MODULE 3: Credit Risks Credit Risk Management models - Introduction, Motivation, Funtionality of good credit. Risk Management models- Review of Markowitz’s Portfolio selection theory –Credit Risk Pricing Model – Capital and Rgulation. Risk management of Credit Derivatives.

1. Chapter - III
Introduction: Credit Risk Management
Credit Risks Credit Risk Management models -
Introduction, Motivation, Functionality of good
credit. Risk Management models- Review of
Markowitz’s Portfolio selection theory –Credit
Risk Pricing Model – Capital and Regulation.
Risk management of Credit Derivatives.

2. Introduction to Operations Risk:
Risk is inherent in all aspects of a commercial operation and
covers areas such as customer services, reputation, technology,
security, human resources, market price, funding, legal, and
regulatory, fraud and strategy. However, for banks and
financial institutions credit risk is the most important factor to
be managed.
The term credit risk is defined, “as the potential that a
borrower or counter-party will fail to meet its obligations in
accordance with agreed terms”.
In simple terms it is the probability of loss from a credit
transaction.

3. Banks are increasingly facing credit risk in various instruments
other than loans, including acceptances, interbank transactions,
trade financing, foreign exchange transactions, financial futures,
swaps, bonds, equities, options and in the extension of
commitments and guarantees, and the settlement of transactions.
Credit risk encompasses both default risk and market risk.
Default risk is the objective assessment of the likelihood that
counterparty will default.
Market risk measures the financial loss that will be experienced
should the client default.
Credit risk includes not only the current replacement value but also
the potential loss from default. For example:-

4. 1. A consumer may fail to make a payment due on a
mortgage loan, credit card, line of credit, or other loan.
2. A company is unable to repay asset-secured fixed or
floating charge debt.
3. A business or consumer does not pay a trade invoice
when due.
4. A business does not pay an employee's earned wages
when due.
5. A business or government bond issuer does not make
a payment on a coupon or principal payment when due.
6. An insolvent insurance company does not pay a
policy obligation.
7. An insolvent bank won't return funds to a depositor.
8. A government grants bankruptcy protection to an
insolvent consumer or business.

5. Definition of Credit Risk:
Possibility of losses associated with decline in the credit quality of
borrowers or counterparties.
Default due to inability or unwillingness of a customer or
counterparty to meet commitments in relation to lending, trading,
settlement and other financial transactions.
Loss from reduction in portfolio value (actual or perceived).
Possibility that borrowers may not meet their obligation in terms of
the loan agreed terms and conditions.
Probability of loss from a credit transaction.
Components of Credit Risk:
1. Credit growth in the organization and composition of the credit folio
in terms of sectors, centers and size of borrowing activities so as to
assess the extent of credit concentration.
2. Credit quality in terms of standard, sub-standard, doubtful and loss-
making assets.
3. Extent of the provisions made towards poor quality credits.
4. Volume of off-balance-sheet exposures having a bearing on the
credit portfolio.

6. According to Reserve Bank of India, the following are the forms
of credit risk:
1. Non-repayment of the principal of the loan and/or the interest
on it.
2. Contingent liabilities like letters of credit/guarantees issued by
the bank on behalf of the client and upon crystallization – amount
not deposited by the customer.
3. In the case of treasury operations, default by the counter-
parties in meeting the obligations.
4. In the case of securities trading, settlement not taking place
when it is due.
5. In the case of cross-border obligations, any default arising
from the flow of foreign exchange and/or due to restrictions
imposed on remittances out of the country.

7. Sources / Classification of Credit Risk:
A. Default risk:
- It is the probability of an event of default
- Depends upon credit standing of the counter party.
- Default probability cannot be measured directly.
- Guidance from historical statistics on large sample over
long period of time.
- Bank faces difficulty in obtaining accurate historical data.
B. Exposure risk:
- Uncertainty associated with future amounts ,
- Credit lines- repayment schedule- exposure risk small
- Other lines of credit - OD, project financing, guarantees
etc. - risk cannot be predicted accurately.
C. Recovery risk:
- Recoveries in the event of default not predictable
- Depend upon type of default ,
- Availability of collaterals and third party guarantees
- Circumstances surrounding the default.

8. Classification of Credit Risk
1. Credit default risk: debtor being unlikely to pay its loan
obligations in full or the debtor is more than 90 days past
due.
2. Concentration risk: single exposure or group of exposures
- threaten a bank's core operations.
3. Country risk: risk of loss arising from a sovereign state
freezing foreign currency payments.
4. Default Risk: A default rate is the percentage of a
population of bonds that are expected to default.
5. Credit Spread Risk: Spreads tend to widen in poor
performing economies: difference in spot/future or actual
and bench mark rate
6. Downgrade Risk: The credit risk deals with the rating
agencies – CRISIL, ICRA, CARE, CIBIL, S&P, Fitch
Ratings, Moody’s, etc.

