Lecture notes - Nikolaos I. Papanikolaou · PDF fileBank risk management 1 Lecture notes – Set 4 Dr Nikolaos I. Papanikolaou University of Sussex School of Business, Management and

Bank risk management

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Lecture notes – Set 4

Dr Nikolaos I. Papanikolaou

University of Sussex

School of Business, Management and Economics

[email protected]

Based on Risk, Management, and Financial Institutions, 3rd Edition, John C. Hull 2012

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Basel Committee on Bank Supervision was set up in 1974.

Banks were regulated using only balance sheet measures such as the ratio of capital to assets.

Minimum levels for bank capital were imposed.

Definitions and required ratios varied from country to country.

Enforcement of regulations varied from country to country.

Regulation paid little attention to the different types of bank risk.

Bank leverage increased during the1980s and 1990s.

Off-balance-sheet derivatives trading also increased.

The pre-1988 era

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a) Asset-to-capital ratio had to be less than 20.

b) The Cooke ratio based on the risk-weighted-capital was introduced:

Both on- and off-balance-sheet items were considered.

Each on-balance-sheet item was assigned a risk weight reflecting its credit risk (e.g., 0% to cash and government bonds; 20% to claims on OECD banks; 50% to residential mortgages; 100% to corporate loans, corporate bonds).

The total Risk-Weighted-Assets (RWA) for N on-balance-sheet items was equal to:

where Li is the principal amount of the ith item and wi is its risk weight.

BIS Accord (Basel I): 1988

N

i

ii LwRWA1

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For each off-balance-sheet item, we first calculate a credit equivalent amount and then apply a risk weight.

The credit equivalent amount is the loan principal that is considered to have the same credit risk. For an OTC derivative product (e.g., interest rate swap, futures contract), the credit equivalent amount is equal to:

Cj = max(Vj,0) + ajLj

where Vj is value, Lj is the principal and aj is an add-on factor

The first term shows the current exposure. If the counterparty

defaults today and V is positive, the derivatives contract is an asset

to the bank and is liable to lose V.

If the counterparty defaults today and V is negative , the contract

is an asset for the counterparty and there will be neither a gain or

a loss to the bank.


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Consider the following two cases:

a) The value of the transaction is zero.

b) The value of the transaction is -$10 million

The current exposure is zero fro the bank in both cases. Therefore,

under Basel I, the capital required is the same in both cases.

In the first case any increase in the value of the transaction will lead

to an exposure since V will become positive.

In the second case, the transaction has to increase in value by more

than $10 million before there is an exposure.


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The second term is called add-on amount and is an allowance for the possibility of the exposure increasing in the future.

It allows for a possibility that the exposure can increase prior to a bad event.

The add on factor α varies from instrument to instrument (e.g. 0.5% for a 1-5 year interest rate swap; 5.0% for a 1-5 year foreign currency swap) and among different maturities to capture the various levels of the underlying risk in different derivatives.

Example: A $100 million swap with 3 years to maturity worth $5 million would have a credit equivalent amount of $5.5 million.

The add-on amount does not depend on V.


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The total RWA for a bank with N on-balance-sheet items and M off-balance-sheet items was:

Regulatory capital had to be 8% of risk weighted amount. At least 50% of the regulatory capital had to be Tier 1.

Tier 1 Capital: it is the core measure of a bank’s financial strength from a regulator’s viewpoint. It absorbs losses without the bank being required to cease trading. It mainly consists of common equity, disclosed reserves, non-cumulative perpetual preferred shares.

Tier 2 Capital: It is a supplementary bank capital that includes items such as revaluation reserves, undisclosed reserves, hybrid instruments and subordinated term debt, cumulative preferred stock, etc.


j

N

i

M

j

jii CwLwRWA

1 1

*

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Components of Tier 2 Capital can be split into two levels: upper and lower. Upper Tier 2 maintains characteristics of being perpetual, and senior to preferred capital and equity. Lower Tier 2 is relatively cheap for banks to issue; it has coupons not deferrable without triggering default; and has subordinated debt with a maturity of a minimum of 10 years.

