What is the difference between risk-neutral and real-world default probabilities?

Risk-neutral probabilities assume that all investors are risk neutral, i.e. they care only about the return. The default probabilities implied from bond yields are risk-neutral.

Real-world probabilities are those implied by historical data. Real-world default probabilities are usually higher than risk-neutral default probabilities because corporate bonds are relatively illiquid, the returns on corporate bonds are higher than they would otherwise be to compensate for this. This is however only a small part of the explanation.

Another reason is that the subjective default probabilities of bond traders are much higher than those given  by historical data. Also, bonds do not default independently of each other. This gives rise to systematic risk and bond traders earn a an excess return over the risk-neutral default probability to bear this risk.

Idiosyncratic risk in the bond market cannot be diversified away as easily as in the equity market because of their limited upside. This further raises the premium.

Summary: "Theory of Risk Capital in Financial Firms".

This is a summary of the article "Theory of Risk Capital in Financial Firms".

The paper develops a concept of risk capial that can be applied to decisions in financial firms. The focus is on firms that has a principal in the ordinary course of business.

Principal activities: asset-related, liability-related, or both

Financial firms have three distinguishing features: credit sensitivity of customers, high cost of risk capital, high sensitivity of profitability to the cost of risk capital .

(1) The customers can be major liability holders. Therefore the customers prefer firms with high credit quality. Investors on the other hand are not sensitive to the creditworthiness of the firm, provided that they are compensated for the risk.

-> This means that A-rated firms can generally raise the funds they need to operate, but are at a disadvantage when competing with an AAA-rated firm in underwriting business.

(2) Financial firms are opaque in nature. They also have relatively liquid balance sheet whiches size and risk can change markdely in the course of a week. Financial firms are also sibject to considerable "event risk".

-> This leads to a high information cost in raising equity capital and in executing various customer transactions

(3) Financial firms operate in competitive financial markets. Their cost of capital is an important determinant of their profitability. Moreover, there is no easy way of allocation cost of risk capital to individual projects. Any risk allocation must also be inputed, highly risky principal transactions often requires little upfron cash expenditure.

-> A comitment made by underwriting is backed by the entire firm.

WHAT IS RISK CAPITAL?
Risk capital is defined as the smallest amount that can be invested to insure the value of the firm's net assets against a loss in value relative to the risk-free investment of those net assets.

Net assets: gross assets minus customer liabilities

Fixed customer liabilities: the riskiness of net assets = riskiness of gross assets
Contingent customer liabilities: riskiness of net assets depends = riskiness of gross assets + riskiness of customer liabilities + covariance of gross assets and customer liabilities

The volatility of net asset value is the most imporant determinant of the amount of risk capital.

Regulatory capital: risk capital measured according to a particular accounting standard
Cash capital: cash needed to execute a transaction

To follow:
1. Examples to show that the amount of risk capital depends only on the riskiness of net assets, and not at all on the form of financing of the net assets. Equity capital is then used to purchase asset insurance from various sources.
2. Failure of standard risk capital accounting methods. The economic cost of risk capital is shown to be the spreads on the price of asset insurance arising from information costs.Implications for risk management and hedging decision
3. Problem that arise in multi-business firms in trying to allocate the risk capital of the firm among its individual businesses.

MEASURING RISK CAPITAL
Case 1. one asset, a 100 million deal = net assets
Risk distribution: 1. 120 million 2. 60 million 3. 0
Cash capital requried: 100 million
The deal is financed by issuing a one year, default free, note to an outside investor. The cost of capital os 10%
How can the bank eliminate default risk?
- purchase an insurance on its assets
- purchase an insurance on its liabilities
Risk capital: smallest possible insurance cost to obtain default-free financing

* Risk capital and Asset Guarantees *
The bank buys insurance on the bridge loan from an AAAA-rated bond insurer for 5 million.
The value of the bank's assets at the end of the year will equal or exceed 110 million.
Risk capital: 5 million
The risk capital would need to be funded with a 5 million cash equity investment.