9. Factors affecting Credit Risk:
A. Internal factors – Bank specific:-
- Adopting proactive loan policy.
- Good quality credit analysis.
- Loan monitoring.
- Sound credit culture.
B. External factors – State of economy, etc.:-
- Diversified loan portfolio.
- Scientific credit appraisal for assessing
financial and commercial viability of loan proposal.
- Norms for single and group borrowers.
- Norms for sectoral deployment of funds.
- Strong monitoring and internal control
systems.
- Delegation and accountability.

10. Credit Risk Management as per RBI:-
I. Measurement of risk through credit scoring.
II. Quantifying risk through estimating loan losses.
III.Risk pricing – Prime lending rate which also accounts for
risk.
IV. Risk control through effective Loan Review Mechanism and
Portfolio Management.
Principles of Credit Risk Management:
a) Board of directors of a bank has to take responsibility for
approving and periodically reviewing credit risk strategy.
b) Senior management has to take the responsibility to
implement the credit risk strategy.
c) Bank has to identify and manage credit risk of all banking
products and activities.

11. Prudential Norms for Credit Risk:
a. Capital adequacy norms.
b. Exposure norms
- Credit exposure and investment exposure norms to
borrowers (individuals and group)
- Capital market exposures
- Individual bank’s internal exposure limits
c. Bank’s internal risk assessment committee norms.
d. Credit rating system and risk pricing policy.
e. Asset liability management requirements.
f. Bank’s loan policy norms.
Expected Losses & Unexpected Losses:
• EL depends upon default probability (PD), Loss given default
(LGD) & exposure at risk (EAD).
• EL = PD x LGD x EAD.
• Unexpected losses (UL): It is the uncertainty around EL and it is
Standard deviation of EL.

12. Process of Credit Risk Management:

13. Tools of Credit Risk Management
• Exposure Ceiling: Prudential Limit is linked to Capital Funds
– say 15% for individual borrower entity, 40% for a group with
additional 10% for infrastructure projects
• Review/Renewal: Multi-tier Credit Approving Authority,
constitution wise delegation of powers, Higher delegated powers for
better-rated customers; discriminatory time schedule for
review/renewal, Hurdle rates and Bench marks for fresh exposures
and periodicity for renewal based on risk rating.
• Risk Rating Model: Set up comprehensive risk scoring
system on a six to nine point scale. Clearly define rating thresholds
and review the ratings periodically preferably at half yearly intervals.
Rating migration is to be mapped to estimate the expected loss.
• Risk based Scientific Pricing: Link loan pricing to expected
loss. High-risk category borrowers are to be priced high. Build
historical data on default losses. Allocate capital to absorb the
unexpected loss. Adopt the RAROC framework.

14. • Portfolio Management: There should be a proper & regular on-
going system for identification of credit weaknesses well in
advance to preserve the desired portfolio quality and integrate
portfolio reviews with credit decision-making process.
• Loan Review Mechanism: It is also referred as Credit Audit
covering review of sanction process, compliance status, review of
risk rating, pick up of warning signals and recommendation of
corrective action with the objective of improving credit quality. It
should target all loans above certain cut-off limit ensuring that at
least 30% to 40% of the portfolio is subjected to LRM in a year so
as to ensure that all major credit risks embedded in the balance
sheet have been tracked
Functionality of Good Credit:
Liquidity, Safety, Stability, Elasticity, Profitability, Reserve
Management, Expansion, etc..

15. Framework for Credit Risk Management:
A. Policy Framework:
1. Strategy and Policy:
o Documented policy specifying target markets.
o Statement of risk acceptance criteria.
o Credit approval authority.
o Credit follow up procedures.
o Guidelines for portfolio management.
o Systems of loan restructuring to manage problem loans.
o Follow up procedures and provisioning of non-performing
loans and advances.
o Consistent approach towards early problem recognition.
o Classification of exposures in problem loans.
o Maintain a diversified portfolio of loans in line with the
desired capital.
o Procedures and systems for monitoring financial
performance of customers.
o Controlling outstanding loan performance so that the non-
performance is within limits.