A bank's reserve requirements include its Tier 2 capital in its calculation, but it is considered less reliable than its Tier 1 capital. A bank with high Tier 1 capital is considered more stable, better able to sustain future losses and less likely to collapse. The bank itself has complete control over Tier 1, so there is low risk of unpleasant surprises.


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Netting:

It refers to a clause in derivatives Master Agreements that were

signed by participants in the OTC markets, which stated that if

a company defaulted on one transaction it should default on all

transactions.

Consider a bank that has three swap transactions outstanding

with a particular counterparty.

Transactions worth +$24m, -$17m, and +$8m for the bank.

If the counterparty defaults on its outstanding obligations, it

would default on the first and third transaction, but not on the

second implying that the bank would incur a loss of $32m.

With netting, the counterparty defaults on all three

transactions and, hence, the bank has a loss of $15m.


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The Amendment of Basel I was implemented in 1998.

It required banks to measure and hold capital for market risk for

all instruments in the trading book including those off balance

sheet.

Marking-to-market practices or Fair Value Accounting (FVA) was

introduced.

Banks were required to use FVA for all assets and liabilities that

were held for trading purposes (e.g., derivatives, marketable

equity securities, foreign currencies, etc.). Those items referred

to the bank’s trading book.

Banks were not required to use FVA for assets which referred to

the baking book (e.g., non-securitised loans, non-market debt

securities, etc.)

The Basel I Amendment

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The Amendment introduced a capital charge for the market risk

associated with all items in the trading book.

Banks started using the Internal model-based approach for

setting market risk capital.

That approach involved the calculation of VaR and its conversion

into a capital requirement using a formula specified by the

Amendment.

where mc is a multiplicative factor chosen by regulators (at least

3), VaR is the 99% 10-day value at risk, and SRC is the specific

risk charge for idiosyncratic risk related to specific companies.

VaRt-1 is the most recently calculated VaR and VaRavg is the

average VaR over the last 60 days.


SRC)VaR,max(VaR avg1- ct m

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The total capital required was equal to:

Total Capital = 0.08 x (Credit Risk RWA +Market Risk RWA)

A bank had more flexibility in the type of capital it used for

market risk.

It could use Tier 1 and Tier 2 Capital together with the newly-

established Tier 3 Capital.

Tier 3 Capital consisted of short-term subordinated debt with an

original maturity of at least two years that was unsecured and

fully paid up.


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Basel II was implemented in 2007 and consisted of three pillars:

I. New minimum capital requirements

II. Supervisory review

III. Market discipline

I) New CARs:

A new capital charge for operational risk was introduced

The general requirement in Basel I that banks must hold a total

capital equal to 8% of RWA remained unchanged.

The total capital required was equal to:

Total Capital = 0.08 x (Credit Risk RWA + Market Risk RWA +

Operational Risk RWA)

Basel II

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II) Supervisory review

It is concerned with the supervisory review process, allowing regulators in different countries some degree of discretion in how rules are applied.

Similar amount of thoroughness in different countries

Importance of early intervention stressed

III) Market discipline

It required banks to disclose more information about the way they allocated capital and the risks they took. Banks were required to disclose:

Scope and application of Basel framework

Nature of capital held

Regulatory capital requirements

Nature of institution’s risk exposures

The idea was for banks to subject to added pressure with the purpose to make sound risk management decisions if shareholders and potential shareholders had more information about their decisions.

Basel II

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For Credit Risk, Basel II specified two main approaches:

a) The Standardised Approach

b) The Internal Ratings Based (IRB) Approach

The Standardised Approach is similar to Basel I except for the

calculation of risk weights (e.g., bank and corporations were

treated similarly, the OECD status of a bank or a country was no

longer considered important).

Supervisors can choose to base capital requirements on the rating

of the country in which the bank is incorporated.

Basel II

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It may be better for a country, bank, or corporation to have no

credit rating at all than a very poor credit rating.