Balance sheet of BANK A
____________________________________________________________
Bridge loan    100      |    Note (default free)    100
Loan insurance    5    |    Shareholder equity    5


Return distribution:
                        Firm stakeholders
    Bridge    Loan         Bridge loan     Note    Shareholder
    loan    insurance    + insurance  
1.    120        0               120              110          10
2.     60        50              110              110            0
3.    0         110              110              110            0

Risk capital balance sheet of BANK A
____________________________________________________________
Bridge loan    100      |    Note (default free)    100
Loan insurance    5    |    Risk capital        5

Here, shareholder equity = risk capital

* Risk Capital and Liability Guarantees *
A parent guarantees the note

Balance sheet of BANK B
____________________________________________________________
Bridge loan    100    |    Note (default free)    100
                                 |    Shareholder equity    0

All asset risk is now borne by the parent company. The guarantee is another asset for the bank that does not appear on the balance sheet. Here we account for it as "G".

Risk capital balance sheet of BANK B
____________________________________________________________
Bridge loan    100      |    Note (default free)    100
Note guarantee    G    |    Risk capital        G

* Liabilities with Default Risk *
BANK issues liabilities with some default risk, no credit enhancements this time.
The note will sell at a discount of D to par. The Bank must find the remainder of the 100 million needed. This will be supplied in the form of a cash equity investment.

Balance sheet of BANK C
____________________________________________________________
Bridge loan    100    |    Note (default free)    100-D
            |    Shareholder equity    D

Risky note + note insurance = default free note
Risky Note = default free note - note insurance
Risky note = default free note - asset insurance


Risk capital balance sheet of BANK C
____________________________________________________________
Bridge loan    100    |    Note (default free)    100
Asset insurance    5    |    Risk capital        5
(from note holder)

Each example has different accounting balance sheets, but very similar risk capital balance sheets

* A More General Case *
Too long to be described in detail

Capital providers have three basic functions:
- provide cash capital (required to enter a transaction)
- sellers of insurance (covering the part not covered by insurance)
- providing risk capital (capital needed to purchase asset insurance)

* Contingent Customer Liabilities *
With contingent liabilities, the riskiness of net assets will in general differ from the riskiness of gross assets.

Firm E
No equity
Liabilities fully supported by a parent
Contingent liability: a S&P tracking note that promises 100 * the return on S&P

Balance sheet of BANK E
____________________________________________________________
Cash        100    |    Note (risky)        100
                           |    Shareholder equity    0

How the firm invests the cash will determine its risk capital
Treasury bills generating 10% return -> Gross assets are riskless, net assets are extremely risky
The position represents a short position in the S&P 500
The risk capital is equal to the value of a European call option on the S&P 500

The firm can instead choose to invest in the S&P 500. The gross assets are risky, but they match the liabilities, leading to net assets being riskless (assuming no transaction costs)it is the riskiness of the net assets that determine the risk capital needed

ACCOUNTING FOR RISK CAPITAL IN THE CALCULATION OF PROFITS
Risk capital is implicitly or explicitly used to purchase insrance on the net assets of the firm. This insurance, and gains or losses on this asset should be included along with the gains or losses on all other assets in the calculation of profitability.
- Standard methods often fail to account for this, for instance from implicit insurance from a parent.
- This can have an important impact on how profits for business subsidiaries are calculated.

THE ECONOMIC COST OF CAPITAL
- Accounting for risk capital is important for after-the-fact profits in reporting and profit-related compensation.
- In decision making before-the-fact, expected profits must incorporate implicit guarantees as well.
- Risk capital is not costly in an economic sense as we get a financial asset in return
- There are however transactioncosts included. A spread is typically paid over the economic value of the insurance, resulting in a deadweight loss to the firm.
- Economic cost = spread paid over fair value

The spread typically arrise from information and agency costs
- Adverse selection
- Moral hazard
- Agency cost

Equity holders bear the brunt of these costs

HEDGING AND RISK MANAGEMENT
- Hedging market risk exposure reduces the required amount of risk capital
- With no spread costs for risk capital, larger amounts of risk capital would impose no additional costs on the firm
- In this case, firms may well be indifferent to hedging or not
- If there are spread costs, and if these costs depend on the amount of risk capital, then a reduction in risk capital from hedging will lead to lower costs of risk capital if the hedges can be acquired at small spreads
- That will ususally be the case with hedging instruments for broad market risks where significant infomational advantages among market participants are unlikely

CAPITAL ALLOCATION AND CAPITAL BUDGETING
- When deciding to enter new businesses the cost fo risk capital can have a major influence
- Businesses that would be unprofitable on their own because of high risk-capital requirements might be profitable within a firm that has other businesses with offsetting risks

The risk capital of a particular business within a firm will be different if it is calculated on a stand-alone basis or as a part of the firm. This is the result of a diversification benefit
- This depends on the correlation between the firms
- The risk capital needed for the entire firm will be less than the sum of the individual businesses risk capital
- But allocating risk based on marginal risk also suffers from problems. The sum of marginal risk capital from a collection of businesses within a firm is less than the total risk capital.