16. 2. Organization Structure:
o Independent group responsible for credit risk management.
o Formulation of credit policies.
o Procedures and controls of all credit risk functions
Corporate banking, Treasury function, Credit cards
Personal banking, Portfolio finance., Securities finance
Payment and settlement systems
o Credit management team responsibility for overall credit risk
o Board is in charge of the overall risk management policy of the
bank
Credit
Liquidity
Interest rate
Foreign exchange
Price risk
o Credit Risk Management Committee: Integration of credit risk
management committee with market risk management committee,
operations risk management committee and asset liability management
committee

17. 3. Operations / Systems support:
o Relationship management phase: Business development,
Product development and System development phase.
o Transaction management phase: Risk assessment, Pricing,
Structuring of the credit operations, internal approvals,
Documentation, Loan administration and Credit monitoring
and measurement.
o Portfolio management phase: Monitoring of portfolio and
Management of problem loans.
B. Credit risk rating framework
1. Credit rating models.
2. Credit rating analysts.
3. Loans to individuals or small businesses.
4. Credit quality assessed through credit scoring.
Annual income, Existing debt, Asset ownership
details and Family status.

18. C. Credit Risk Limits:
1. Credit limits exposure for each client (borrowers and
counterparties).
2. Total credit limits exposure for a firm.
3. Total credit limits exposure for an industry.
4. Total credit limits exposure for a region / division.
5. Total credit limits exposure for the bank.
6. Reserve Bank of India Guidelines:
not more than 15% of capital to individual
borrower
not more than 40% of capital to a group borrower
Aggregate ceiling in unsecured advances not to
exceed 15% of total demand and time liability (DTL) of the
bank.
7. Threshold limits:
• Credit rating of the borrower
• Past financial records
• Willingness and ability to repay
• Borrower’s future cash flow projections

19. D. Credit Risk Modeling
1. Altman Z-Score Management Model: The Z-score formula for
predicting bankruptcy was published in 1968 by Edward I. Altman, who
was, at the time, an Assistant Professor of Finance at New York University.
The formula may be used to predict the probability that a firm will go
into bankruptcy within two years. Z-scores are used to predict corporate
defaults and an easy-to-calculate control measure for the financial distress
status of companies in academic studies. The Z-score uses multiple
corporate income and balance sheet values to measure the financial health
of a company.
The Z-score is a linear combination of four or five common business ratios,
weighted by coefficients. The coefficients were estimated by identifying a
set of firms which had declared bankruptcy and then collecting a matched
sample of firms which had survived, with matching by industry and
approximate size (assets). Altman applied the statistical method of
discriminant analysis to a dataset of publicly held manufacturers. The
estimation was originally based on data from publicly held manufacturers,
but has since been re-estimated based on other datasets for private
manufacturing, non-manufacturing and service companies.

20. The original Z-score formula was as follows:
Z = 1.2T1 + 1.4T2 + 3.3T3 + 0.6T4 + 0.99T5.
- T1 = Working Capital / Total Assets. (Measures liquid
assets in relation to the size of the company.)
- T2 = Retained Earnings / Total Assets. (Measures
profitability that reflects the company's age and earning power.)
- T3 = Earnings before Interest and Taxes / Total Assets.
(Measures operating efficiency apart from tax and leveraging
factors. It recognizes operating earnings as being important to
long-term viability.)
- T4 = Market Value of Equity / Book Value of Total
Liabilities. (Ads market dimension that can show up security
price fluctuation as a possible red flag.)
- T5 = Sales/ Total Assets. (Standard measure for total asset
turnover (varies greatly from industry to industry).
Altman found that the ratio profile for the bankrupt group fell at -0.25
avg, and for the non-bankrupt group at +4.48 avg.

21. A. Public Limited Company:-
(Ratios are stated above to calculate T1 to T5)
Z score bankruptcy model:
Z = 1.2T1 + 1.4T2 + 3.3T3 + 0.6T4 + .999T5
Zones of Discrimination:
Z > 2.99 -“Safe” Zones, 1.81 < Z < 2.99 -“Grey” Zones,
Z < 1.81 -“Distress” Zones
B. Private Firms:
T1 = (Current Assets − Current Liabilities) / Total Assets
T2 = Retained Earnings / Total Assets
T3 = Earnings before Interest and Taxes / Total Assets
T4 = Book Value of Equity / Total Liabilities
T5 = Sales/ Total Assets
Z' Score Bankruptcy Model:
Z' = 0.717T1 + 0.847T2 + 3.107T3 + 0.420T4 + 0.998T5
Zones of Discrimination:
Z' > 2.9 -“Safe” Zone, 1.23 < Z' < 2.9 -“Grey” Zone,
Z' < 1.23 -“Distress” Zone