Basel II

Risk weights as a % of principal for exposures to countries,

banks, and corporations under Basel II’s standardised approach

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Under the IRB approach, regulators base the bank capital

requirements on the 99.9% Worst Case Default Rate (WCDR):

where:

PDi is the probability that the counterparty (borrower/investor) i

will default within one year

ρ is the correlation between the various counterparties and is given

by the following formula:

Basel II

.NPDN

NWCDR-

i

-

i

1

)9990()( 11

]1[12.0 50 PDe

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Under the IRB approach, the required bank capital relies on the

difference between WCDR and the Expected Loss as shown

graphically below:

Basel II

0 1 2 3 4

Expected

Loss

X% Worst

Case Loss

Required

Capital

Loss over time

horizon

0 1 2 3 4

Expected

Loss

X% Worst

Case Loss

Required

Capital

Loss over time

horizon

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The formula for the required bank capital on the basis of the IRB approach is given by:

𝐸𝐴𝐷𝑖 ∗ 𝐿𝐺𝐷𝑖 ∗ 𝑊𝐶𝐷𝑅𝑖 − 𝑃𝐷𝑖 ∗ 𝑀𝐴

where:

𝐸𝐴𝐷𝑖is the Exposure At Default of the ith counterparty and shows the amount that is expected to be owed by the ith counterparty at the time of default. If, e.g., there is a single loan outstanding to the ith counterparty, this will be equal to the principal amount outstanding on the loan.

𝐿𝐺𝐷𝑖 is the Loss Given Default for the ith counterparty, showing the proportion of 𝐸𝐴𝐷𝑖 that is expected to be lost in the event of default. For example, if the bank is expected to recover 30% of the amount owed in case of default of the ith counterparty, then 𝐿𝐺𝐷𝑖will be equal to 70%.

Basel II

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MA is the Maturity Adjustment and is defined as:

MA is designed to allow for the fact that, if an instrument lasts

longer than one year, there is a one-year credit exposure arising

from a possible decline in the creditworthiness of the

counterparty as well as from a possible default by the

counterparty.

Basel II

urityaveragematM

PDb

b

b

2)]ln(05478.011852.0[

:where

5.11

)5.2M(1MA

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The RWA is given by the following formula:

RWA = 12.5 ∗ 𝐸𝐴𝐷𝑖 ∗ 𝐿𝐺𝐷𝑖 ∗ 𝑊𝐶𝐷𝑅𝑖 − 𝑃𝐷𝑖 ∗ 𝑀𝐴

The required total (Tier 1 and Tier 2) capital is equal to 8% of the

RWA. At least half of this must be Tier 1 capital.

Basel II

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Suppose that the assets of a bank consist of $500 million of

loans to BBB-rated corporations.

The PD for the corporations is estimated as 0.3%.

The average maturity is three years and the LGD is 60%.

What is the total risk-weighted assets for credit risk under the

Basel II advanced IRB approach?

How much total (Tier 1 and Tier 2) capital is required?

What is the risk weight under the Basel II standardised approach

and under Basel I? Calculate the capital in each case.

Basel II

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Stress testing is an analysis conducted under unfavourable

economic scenarios which is designed to determine whether a

bank has enough capital to withstand the impact of adverse

developments.

Stress tests can either be carried out internally by banks as part

of their own risk management, or by supervisory authorities as

part of their regulatory oversight of the banking sector.

These tests are meant to detect weak spots in the banking system

at an early stage, so that preventive action can be taken by the

banks and regulators.

Scenario Analysis and Stress Testing

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Stress tests focus on a few key risks – such as credit risk, market

risk, and liquidity risk – to banks' financial health in crisis

situations.

The results of stress tests depend on the assumptions made in

various economic scenarios, which are described by the

International Monetary Fund as "unlikely but plausible."

Bank stress tests attracted a great deal of attention in 2009, as the

worst global financial crisis since the Great Depression left many

banks and financial institutions severely under-capitalised.


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Key Questions

How do we generate the scenarios?

How do we evaluate the scenarios?

What do we do with the results?