The correlation between businesses is important sindce it affacets the total economic costs of risk capital. CAPM assumes that only correaltion between the firm and outside markets matter, this does not account for the economic cost of risk capital.
- The riskiness of the net assets is affected by correlations among business units
- The value of net assets is affected by their correlation with the broader market

SUMMARY AND CONLCUSIONS
Risk capital = the minimum amount of capital required to insure the net assets against default. This leads to the following conclusions:
1. The amount of risk capital is uniquely determined, and depends only on the riskiness of the net assets. It is not affected by the form of financing of net assets.
2. Tisk capital funds are provided by the firm's residual claimaints (equity holders). This capital is used to purchase asset insurance (implicitly or explicitly)
3. The economic costs of risk capital to the firm are the spreads on the price of asset insurance that stem from information costs and agency costs
4. For a given configuration, the risk capital of a multi-business firm is less than the aggregate risk capital of the businesses on a stand-alone basis. Full allocation of risk-capital across the individual businesses of the firm therefore is generally not feasible. Attempts at such a full allocation can significantly distort the true profitability of individual businesses.

Summary of the article "A FRAMEWORK FOR RISK MANAGEMENT"

Companies have become aware of how fluctuations in economic and financial variables can have a destabilizing effect on their performance. More and more companies are using derivatives markets to insulate themselves against macro risks. 

The growth in derivatives trading has mainly come from companies. A large part of this growth is due to innovations by financial theorists, sic as Black-Scholes option-pricing formula, to value derivatives.

However, the theorists insights provide little guidance to management when it comes to risk management decisions. What is the goal of risk management?

If a company takes positions in derivatives that does not fit well with the overall strategy, it can result in major losses. The goal of the article is to present a framework to guide managers in the risk-management strategy.

The risk-management framework rests on three principles:

1. Corporate value comes from making good investments

2. Good investments depend on generating enough cash internally to fund those investments

3. Cash flows can be disrupted by external movements in exchange rates and commodity prices, compromising the company's ability to make good investments

The goal of a risk-management program is to ensure that the company has enough cash available to make valuable investments.

With this goal in mind, it becomes easier to identify the basic question of risk-management: which risks should be hedged?

FROM PHARAOH TO MODERN FINANCE

In the old testament, the pharaoh hedged the risk of bad harvests by storing corn. In the middle ages, hedging was made easier by futures markets. Consumers could ensure availability and price by buying crops for delivery at a future date. 

Today, most new financial products are designed with corporations hedging needs in mind. It is however not as clear why a large public corporation would like to hedge since investors can hedge on their own.

Modigliani and Miller famously argued that value in a company is created by its assets, not its liabilities. When companies make good investments, they create value. How they finance those investments is irrelevant.

The postmodern paradigm accepts the key insights of M&M - that value is created by making good investments - but go on to argue that financial policy is critical in enabling these investments. 

The key here is that different financing comes at different costs, also known as the pecking order theory. Because of information costs, equity is more costly than debt, and debt is more costly than retained earnings. Companies that can finance their investments with retained earnings will have a lower cost of capital. This lower cost of capital makes more investments profitable.

The pecking order theory forms the basis for the view stated earlier; financial policy is critical in enabling profitable investments.

WHY HEDGE?

An international company has exchange rate risk and a fixed investment target. The company is also too leveraged to borrow more, so retained earnings is the only financing source. Fluctuations in the exchange rate can therefore have an important effect on their ability to invest, either leaving them with too much or too little capital.

By eliminating the risk of not being able to invest, hedging the currency risk will increase the company's value. In general, the supply of internal funds does not equal the investment demand of funds. Hedging allows the company to conserve their valuable internal capital.

WHEN TO HEDGE – OR NOT

In the previous example we assumed that the demand of funds is not correlated with the availability of funds. In many cases, exchange rates, commodity prices or interest rates do affect the value of a company's investment opportunities. 