22. C. Non-Manufacturers & Emerging Markets:
T1 = (Current Assets − Current Liabilities) / Total Assets
T2 = Retained Earnings / Total Assets
T3 = Earnings before Interest and Taxes / Total Assets
T4 = Book Value of Equity / Total Liabilities
Z-Score bankruptcy model:
Z = 6.56T1 + 3.26T2 + 6.72T3 + 1.05T4
Zones of discriminations:
Z > 2.6 -“Safe” Zone, 1.1 < Z < 2.6 -“Grey” Zone,
Z < 1.1 -“Distress” Zone
2. Value-at-Risk Model:
Estimate of potential loss in loan portfolio over a given
holding period at a given level of confidence.
Probability distribution of a loan portfolio value reducing
by an estimated amount over a given time horizon.
Time horizon estimate is over a daily, weekly or monthly
basis.

23. 3. Credit Metrics Model: Assessment of portfolio risk due to changes in
debt value caused by changes in credit quality. Applications:-
a. Reduces portfolio risk
b. Sets exposure limits
c. Identify correlations across portfolio
Reduce potential risk concentration
Results in diversified portfolio
Reduction of total risk
4. Merton Model:
o Bank would default only if its asset value falls below
certain level (default point), which is a function of its liability.
o Estimates the asset value of the bank and its asset
volatility from the market value and the debt structure in the
option theoretic framework.
o A measurement that represents the number of standard
deviation that the bank’s asset value would be away from the
default point.
o (Merton’s (1973))

24. Model Efficiency Difference between the estimated default values
and actual default rate

26. 2. KMV Approach: The KMV approach follows the same logic as
the structural approach to a point, i.e., the firm defaults when the
value of assets falls below a certain level. But as an end product, it
comes up with the expected default frequency (EDF) (i.e. the
probability of default). default happens when the value of assets falls
below a certain value, called the ‘default point’. Under KMV, the
value of the firm’s assets is assumed to be log-normally distributed,
i.e. the returns on the assets are normally distributed. There are
essentially three steps to the credit risk assessment process :
Step 1: Determine the value of assets (V) and their volatility (σ)
The value of equity (as represented by the stock price, S) is driven by:
• Value of the firm’s assets (V)
• The volatility of the assets (σ)
• The leverage ratio (L)
• The coupon on long term debt (c) and
• The risk-free rate (r)

27. Of the above, the last three are known variables, and so is the stock
price. The only unknown variables are V and σ. The volatility of the
assets is not the same as the volatility of the stock price, as the latter is
driven by the value of the assets. KMV uses an iterative approach to find
out V and σ, given knowledge of the S, L, c and r.
Step 2: Calculate the ‘distance to default’ (DD)
A key concept underlying the KMV approach is the recognition that a
firm does not have to default the moment its asset value falls below the
face value of debt – in fact default happens when value of the firm’s
assets falls somewhere between the value of the short term debt and the
value of the total debt.
KMV sets the default point as somewhere between short term debt
(STD) and the total debt as the total of the short term debt and half the
value of the long term debt.

28. Next, the KMV approach determines what the ‘distance-to-default’ is.
The distance to default is the number of standard deviations assets have
to lose before getting to the default point (DPT). It is calculated as
follows:
Where, σ is the standard deviation of future asset returns. Each of the
terms in the equation above is explained below:

29. Step 3: Determination of the EDFs
The last step is the determination of the expected default
frequencies – which is a mapping of the distance-to-default to
probabilities of default based upon a proprietary database
(provided to customers using the ‘Credit Monitor’ service).
Based upon what was explained in 2 above, EDFs are affected
by:
• Stock price
• Leverage ratio and
• Asset volatility.
This can be expressed another way – as a multiple of the standard
deviation of the expected returns.
Where, μ and σ are the mean and volatility of the asset returns.

30. E. Credit Risk Pricing: Risk Adjusted Rate of Capital for Banks
(RAROC)
o Mark-to-market concept
o Allocates capital to a transaction at an amount equal to the
maximum expected loss (at a 99 percent confidence level)
o Basic risk categories
o Interest rate risk
o Credit risk
o Operational risk
o Foreign exchange risk
Model:
Quantify the risk in each category
Risk factor = 2.33 x weekly volatility x square root of 52 x
(1 – tax rate)
o 2.33 gives the volatility at 99% confidence level
o 52 weekly price movement is annualized
o (1 – tax rate) converts this to an after-tax basis
Capital required for each category
Multiplying the risk factor by the size of the position

