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TABLE OF CONTENTS
Sr.no. Particulars Page
No.
I Executive Summary 2
1 Introduction to Treasury Management 3
2 The Federal Bank - An Overview 5
2.1 The Federal Bank - Treasury Department 6
3 Cash Credit Ratio & Statutory Liquidity Ratio 8
4 Asset Liability Management 12
4.1 Models of ALM 16
5 Capital Adequacy 23
5.1 Calculation of Capital Charge (Market Risk) 27
5.2 Pillar II : SREP 39
5.3 Pillar III : Market Discipline 41
6 Internal Model Approach (IMA) 42
7 Value at Risk (VaR) 45
7.1 VaR Parameters 47
7.2 VaR Models 49
7.3 Interpretation of VaR 52
7.4 Backtesting of VaR 56
7.5 Expected Shortfalls 58
8 Learnings and Shortfalls 59
9 References 61
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I. EXECUTIVE SUMMARY
Treasury management in an organization helps maintain adequate liquidity to ensure that the
right amount of cash resources are available in the right place in the right currency and at the
right time in such a way as to maximize the return on surplus funds, minimize the financing
cost of the business, and control interest rate risk and currency exposure to an acceptable
level.
This project covers functions of treasury management operations in banks, organizational
structure, objectives and functions of treasury which plays an important role in banks and a
genuine attempt to study, understand the basics of Risk management in Banks with a
special focus on Market Risk- valuation and computation of capital charge, Asset-Liability
Management and also a brief overview of the risk management guidelines laid down by
RBI.
The project also involves the study of the responsibilities of the Bank’s treasury in managing
cash reserve ratio (CRR), statutory liquidity ratio (SLR), government securities, etc.
We have also tried to cover future scope / challenges in treasury management, role of
information technology in treasury management and a study of Federal Bank’s treasury.
Treasury Management is fast emerging as a specialization in many companies and its
accounting function is being de-linked from the finance managing the treasury profit center
successfully.
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1. Introduction to Treasury Management
In general terms and from the perspective of commercial banking, treasury refers to the fund
and revenue in the bank’s possession and day-to-day management of the same. Idle funds are
usually source of loss, real or opportune, and, thereby need to be managed, invested, and
deployed with intent to improve profitability. Thus, treasury operations seek to maximize
profit and earning by investing available funds at an acceptable level of risks. Returns and
risks both need to be managed. Moreover there is a trend among banks that they are under
pressure to get best returns even from the surplus/idle funds
In this context, treasury operations are becoming more and more important to the banks and a
need for integration, both horizontal and vertical, has come to the attention of the corporate.
The basic purpose of integration is to improve portfolio profitability, risk-insulation and also
to synergize banking assets with trading assets. In horizontal integration, dealing/trading
rooms engaged in the same trading activity are brought under same policy, technological and
accounting platform, while in vertical integration, all existing and diverse trading and
arbitrage activities are brought under one control with one common pool of funding and
contributions.
Treasury management in an organization helps maintain adequate liquidity to ensure that the
right amount of cash resources are available in the right place in the right currency and at the
right time in such a way as to maximize the return on surplus funds, minimize the financing
cost of the business, and control interest rate risk and currency exposure to an acceptable
level.
In other words, Treasury management (or treasury operations) includes the management of an
enterprise's holdings in and trading in government and corporate bonds, currencies, financial
futures, options and derivatives, payment systems and the associated financial risk
management. It binds together liquidity management, asset/liability management (ALM),
capital requirements and risk management. At one end of the spectrum it manages balance
sheets and liquidity, and does good things to enhance the yield on assets and minimize the
cost of liabilities, mostly through the clever and intelligent use of derivatives. At the other
end of the spectrum, treasury can help restructure the balance sheet and provide new
products.
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Integrated Treasury:
We see integration of segmented financial markets- money market, debt and capital market
and Forex market, etc., at the macro level and integration of treasury operations at the
operational level of banks. The term ‘integration’ means merger or centralization or
consolidation. The reforms that were initiated in 90s made domestic markets closely linked to
global markets. The domestic market is in integration with global market at the micro level,
which has raised the need for integration of micro level units. Relaxation of regulations has
almost integrated different segments of financial markets- debt market, money market, capital
market, Forex market, etc., which enabled free flow of money from one market to another.