An oil company's main risk is the price of oil. When oil prices rise, so does the firm's cash flows. But when oil prices increase, so does the available investment opportunities. This reduces the need for hedging, in fact, hedging too much of oil risks can lead to the company not having enough retained earnings during peak prices to invest fully.

A proper risk-management strategy ensures that companies have the cash when they need it for investment, but it does not seek to insulate them completely from tis of all kinds.

This approach helps managers address two key issues. (1) What is worth hedging and what isn't. Stock price volatility in itself is not the goal, individual investors can hedge or diversify this risk themselves. Investment volatility however, is worth controlling through risk management. (2) This approach helps managers decide how much hedging is necessary.

Managers should ask two questions: (1) How sensitive are cash flows to external risk variables, and (2) how sensitive are investment opportunities to those risk variables.

GUIDELINES FOR MANAGERS

1. Companies in the same industry do not necessarily have the same hedging needs. Companies in the same industry are exposed to the same external risk variables, but the sensitivity of their investment opportunities may vary.

2. Companies may benefit from risk management even if they have no major investments in plant and equipment. For companies that don't have plants to put up as collateral, internal funds are even more important.

3. Even companies with conservative capital structures – no debt, lots of cash – can benefit form hedging. Managers with a large cash cushion should ask themselves why they have a conservative capital structure. If the answer is to protect themselves from risk, they might reap tax benefits from taking on more debt and using derivatives instead to protect themselves.

4. Multinational companies must recognize that foreign-exchange risk affects not only cash flows but also investment opportunities. If a US company is investing in plants in Germany, and selling the products there, they need to hedge their exchange rate risk to maintain the same level of investments regardless of fluctuations.

If the same company is selling the cameras produced in Germany in the US, their investment opportunities will fluctuate with the exchange rate. The value of a new plant declines with a higher exchange rate as the demand for the cameras in the US will drop due to the higher price in US dollars.

5. Companies should pay close attention to the hedging strategies of their competitors. If a camera competitor that doesn't hedge is also considering building plants in Germany, but find themselves cash-strapped, the investment opportunity is even greater because of reduced capacity.

In this case, the investment opportunities depend on the overall structure of the industry and on the financial strengths of its competitors.

6. The choice of specific derivatives cannot simply be delegated to the financial specialists in the company. Management must be aware of the cash-flow implications of hedging instruments. Exchange traded derivatives that must be marked to market may require additional collateral, cutting into the company's cash flow. Secondly, the type of derivative must be considered (linear or non-linear). 

The decisions of which contracts to use should be driven by the objective of aligning the demand and supply of funds within the company.

In conclusion, managers cannot ignore risk management, and risk management decisions cannot be delegated to financial staff. The risk management strategy must be aligned with broader corporate objectives with the goal of making good investments.

Estimating default probabilities with credit ratings

Moody's, S&P and Fitch provide ratings describing the creditworthiness of corporate bonds. Credit ratings are designed to change infrequently. Credit rating companies are careful to avoid rating reversals, and also try to take the business cycle into account when assigning ratings.

Banks also produce internal credit ratings. This is necessary since not all corporate bonds are covered by the rating agencies. The internal ratings based approach in Basel II allows banks to use their internal credit ratings when determining the probability of default. Those banks deemed sophisticated enough by regulators are also allowed to use internal measures of the loss given default, the exposure at default, and the maturity.

The Z-score is one internal credit rating method based on discriminant analysis on accounting ratios to assign default probabilities to corporate bonds.

Estimating default probabilities for credit risk: overview

Credit risk comes from the risk of a counterparty not fulfilling its obligations towards the bank. Credit risk was recognized already under Basel I. Under Basel II, banks can use their internal estimates of default probabilities to determine their capital requirement.

There are a number of different approaches to estimating default probabilities: credit ratings, historical default probabilities, recovery rates, credit default swaps, and credit spreads are all used. It is also important to understand the difference between risk-neutral and real-world estimates of credit risk.

Q: Explain how an interest rate swap is mapped into a portfolio of zero-coupon bonds for VaR calculation

How is an interest rate swap mapped into a portfolio of zero-coupon bonds with standard maturities for the purpose of calculating VaR?