31. F. Credit Risk Mitigation:
1. Credit risk mitigation reduces exposure of credit risk
Safety net of tangible assets
Safety from realizable (marketable) securities
Reduces exposure of risk from counterparty
dealings in guarantees and insurance
2. Risk mitigation measures
Collateral securities, Guarantees, Credit
derivatives, Balance sheet netting
G. Credit Audit:
o Compliance with pre-sanction & post-sanction processes -
external & internal audit committee
o Special compliance requirement by the credit risk
management committee of the Board of Directors of the bank

32. o Bank credit audit:-
• Quality of credit portfolio,
• Review of loan process,
• Compliance status of large loans
• Report on regulatory compliance,
• Independent audit of credit risk measurement
• Identification of loan distress signals,
• Review of employee credit skills
• Review of loan restructuring decisions in terms of
distress loans
• Review of credit quality and Review of credit
administration

33. RBI Guidelines on Credit Exposure and Management:
1. Bank cannot grant loans against security of its own shares.
2. Prohibition on remission (remitting) of debts for Urban
Cooperative Banks (UCBs) without prior approval of RBI.
3. Restrictions on loans and advances to Directors and their
relatives.
4. Ceiling on advances to Nominal Members – With deposits up to `
50 crore (` 50,000/- per borrower) and ` 1,00,000/- for above ` 50
crore.
5. Prohibition on Urban Cooperative Banks (UCBs) for bridge loans
including that against capital / debenture issues.
6. Loans and advances against shares, debentures.
a. UCBs are prohibited to extend any facilities to stock
brokers.
b. Margin of 40 per cent to be maintained on all such
advances.
7. Restriction on advances to real estate sector
a. Genuine construction and not for speculative purposes.

34. Different approaches to the Credit Evaluation Process:
1. Approach Methodology: Judgmental methods apply the
assessor’s experience and understanding of the case to the
decision to extend or refuse credit.
2. Expert systems (e.g. lending committees) use a panel
approach to judge the case or formalize judgmental decisions
via lending system and procedures.
3. Analytic models use a set of analytic methods, usually
on quantitative data, to derive a decision.
4. Statistical models (e.g. credit scoring) uses statistical
inference to derive appropriate relationships for decision
making.
5. Behavioral models observe behavior over time to
derive appropriate relationships for reaching a decision.
6. Market models rely on the informational content of
financial market prices as indicators of financial solvency.

35. HARRY MARKOWITZ MODERN PORTFOLIO THEORY –
MPT was developed in the 1950s through the early 1970s and was
considered an important advance in the mathematical modeling of
finance. Since then, some theoretical and practical criticisms have been
leveled against it. These include evidence that financial returns do not
follow a Gaussian distribution or indeed any symmetric distribution, and
that correlations between asset classes are not fixed but can vary
depending on external events (especially in crises).
Further, there remains evidence that investors are not rational and
markets may not be efficient. Finally, the low volatility anomaly
conflicts with CAPM's trade-off assumption of higher risk for higher
return; it states that a portfolio consisting of low volatility equities (like
blue chip stocks) reaps higher risk-adjusted returns than a portfolio with
high volatility equities (like illiquid penny stocks). A study conducted by
Myron Scholes, Michael Jensen, and Fischer Black in 1972 suggests that
the relationship between return and beta might be flat or even negatively
correlated.

36. The Harry Markowitz Model: MPT - Modern Portfolio Theory -
represents the mathematical formulation of risk diversification in investing,
that aims at selecting a group of investment assets which have collectively
lower risk than any single asset on its own. This becomes possible, since
various asset types frequently change in value in opposite directions.
Actually investing, being a tradeoff between risk and return, presupposes
that risky assets have the highest expected returns.
Thus, MPT shows how to choose a portfolio with the maximum possible
expected return for the given amount of risk. It also describes how to choose
a portfolio with the minimum possible risk for the given expected return.
Therefore, Modern Portfolio Theory is viewed as a form of diversification
which explains the way of finding the best possible diversification strategy.
Harry Markowitz model (HM model), also known as Mean-Variance Model
because it is based on the expected returns (mean) and the standard
deviation (variance) of different portfolios, helps to make the most efficient
selection by analyzing various portfolios of the given assets. It shows
investors how to reduce their risk in case they have chosen assets not
“moving” together.

37. MPT ASSUMPTIONS MODERN PORTFOLIO THEORY
• For buying and selling securities there are no transaction costs.
• An investor has a chance to take any position of any size and in any
security. The market liquidity is infinite and no one can move the
market.
• While making investment decisions the investor does not consider
taxes and is indifferent towards receiving dividends or capital gains.
• Investors are generally rational and risk adverse.
• The risk-return relationships are viewed over the same time horizon.
Both long term speculator and short term speculator share the same
motivations, profit target and time horizon.
• Investors share identical views on risk measurement.
• Investors seek to control risk only by the diversification of their
holdings.
• In the market all assets can be bought and sold including human
capital.
• Politics and investor psychology have no influence on market.
• Analysis is based on a single period model of investment.