Generating the scenarios

Stress individual variables

Choose particularly days when there were big market

movements and stress all variables by the amount they moved

on those days

Form a stress testing committee of senior management and ask

it to generate the scenarios


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If scenario generated involves only a few “core” variables, regress

other “peripheral” variables on the core variables to determine

their movements.

Ideally the relationship between peripheral and core variables

should be estimated for stressed market conditions.

Do regulators provide their own scenarios to be used by all

banks?

Part of the Basel Committee’s consultative document suggests

that it is thinking about this as a possibility.

There is a danger that, if the scenarios are announced in advance,

financial institutions will hedge only against the scenarios


Credit risk arises from the possibility that borrowers, bond issuers, counterparties in derivatives transactions and the like may default.

As discussed, regulators require banks to hold capital for credit risk.

Banks use their own estimates of default probabilities to determine the amount of capital they are required to keep.

There are several different approaches to estimate credit risk and the relevant default probabilities. The most common are:

Use of historical data

Use of Credit Default Swaps

Use of Credit spreads (other than CDS)

Use of the Black-Scholes-Merton’s model

Credit Risk: Estimating Default Probabilities

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Historical data:

They are mainly provided by rating agencies and can be used to estimate the probability of default. The table below shows the Cumulative Average Default Rates % (1970-2010, Moody’s).

A company with an initial credit rating of Baa has a probability of 0.181% of defaulting by the end of the first year, 0.510% by the end of the second year, and so on.

For a company that starts with a good credit rating default probabilities tend to increase with time

For a company that starts with a poor credit rating default probabilities tend to decrease with time


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Time (years)

1 2 3 4 5 7 10

Aaa 0.000 0.013 0.013 0.037 0.104 0.244 0.494

Aa 0.021 0.059 0.103 0.184 0.273 0.443 0.619

A 0.055 0.177 0.362 0.549 0.756 1.239 2.136

Baa 0.181 0.510 0.933 1.427 1.953 3.031 4.904

Ba 1.157 3.191 5.596 8.146 10.453 14.440 20.101

B 4.465 10.432 16.344 21.510 26.173 34.721 44.573

Caa 18.163 30.204 39.709 47.317 53.768 61.181 72.384

Credit Default Swaps (CDS) The buyer of the instrument acquires protection from the

seller against a default by a particular company or country (the reference entity).

Example: the buyer pays a premium of 90 bps per year for $100 million of 5-year protection against company X.

Premium is known as the credit default spread. It is paid for the life of the contract or until default.

If there is a default, the buyer has the right to sell bonds with a face value of $100 million issued by company X for $100 million.

The seller agrees to buy back the instrument when a credit event occurs.

The CDS markets: Allow credit risks to be traded in the same way as market risks

Can be used to transfer credit risks to a third party.

Can be used to diversify credit risks.


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An estimate of the average probability of default between two

specific points in time using CDS is given by the following

formula:

where:

𝜆 is the average hazard rate between time 0 and time T

s(t) is the credit spread calculated for a maturity of t

R is the recovery rate: it is defined as the examined asset 30 days

after default as a percent of the asset’s face value

R

ts

1

)(

Credit spreads

The credit spread is the additional rate of interest per annum required by investors for bearing credit risk.

CDS spreads are just one type of credit spread.

Another key type is the bond yield spread.

Bond yield spread refers to the amount by which the yield on a corporate bond exceeds the yield on a similar risk-free bond.


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Credit spreads-Example

A company has one- and two-year bonds outstanding, each providing a coupon of 8% per year payable annually.

The yields on the bonds (expressed with continuous compounding) are 6.0% and 6.6%, respectively.

Risk-free rates are 4.5% for all maturities.

The recovery rate is 35%.

Defaults can take place half way through each year.

Estimate the risk-neutral default rate each year.


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Lecture notes - Nikolaos I. Papanikolaou · PDF fileBank risk management 1 Lecture notes – Set 4 Dr Nikolaos I. Papanikolaou University of Sussex School of Business, Management and