When a final exchange of principal is added, the floating leg is the equivalent of a zero-coupon bond with a maturity date equal to the date of the next payment. The fixed side is a coupon bearing bond which is equal to a portfolio of zero-coupon bonds. The swap can be mapped into a portfolio of zero-coupon bonds with maturity dates equal to the payment dates. Each of the zero-coupon bonds can then be mapped into positions in the adjacent standard-maturity zero-coupon bonds.

The three ways for handling interest-rate-dependent instruments under the model building approach for market risk VaR

Interest-rate-dependent instruments can be handled in the model building approach with (a) the duration model, (b) cash-flow mapping, or (c) principal component analysis.

Example of how to calculate VaR

We have a position consisting of a €100000 investment in asset A and a €100000 in B. Daily volatilities of both assets are 1% and the coefficient of correlation between their returns is 0.3. What is the 5-day 99% VaR for the portfolio?

s(A) = €100000 * 1% = €1000
s(B) = €100000 * 1% = €1000

Var(A+B) = sqrt(s(A)^2 + s(B)^2 + 2ps(x)s(y))
Var(A+B) = sqrt(1000^2 + 1000^2 + 2*0.3*1000*1000) = 1612.5

Assuming that the mean change is zero and that the change is normally distributed, the on day 99% VaR is 1612.5 * 2.33 = 3757.13.

The five day VaR is 2757.13*sqrt(5) = 8401.2.

Three methods for calculating operational risk exposure under Basel II

There are three methods for calculating the operational risk exposure under Basel II; the basic indicator approach, the standardized approach and the advanced measurement approach.

Under the basic indicator approach, operational risk exposure is calculated as the bank's average annual gross income over three years multiplied by 0.15. Under the standardized approach, the calculation is the same, except that a different factor is applied to the gross income from different business lines. In the advanced measurement approach, banks are allowed to account for risk-mitigating impact of insurance contracts.

Adjusting capital for collateral under Basel II

There are two methods for adjusting capital requirements for collateral under Basel II. The simple approach and the comprehensive approach. Banks can choose which approach they wish to use in the banking book. In the trading book they must use the comprehensive approach.

Under the simple approach, risk weights of the counterparty is replaced by the risk weight of the collateral for the part that is covered by the collateral. For any exposure not covered by the collateral, the risk weight of the counterparty is used.

Under the comprehensive approach, the bank adjusts the capital requirements upwards to allow for an increase in the credit risk. The bank also adjusts the value of the collateral downward to allow for a decrease in value.

Methods for calculating market risk VaR

There are two common methods for calculating the market risk value at risk under Basel II: the historical simulation approach and the model-building approach.

Historical simulation is the most commonly used approach. We use the day-to-day changes in the historical values of market variables to calculate the probability distribution fo the changes in the value of the current portfolio between today and tomorrow. More advanced methods for historical simulation includes weighing the estimate towards more recent observations.

The model-building approach involves assuming a model for the joint distribution of changes in market variables and using historical data to estimate the model parameters. This approach is most commonly used for portfolios that consists of both long and short positions in stocks, bonds, commodities and other products. The mean and standard deviation of a portfolio is calculated from the distribution of the underlying assets returns and the correlation between those returns.

The model-building approach is most effective if we can assume that the distribution of the underlying assets is multivariate normal. Relaxing this assumptions makes this approach much more challenging.

Model building vs. historical simulation
The advantage of the model building approach is that results can be produced quickly. It is also easy to use together with volatility and correlation updating procedures. The biggest drawback of the model building approach is that it assumes a multivariate normal distribution. We must rely on the central limit theorem applies to the data.

The advantage of the historical simulation approach is that the joint probability distribution of the market variables is determined by historical data. It is also easier to handle interest rates in a historical simulation. Historical simulation is however computationally slow.

The model building approach is most often used for investment portfolios and not so commonly used to calculate VaR.

The standardized, the IRB, and the advanced IRB approach

Under Basel II, there are three approaches to calculating credit risk capital; The standardized approach, the IRB approach, and the advanced IRB approach. Banks can choose between these depending on their sophistication.

The standardized approach is similar to that under Basel I, except for how risk weights are calculated. External ratings are used to determine capital requirements.

The internal ratings based (IRB) approach bases the capital requirement on the one year value at risk. The capital required is the value at risk minus the expected loss. The banks supply their own calculations of the probability of default, while loss given default, exposure at default and maturity of the exposure is set by the Basel committee.