38. Choosing the Best Portfolio: Two essential decisions are necessary to
be made to choose the best portfolio from a number of possible
portfolios, each with its risk and return opportunities:
1. Determine a set of efficient portfolios.
2. Select the best portfolio out of the efficient set.
Determining the Efficient Set: A
portfolio that gives maximum return
for a given risk, or minimum risk for
given return is an efficient portfolio.
Thus, portfolios are selected as
follows:
(a) From the portfolios that have the
same return, the investor will prefer the
portfolio with lower risk, and
(b) From the portfolios that have the
same risk level, an investor will prefer
the portfolio with higher rate of return.

39. As the investor is rational, they would like to have higher return. And
as he is risk averse, he wants to have lower risk. In Figure 1, the
shaded area PVWP includes all the possible securities an investor can
invest in. The efficient portfolios are the ones that lie on the boundary
of PQVW. For example, at risk level x2, there are three portfolios S,
T, U. But portfolio S is called the efficient portfolio as it has the
highest return, y2, compared to T and U. All the portfolios that lie on
the boundary of PQVW are efficient portfolios for a given risk level.
The boundary PQVW is called the Efficient Frontier. All portfolios
that lie below the Efficient Frontier are not good enough because the
return would be lower for the given risk. Portfolios that lie to the right
of the Efficient Frontier would not be good enough, as there is higher
risk for a given rate of return. All portfolios lying on the boundary of
PQVW are called Efficient Portfolios. The Efficient Frontier is the
same for all investors, as all investors want maximum return with the
lowest possible risk and they are risk averse.

40. The above figure shows the risk-return
indifference curve for the investors.
Indifference curves C1, C2 and C3 are
shown. Each of the different points on
a particular indifference curve shows a
different combination of risk and
return, which provide the same
satisfaction to the investors. Each
curve to the left represents higher
utility or satisfaction. The goal of the
investor would be to maximize his
satisfaction by moving to a curve that
is higher. An investor might have
satisfaction represented by C2, but if
his satisfaction/utility increases, he/she
then moves to curve C3 Thus, at any
point of time, an investor will be
indifferent between combinations S1
and S2, or S5 and S6.

41. The investor's optimal portfolio is found at the point of tangency of the
efficient frontier with the indifference curve. This point marks the highest
level of satisfaction the investor can obtain. This is shown in Figure 3. R is
the point where the efficient frontier is tangent to indifference curve C3,
and is also an efficient portfolio. With this portfolio, the investor will get
highest satisfaction as well as best risk-return combination (a portfolio that
provides the highest possible return for a given amount of risk). Any other
portfolio, say X, isn't the optimal portfolio even though it lies on the same
indifference curve as it is outside the feasible portfolio available in the
market. Portfolio Y is also not optimal as it does not lie on the best feasible
indifference curve, even though it is a feasible market portfolio. Another
investor having other sets of indifference curves might have some different
portfolio as his best/optimal portfolio.
All portfolios so far have been evaluated in terms of risky securities only,
and it is possible to include risk-free securities in a portfolio as well. A
portfolio with risk-free securities will enable an investor to achieve a
higher level of satisfaction. This has been explained in Figure 4.

42. R1 is the risk-free return, or the return from government securities, as
government securities have no risk. R1PX is drawn so that it is tangent to
the efficient frontier. Any point on the line R1PX shows a combination of
different proportions of risk-free securities and efficient portfolios. The
satisfaction an investor obtains from portfolios on the line R1PX is more
than the satisfaction obtained from the portfolio P.

43. All portfolio combinations to the left of P show combinations of risky and
risk-free assets, and all those to the right of P represent purchases of risky
assets made with funds borrowed at the risk-free rate. In the case that an
investor has invested all his funds, additional funds can be borrowed at
risk-free rate and a portfolio combination that lies on R1PX can be
obtained. R1PX is known as the Capital Market Line (CML). this line
represents the risk-return trade off in the capital market. The CML is an
upward sloping curve, which means that the investor will take higher risk
if the return of the portfolio is also higher. The portfolio P is the most
efficient portfolio, as it lies on both the CML and Efficient Frontier, and
every investor would prefer to attain this portfolio, P. The P portfolio is
known as the Market Portfolio and is also the most diversified portfolio. It
consists of all shares and other securities in the capital market. In the
market for portfolios that consists of risky and risk-free securities, the
CML represents the equilibrium condition. The Capital Market Line says
that the return from a portfolio is the risk-free rate plus risk premium. Risk
premium is the product of the market price of risk and the quantity of risk,
and the risk is the standard deviation of the portfolio.