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2. The Federal Bank Ltd –An Overview
Federal Bank is one of the leading private sector banks in India with a banking history of
around 70 years and its head office is located at Aluva near Kochi, Kerala. Federal bank has a
wide network of more than 950 branches covering almost all major cities in the country with a
major share in the state of Kerala .Federal Bank has played a pioneer role in developing and
deploying technology assisted customer friendly products and services. The Bank has also the
distinction of being one of the first banks in the country to deploy technology enabled services
at the smaller branches including rural and semi-urban areas.
The Bank has the full range of delivery channels including, Internet Banking, Mobile Banking
and Alerts, Any Where (Branch) Banking, Interconnected Visa enabled ATM network, E-
mail Alerts, Telephone Banking and a Centralized customer Call Centre with toll free number.
The Bank has now emerged into a financial supermarket giving the customers a range of
products and services. Apart from the entire slew of banking products and delivery channels
the bank also provides a variety of fee based services such as merchant banking services,
depository services etc to name a few.
The Federal Bank Ltd has a three tier organizational structure; consisting of branches which
are intended to be the profit centre for the Bank, the regional offices which are responsible for
the administration, growth and development of the branches, and the central office which
provides strategies, as well as well-defined systems and procedures for the operation of the
regional office and branches. The bank is currently headed by its MD& CEO, Mr. Shyam
Srinivasan
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2.1 The Federal Bank Ltd-Treasury Department
Federal Bank Ltd has an Integrated Treasury, managed by the Front Office, Mid Office
that is mainly concerned with Risk Management, the Back Office where the settlements
take place and the Audit group.
Front office:
The dealing room comprises the front office that handles transactions for mainly Banks
(proprietary deals) and also for its the clients. They are the first point of interface with other
participants in the market (dealers of other banks, brokers and customers). The dealers have
access to information on prices and volumes of trade in securities worldwide through News
Screen/platforms like Reuters and Bloomberg and strike the best possible deals for the
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purpose of complying with statutory requirements and optimizing profits. In the Federal Bank
Ltd there are four sections in the front office:
The G-Sec Desk
The Money Market and Derivative Desk
The Equity Desk
The FOREX desk
Mid- office:
Mid-office is responsible for onsite risk measurement, monitoring and management, reporting
and analysis, reports directly to the top management for control. This unit is responsible for
daily tracking of risk exposures, individually as well as collectively. They report directly to
the Integrated Risk Management Department (IRMD).
Back - office functions:
The back office undertakes accounting, settlement and reconciliation operation. The key
functions of back-office are-:
Deal slips verification and Monitoring approved exposure and position limits.
Generation and dispatch of interbank confirmations and confirmations on forward
contracts.
Effecting/receiving payments and Monitoring receipt of FOREX funds in interbank
contracts
Settlement through CCIL or direct through NOSTRO as applicable
Statutory reports to RBI
The audit group independently inspects/audits daily operations in the treasury
department to ensure adherence to internal/regulatory systems and procedures.
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3. Cash Reserve Ratio (CRR) and Statutory Liquidity Ratio (SLR)
With a view to monitoring compliance of maintenance of statutory reserve requirements viz.
CRR and SLR by the SCBs, the Reserve Bank of India has prescribed statutory returns
CRR: At present, the CRR is prescribed at 4.75 per cent of a bank's total of DTL (Demand &
Term Liabilities)
Computation of DTL for the purpose of CRR compliances: Liabilities of a bank may be in the
form of demand or time deposits or borrowings or other miscellaneous items of liabilities
Demand Liabilities- E.g. (current deposits, demand liabilities portion of savings bank
deposits, margins held against letters of credit/guarantees, balances in overdue fixed
deposits, cash certificates and cumulative/recurring deposits, outstanding Telegraphic
Transfers (TTs), Mail Transfer (MTs), Demand Drafts (DDs), unclaimed deposits,
credit balances in the Cash Credit account and deposits held as security for advances
which are payable on demand. Money at Call and Short Notice from outside the
Banking System should be shown against liability to others).