The advanced IRB approach, banks supply their own estimates of the probability of default, exposure at default, loss given default and the maturity of the exposure.

What is regulatory arbitrage?

Regulatory arbitrage is the act of trading in a bank for the sole purpose of reducing regulatory capital requirements.

Why Basel I made banks unwilling to lend to highly creditworthy companies

Since all companies were assigned the same risk weight under Basel I, the return on the debt to AAA companies was too low to justify the risk. Instead, banks preferred to assist them in issuing debt securities. Under Basel II, this has changed as companies of different credit ratings are assigned different risk weights.

The difference between the trading and banking book

What is the difference between the trading book and the banking book of a bank?

The trading book is an accounting term that refers to assets held by a bank that are regularly traded. The trading book is required under Basel II and III to be marked to market daily. The value-at-risk for assets in the trading book is measured on a ten-day time horizont under Basel II.

The banking book is also an accounting term that refers to assets on a bank's balance sheet that are expected to be held to maturity. Banks are not required to mark these to market. Unless there is reason to believe that the conter-party will default on its obligation, they are held at historical cost.

If a client wishes to sell debt securities to a bank instead of taking a loan, the asset will now be assigned to the trading book instead. The bank will then keep specific risk capital for the securities as well as market risk capital.

The main differences are:
1. Assets that are held for trading are put in the trading book, assets that are held to maturity are held in the banking book
2. Assets in the trading book are marked-to-market daily, assets in the banking book are held at historic cost
3. The value-at-risk for assets in the trading book is calculated at a 99% confidence level based on a 10-day time horizon. The value-at-risk for assets in the banking book are calculated at a 99.9% confidence level on a one-year horizon.

Number three was amended in 2009 by the Basel committee when it was recognized that banks would incur a lower risk charge by holding assets in the trading book rather than in the banking book. It was also recognized that the losses incurred in 2008 was the results of widening spreads due to credit downgrades, loss of liquidity and widening credit spreads, and not the result of defaults. 

An incremental risk charge (IRC) was agreed upon in 2009 to account for this. The IRC requires banks to calculate a one-year 99.9% value-at-risk measure for credit-sensitive products in the trading book, and also to account for the risk of credit downgrades.

Sources: 
"Risk Management and Financial Institutions" (John Hull)
Summary of the book

"Guidelines for Computing Capital for Incremental Risk in the Trading Book" (Base Committee on Banking Supervision, July 2009)

Converting risk into risk weighed assets under Basel II

Why is credit risk, market risk and operational risk multiplied by 12.5 in the end under Basel II?

It is multiplied by 12.5 to convert it into a risk weighted asset. Capital required equals 8% of risk weighed assets.

Derivatives credit risk under Basel I

Does an interest rate swap with a negative value increase the credit risk of a financial institution? 

Yes. If the value of the swap becomes positive during its lifetime, and the counter-party defaults, it constitutes a loss.

How is the capital requirement calculated under Basel 1?

Under Basel 1, the add-on factor for interest rate derivatives with a maturity under five years is 0.5% of the principal.

Interest rate swaps and credit risk

What is the nature of the credit risk for a bank when it enters into a interest rate swap? The credit risk in the case of an interest rate swap is the risk of the counter-party defaulting in the future while the swap has a positive value to the bank.

Currency swaps and credit risk

In a currency swap, interest on a principal in one currency is exchanged for the interest on a principal in another currency. The principals are exchanged at the end of the life of the swap. A currency swap carries more risk than an interest rate swap since a default in the counter-party involves the loss of the interest as well as the principal.

Deposit insurance and regulation

How does deposit insurance impact the importance of minimum capital requirements?

Deposit insurance makes depositors less concerned about the credit worthiness of the bank they do business with since the state guarantees that they will get their assets back in case of a bankruptcy. This makes it possible for banks to take on bigger risks without losing customers.

Another way to look at it is from a moral hazard point of view. Since the bank doesn't bear the full risk of its operations, it has an incentive to take on more risk than is optimal. Oversized risks and moral hazard makes it necessary for regulators to specify minimum capital requirements.

Why do bank bankruptcies have a negative impact on their competitors?

If an industrial company goes belly up, its competitors stock price rise. If a bank goes bankrupt, its competitors do not always benefit. Why?