44. The CML equation is : RP = IRF + (RM - IRF)σP/σM
Where,
RP = Expected Return of Portfolio
RM = Return on the Market Portfolio
IRF = Risk-Free rate of interest
σM = Standard Deviation of the market portfolio
σP = Standard Deviation of portfolio
(RM - IRF)/σM is the slope of CML. (RM - IRF) is a measure of
the risk premium, or the reward for holding risky portfolio
instead of risk-free portfolio. σM is the risk of the market
portfolio. Therefore, the slope measures the reward per unit of
market risk.

45. The characteristic features of CML are:
1. At the tangent point, i.e. Portfolio P, is the optimum
combination of risky investments and the market portfolio.
2. Only efficient portfolios that consist of risk free
investments and the market portfolio P lie on the CML.
3. CML is always upward sloping as the price of risk has to
be positive. A rational investor will not invest unless he
knows he will be compensated for that risk.

46. Figure 5 shows that an investor will choose a portfolio on the efficient
frontier, in the absence of risk-free investments. But when risk-free
investments are introduced, the investor can choose the portfolio on
the CML (which represents the combination of risky and risk-free
investments). This can be done with borrowing or lending at the risk-
free rate of interest (IRF) and the purchase of efficient portfolio P.
The portfolio an investor will choose depends on his preference of
risk. The portion from IRF to P, is investment in risk-free assets and is
called Lending Portfolio. In this portion, the investor will lend a
portion at risk-free rate. The portion beyond P is called Borrowing
Portfolio, where the investor borrows some funds at risk-free rate to
buy more of portfolio P.
Under the model:
• Portfolio return is the proportion-weighted combination of the
constituent assets' returns.
• Portfolio volatility is a function of the correlations ρij of the
component assets, for all asset pairs (i, j).

47. In general:
• Expected return:
Where is the return on the portfolio, is the return on asset i and
is the weighting of component asset (that is, the proportion of asset "i"
in the portfolio).
• Portfolio return variance:
Where is the correlation coefficient between the returns on assets i
and j. alternatively the expression can be written as:
Where for i=j.

48. Portfolio Return Volatility (standard deviation):
Portfolio Return:
Portfolio Variance:
FOR A THREE ASSET PORTFOLIO:
Portfolio Return:
Portfolio Variance:

49. Credit Risk Management in Banks - Introduction: Banks in the
process of financial intermediation are confronted with various kinds of
financial and non-financial risks viz., credit, interest rate, foreign
exchange rate, liquidity, equity price, commodity price, legal, regulatory,
reputational, operational, etc. These risks are highly interdependent and
events that affect one area of risk can have ramifications for a range of
other risk categories. Thus, top management of banks should attach
considerable importance to improve the ability to identify measure,
monitor and control the overall level of risks undertaken.

50. The broad parameters of risk management function should
encompass:
- Organizational structure; and comprehensive risk
measurement approach;
- Risk management policies approved by the Board which
should be consistent with the broader business strategies,
capital strength, management expertise and overall
willingness to assume risk;
- The guidelines and other parameters used to govern risk
taking including detailed structure of prudential limits.
- Strong MIS for reporting, monitoring and controlling
risks;
- Well laid out procedures, effective control and
comprehensive risk reporting framework;
- Separate risk management framework independent of
operational Departments and with clear delineation of levels
of responsibility for management of risk; and
- Periodical review and evaluation.

51. Loan Review Mechanism (LRM): LRM is an effective tool for constantly
evaluating the quality of loan book and to bring about qualitative
improvements in credit administration. Banks should, therefore, put in place
proper Loan Review Mechanism for large value accounts with responsibilities
assigned in various areas such as, evaluating the effectiveness of loan
administration, maintaining the integrity of credit grading process, assessing
the loan loss provision, portfolio quality, etc. The main objectives :
a) To identify promptly loans which develop credit weaknesses
and initiate timely corrective action;
b) To evaluate portfolio quality and isolate potential problem
areas;
c) To provide information for determining adequacy of loan loss
provision;
d) To assess the adequacy of and adherence to, loan policies and
procedures, and to monitor compliance with relevant laws and
regulations; and
e) To provide top management with information on credit
administration, including credit sanction process, risk evaluation and
post-sanction follow-up.

