more than compensate the lowest profitability transactions originated to build up business volume with a client.

AIS – EL in value plotted against capital shows the numerator and the denominator of the RaRoC ratio (Figure 56.8). All points above the 25% line create values and all points below the line destroy values. All points above the 38% line are richer than the portfolio average, and conversely. Mispricings are gaps between the points and the two lines representing 25% x K and 38% x K. The graph shows both what the pricing should be (in terms of risk-adjusted return) and what it is effectively. It also allows us to identify over- and underpriced facilities compared with either the hurdle rate or the average return.

The plot of RaRoC versus exposure provides another view of mispricing (Figure 56.9). It shows which facilities are above the 25% hurdle rate. All points above the horizontal 25% line create values, and all points below destroy values. Similarly, all points above the 38% average contribute to increasing the portfolio RaRoC above the average, and vice versa.

SVA Reports

The SVA reports are in value (Figure 56.10). The graphs compare each facility SVA with the arithmetic average of the portfolio. This is convenient, but not accurate, since the SVA combines both size and profitability. An alternative graph would show the unit exposure SVA of each facility and compare it with the average unit exposure SVA of the portfolio. In any case, there are negative SVAs, which correspond to RaRoC points lower than the 25% hurdle rate. The 25% RaRoC value corresponds here to the zero SVA value.

A number of simplifying assumptions help without loss of generality. The exposure of A remains constant and equal to 50; the exposure of B is initially 10 and progressively increases; A and B share the same default probability 1% and the same zero recovery rate; the risk of A and B are independent; the percentage AIS or ROA remains constant at 1%; regulatory capital is 4% of exposure; the required return on capital, economic or regulatory, is 25% pre-tax; the loss volatilities, both standalone and marginal, are used as a proxy for economic capital.

We first check that the 1% ROA provides an AIS in line with the target return of A using regulatory capital. For A, the AIS is 1% x 50 = 0.5, the regulatory capital is 4% x 50 = 2, and the ratio AIS/capital is 0.5/2 = 25%. The AIS of B is usually proportional to exposure. It would here be 1% x exposure, resulting in a return to regulatory capital of 1%/ 4% = 25%, since regulatory capital is 4% of exposure.

Instead of referring to the contractual AIS, we now look at what it should be when Bs exposure increases, using a target return on economic capital of 25%. The required AIS is no longer proportional to exposure because economic capital is not. We simulate the behaviour of the required AIS of B based on a target return on marginal risk contribution to the portfolio loss volatility, when the exposure of B increases.

If the exposure of B is 10, we first derive its marginal contribution to the portfolio volatility. Since the default probabilities are 1%, the standalone unit loss volatilities are s/d x (1 – d) = Vl% x 99% = 9.950%. Accordingly, the standalone loss volatilities of A and B are respectively 50 x 9.950% = 4.975 and 9.950% x 10 = 0.995. Since risks are independent, the portfolio loss volatility is the square root of the portfolio variance, which sums up the standalone variances. The sum of variances is 24.750 + 0.990 = 25.740 and the portfolio loss volatility is the square root, or 5.074. The initial portfolio volatility with A only was 4.975. The incremental loss volatility due to B is the difference 5.074 — 4.975 = 0.099. By contrast, the additional regulatory capital due to B is 10 x 4% = 0.04. It is much lower than its marginal risk contribution.

Now, we increase the size of Bs exposure up to 50 and calculate again its marginal risk contribution and its incremental regulatory capital. The new standalone loss volatility of B becomes 50 x 9.95% = 4.975, identical to that of A because exposures share the same characteristics. The portfolio loss variance 24.750 + 24.750 = 49.50 under independence of risks, and the portfolio loss volatility increases to V49.50 = 7.036. The marginal risk contribution to volatility is now 7.036 — 4.975 = 2.061. The marginal regulatory capital is only 4% x 50 = 2. We observe that the marginal risk contribution now gets higher than the marginal capital, whether it was lower when the exposure of B was only 10 or not.

The required AIS on marginal risk contribution is 25% x 2.061 = 0.515, while it is still 25% x 2 = 0.5 for regulatory capital. Conversely, the effective return on marginal risk contribution at the 1% AIS is 1% x 50 = 0.5 and the return on risk contribution is 0.5/2.061 = 24.264%, now lower than the current 0.5/2 = 25% on regulatory capital. The size of 50 is very close to the break-even value at which the new exposure fails to meet the target return on economic capital when we stick to a contractual ROA of 1%. Trying a higher size would confirm this finding, the constant 1% ROA providing a decreasing return on economic capital, while maintaining the 25% on regulatory capital. This break-even value is the risk-based limit.

The underlying reason for the existence of this economic limit is that economic capital increases more than proportionally to exposure, while the ROA remains constant. The purpose of this analysis is to demonstrate that setting limits has a purely economic rationale.

In Figure 57.1, the required return as a percentage of exposure based on marginal risk contribution grows with size. The return on exposure (or ROA%) is a constant, implying that revenues grow proportionally with exposure. It is at least above or equal to the minimum return required on capital. There is an optimal size for the transaction since the ROA no longer compensates the additional risk contribution beyond a certain size.

Other reasons, such as the size of the exposure relative to the borrowing capacity of the obligor, limit the size per obligor. The economic rationale provides a basis for setting limits, when no other constraint is binding.

For instance, when doubling the exposure, from 50 up to 100, the absolute risk contribution to loss volatility increases from around 5 up to around 15, or three times as much. Hence, the risk-reward profile deteriorates when Bs exposure increases.