When a bank goes bankrupt, its competitors gain in terms of available market share, just as is the case in other industries. What differs is that the banking system is heavily reliant on trust. Since it is hard to determine what exposures the rest of the banking sector has to a failing bank, we must assume that all banks may be exposed to losses when there is a bankruptcy in the financial sector.

This leads to an increased cost of lending for banks In extreme cases it can mean that lending stops completely, leading to a liquidity crisis.

The 1996 Basel Amendment

In 1996, an amendment to the Basel accord from 1988 was created to account for the shortcoming of the initial accord. It involves keeping capital for assets and liabilities held for trading

The 1996 amendment introduced marking to market for the trading book. Assets in the trading book now had to be reevaluated daily to their market price. The trading book include assets such as equities, most derivatives, foreign currencies, and commodities. The banking book consists of assets that are expected to be held to maturity and are not market to market. These include loans and som debt securities.

Under the 1996 amendment, the credit risk capital charge from the 1988 accord continued to apply to on- and off-balance sheet items in the trading and banking book. Some items in the trading book were excluded, such as equities and debt traded securities, as well as positions in commodities and foreign exchange. A market risk charge for the trading book was also introduced to account for the risk inherent in trading.

The standardized approach for measuring the market risk charge is to assign it to each set of securities separately. No account is taken for the correlation between for instance debt and equity instruments. More sophisticated banks were allowed to use an internal model-based approach. The banks calculate a VaR measure and convert it into a capital requirement using a pre-specified formula. The internal model-based approach was often preferred as it allowed banks to take the benefits of diversification into account.

The formula used to convert the internal model-based approach to a capital requirement is: k x VaR + "Specific Risk Charge".


k is minimum 3 and is set by regulators. The specific risk charge accounts for the idiosyncratic risk related to individual companies. A corporate bond for instance has two risk components, interest rate risk (captured by VaR) and credit risk that is captured by the specific risk charge.

The total capital a bank had to keep under the amendment was 0.08 x (Credit risk RWA + Market risk RWA)

Where
Market Risk, Risk Weighted Assets = 12.5 * (k x VaR + SRC)
Credit Risk, Risk Weighted Assets = sum(w*on balance sheet items) + sum(w*off balance sheet items)

Financial regulation after 1988 - G-30 policy recommendations and netting

A report called the "Derivatives: Practices and Principles" was published 1993 by the Group of 30 that came to be very influential. They gave 20 policy recommendations in the field of risk management for legislators and regulators. They are summarized below:

Dealers and end-users of derivatives should:
1. Determine at the highest level of policy making the scope of the institution's involvement in derivatives activities
2. Value derivatives position at market value
3. Quantify its market risk under adverse market conditions
4. Assess the credit risk arising from derivatives activities
5. Reduce credit risk by broadening the use of multi-product master agreements with close-out netting provisions
6. Establish market and credit risk management functions with clear authority independent of the dealing function
7. Authorize only professionals with the requisite skills and experience to transact and mange the risk
8. Establish management information systems sophisticated enough to measure, manage, and report the risks of derivatives activities
9. Voluntary adopt accounting and disclosure practices for international harmonization and greater transparency

There are also four recommendations for legislators, regulators and supervisors:

10. Recognize close-out netting arrangements
11. Work with market participants to remove legal and regulatory uncertainties regarding derivatives
12. Amend tax regulations that disadvantage the economic use of derivatives
13. Provide comprehensive and consistent guidance on accounting and reporting of derivatives

Netting is mentioned in number 10 above. Netting refers to a clause in the master agreement between two companies. If one of the companies in a transaction defaults that is covered by the master agreement, it must default on all of its obligations. This has the effect of reducing credit risk.

In mathematical terms, the value before netting is sum(max(V, 0)) and after netting max(sum(V, 0)). In 1995, netting had been tested in court and was subsequently added to the Basel accord in accordance with the G-30 recommendations.

Basel II: Overview

The pillars
Pillar 1, capital requirements, calculates minimum capital requirement for credit risk in the banking book in a new way that accounts for the credit ratings of the counter parties. The capital requirement for market risk is unchanged.

Pillar 2, supervisory review, gives supervisors in different countries some discretion in how they apply the rules to account for local conditions. Emphasis is however placed on overall consistency and early intervention

Pillar 3, market discipline, requires banks to make more information public. The hope is that this will increase pressure from investors and markets to make sound risk management decisions.