52. Credit Risk Derivatives: Credit Default Swaps, Credit Default Index
Swaps (CDS index), Collateralized Debt Obligations, Total Return
Swaps, Credit Linked Notes, Asset Swaps, Credit Default Swap Options,
Credit Default Index Swaps Options and Credit Spread
Forwards/Options.
1. Credit Default Swaps: In a credit default swap the seller agrees,
for an upfront or continuing premium or fee, to compensate the buyer
when a specified event, such as default, restructuring of the issuer of the
reference entity, or failure to pay, occurs. Buyers of credit default swaps
can remove risky entities from their balance sheets without selling them.
Sellers can gain higher returns from investments or diversify their
portfolios by entering markets that are otherwise difficult to get into. The
value of a default swap depends not only on the credit quality of the
underlying reference entity but also on the credit quality of the writer,
also referred to as the counterparty. If the counterparty defaults, the buyer
of a default swap will not receive any payment if a credit event occurs.

53. 2. Credit-Linked Notes: A credit-linked note, also known as a
credit default note, is a fixed or floating rate note where the principal
and/or coupon payments are referenced to a credit or a basket of credits.
If there is no credit event of the reference credit(s), all the coupons and
principals will be paid in full. However, if there is a credit event, the
payments of the principal and, possibly, also the coupon of the note will
be reduced.
3. Total Return Swaps: A total return swap is a means to transfer
the total economic exposure, including both market and credit risk, of the
underlying asset. The payer of a total return swap can confidentially
remove all the economic exposure of the asset without having to sell it.
The receiver of a total return swap, on the other hand, can access the
economic exposure of the asset without having to buy the asset. Typical
reference assets of total return swaps are corporate bonds, loans and
equities.

54. 4. Credit Default Swap Options: A credit default swap option is
also known as a credit default swaption. It is an option on a credit default
swap (CDS). A CDS option gives its holder the right, but not the
obligation, to buy (call) or sell (put) protection on a specified reference
entity for a specified future time period for a certain spread. The option is
knocked out if the reference entity defaults during the life of the option.
This knock-out feature marks the fundamental difference between a CDS
option and a vanilla option. Most commonly traded CDS options are
European style options.
5. Credit Spread Options and Forwards: Credit spread options
are options where the payoffs are dependent on changes to credit spreads.
The transaction may be either based on changes in a credit spread
relative to a risk-free benchmark (e.g. LIBOR or US Treasury) or
changes in the relative spread between two credit instruments. A credit
spread option may be a vanilla option or an exotic option, such as an
Asian option, a loopback option, etc. The option style may be European
or American.

55. 6. Credit Default Index Swap Options: A credit default index
swap option (CD index swap option, or CD index swaption, or CDS
index option) is an option to buy or sell the underlying CDIS at a
specified date. A payer swaption gives the holder of the option the right
to buy protection (pay premium) and a receiver swaption gives the holder
of the option the right to sell protection (receive premium). Unlike a CD
index swap, which is a natural extension of a CDS on a single-entity to a
CDS on a portfolio of entities, a CD index swaption is significantly
different from a CDS option, an option on a single-entity CDS. In the
case of an option on a single-entity, if the reference entity defaults before
the option's expiry, the option will be knocked out and become worthless.
For an option on a CDIS, when a reference entity defaults before the
option's expiry, the loss will be paid by the protection seller to the
protection buyer when the option is exercised.

56. 7. Asset Swaps: An asset swap is a combination of a defaultable
bond with a fixed-for-floating interest rate swap that swaps the coupon of
the bond into the cash flows of LIBOR plus a spread. In the case of a
cross currency asset swap, the principal cash flow may also be swapped.
In a typical asset swap, a dealer buys a bond from a customer at the
market price and sells to the customer a floating rate note at par. The
dealer then enters into a fixed-for-floating swap with another
counterparty to offset the floating rate obligation and the bond cash
flows.

57. 8. Synthetic Collateralized Debt Obligations (CDOs): Synthetic
CDOs are credit derivatives on a pool of reference entities that are
"synthesized" through more basic credit derivatives, mostly, credit
default swaps (CDSs) and credit linked notes (CLNs). A common
structure of CDOs involves slicing the credit risk of the reference pool
into a few different risk levels. The level with a higher credit risk
supports the levels with lower credit risks. The risk range of two adjacent
risk levels is called a tranche. The lower bound of the risk level of a
tranche is often referred to as an attachment point and the upper bound a
detachment point. The most common CDO credit derivatives are CDSs
on CDO tranches and CDO notes (tranche-linked notes or CLN on
tranches). The most popular synthetic CDOs are the so-called
standardized CDOs (sometimes are simply called standardized tranches).