Background
I have previously talked about the BIS (1988) Accord and the 1996 Amendment. These belong to what we today refer to as Basel I. In 1999 these rules were replaced by Basel II to account for some serious weaknesses in Basel I.

These were (1) all loans from banks to corporations carried a risk weight of 100%, making lending to AAA companies unprofitable, and (2) no model for default correlation.

Basel II consists of three pillars: capital requirements, regulatory review, and market discipline. The capital requirements calculations has changed from Basel I to account for different credit ratings of the counterparty. The capital requirement from market risk is unchanged and there is a new capital charge for operational risk.

Total risk = 0.08 x (Credit risk RWA + Market risk RWA + Operational risk RWA)

Credit risk RWA = sum(w*on balance sheet assets) + sum(w*off balance sheet assets)

Market risk RWA = 12.5 x (k*VaR + SRC)

If a capital requirement for risk is calculated so that it does not involve RWAs, it is multiplied by 12.5 to convert it.

Bank regulation up to 1988

Before 1988, bank regulation focused on setting minimum levels for the ratio of capital to total assets. Since capital requirement levels as well as regulatory enforcement varied between countries, banks could gain a competitive edge by operating from countries with a laxer regulatory environment.

The emergence of over-the-counter derivatives markets made further complicated things for regulators. Instruments such as interest rate swaps, currency swaps, and foreign exchange options increased the credit risk of banks without increasing the level of capital required.

A way of determining total risk in a bank, including these off-balance sheet items, was needed.

In 1988 the BIS accord made the first attempt to address these issues by setting an international risk-based standard for capital requirements. The accord was signed by all 12 members of the Basel Committee and paved the way for the Basel accords.

The BIS accord included two requirements: the ratio of bank's assets to its capital had to be less than 20, and the Cooke ratio. The Cook ratio takes both on-balance sheet and off-balance sheet items into account to form a measure of a bank's total risk exposure, also called the risk-weighed assets.

The risk weights under the BIS accord

OECD governments, gold, cash 0%

OECD banks 20%

Uninsured mortgage loans 50%

Corporate bonds 100%

An important part of the risk weighed assets is how off-balance sheet items are given a risk-weight. The credit equivalent amount for non-derivatives is calculated as the loan principal that is considered to have the same credit risk.

For OTC-derivatives, the credit equivalent amount is calculated as max(V, 0) + aL. V is the current value to the bank, a is an add-on factor, and L is the principal. The add-on factor accounts for the fact that the exposure might increase in the future.

The BIS accord requires that banks keep a capital buffert equal to 8% of the risk-weighted assets. The capital consists of tier 1 capital, equity and noncumulative perpetual preferred stock (net of goodwill), and tier 2 capital, cumulative perpetual preferred stock, certain types of long debenture issues and subordinate debt. A minimum of 50% tier 1 capital is required.

Why should banks be regulated?

Background from Risk Management and Financial Institutions, Regulation, Basel II and Solvency II

The main purpose of bank regulation is to ensure that banks have enough capital in relation to the risks they take. It isn't possible to eliminate all risk - after all, taking risks is very much the business of banks - but regulators want to make the probability of default for any given bank very small.

Even though the economic self interest of banks would argue for banks maintaining adequate capital requirements on their own, historical experience has shown that this is not always the case.

According to John C. Hull (Risk Management and Financial Institutions), regulation has played an important role in increasing banks capital and making them more aware of their risks.

Another reason to regulate banks is deposit insurance. Without it, risky banks would find it hard to attract customers. Deposit insurance makes depositor less discriminating between banks, as the government bears the final responsibility for their assets. To overcome the moral hazard inherent in such risk allocation, regulators need to insure that banks keep sufficient capital to the risks they bear.

Another reason banks need to be regulated is systematic risk. This is a topic that is central in the current bail-out debate in Europe. If a bank is allowed to fail, the opaque nature of banks obligations to each other can cause reduced trust in the system. This increases borrowing costs for all banks. If trust falls enough, it can even lead to banks refusing to lend to each other.

To deal with the problem of systematic risk, it's imprudent for regulators to issue bail-outs frequently as it increases the moral hazard in the system. Banks start assuming that their risk levels are unimportant as the government bears the ultimate cost of it. To address this issue, regulators impose minimum capital requirements on banks based on their risk profiles.