Time Liabilities- Eg.(fixed deposits, cash certificates, cumulative and recurring
deposits, time liabilities portion of savings bank deposits, staff security deposits,
margin held against letters of credit, if not payable on demand, deposits held as
securities for advances which are not payable on demand and Gold deposits).
Other Demand and Time Liabilities (ODTL)- Eg.( interest accrued on deposits, bills
payable, unpaid dividends, suspense account balances representing amounts due to
other banks or public, net credit balances in branch adjustment account, any amounts
due to the banking system which are not in the nature of deposits or borrowing).
Assets with the Banking System-Eg. ( balances with banks in current account,
balances with banks and notified financial institutions, loans or deposits repayable at
call or short notice of a fortnight or less and loans other than money at call and short
notice made available to the banking system)
Borrowings from abroad by banks in India
Arrangements with Correspondent Banks for Remittance Facilities
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Liabilities not to be included for DTL/NDTL computation
Paid up capital, reserves, any credit balance in the Profit & Loss Account of the bank,
amount of any loan taken from the RBI and the amount of refinance taken from
EXIM Bank, NHB, NABARD, SIDBI
Net income tax provision
Amount received from DICGC towards claims and held by banks pending
adjustments thereof; ECGC by invoking guarantee.
The liabilities arising on account of utilization of limits under Bankers Acceptance
Facility (BAF)
District Rural Development Agency (DRDA) subsidy of Rs.10, 000/- kept in Subsidy
Reserve Fund account in the name of Self Help Groups;
Subsidy released by NABARD under Investment Subsidy Scheme for
Construction/Renovation/Expansion of Rural Godowns;
Net unrealized gain/loss arising from derivatives transaction under trading portfolio;
Income flows received in advance such as annual fees and other charges which are not
refundable.
Bill rediscounted by a bank with eligible financial institutions as approved by RBI
Provision not being a specific liability arising from contracting additional liability and
created from profit and loss account.
Exempted Categories
SCBs are not required to include inter-bank term deposits/term borrowing liabilities
of original maturities of 15 days and above and up to one year in "Liabilities to the
Banking System". Similarly banks should exclude their inter-bank assets of term
deposits and term lending of original maturity of 15 days and above and up to one
year in "Assets with the Banking System" (item III of Form A return) for the purpose
of maintenance of CRR. The interest accrued on these deposits is also exempted from
reserve requirements.
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Maintenance of CRR on Daily Basis
With a view to providing flexibility to banks in choosing an optimum strategy of holding
reserves depending upon their intra fortnight cash flows, all SCBs are required to maintain
minimum CRR balances up to 70 per cent of the average daily required reserves for a
reporting fortnight on all days of the fortnight with effect from the fortnight beginning
December 28, 2002.
The Reserve Bank does not pay any interest on the CRR balances maintained by SCBs with
effect from the fortnight beginning March 31, 2007.
Penalties
Default in maintenance of CRR requirement on a daily basis (70% of total CRR
requirement): penal interest will be recovered for that day at the rate of three per cent per
annum above the Bank Rate & if the shortfall continues on the next succeeding day/s, penal
interest will be recovered at the rate of five per cent per annum above the Bank Rate.
Default in maintenance of CRR on average basis during a fortnight, penal interest will be
recovered as envisaged in sub-section (3) of Section 42 of Reserve Bank of India Act, 1934.
SCBs are required to furnish the particulars such as date, amount, percentage, reason for
default in maintenance of requisite CRR and also action taken to avoid recurrence of such
default.
Fortnightly Return Form:
SCBs are required to submit to Reserve Bank a provisional Return in Form 'A' within 7 days
from the expiry of the relevant fortnight. For reporting in Form 'A' return, banks should
convert their overseas foreign currency assets and bank credit in India in foreign currency in
four major currencies viz., US dollar, GBP, Japanese Yen and Euro into rupees at the Foreign
Exchange Dealers Association of India's (FEDAI) noon mean rate on reporting Friday.
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Maintenance of SLR
The value of such assets of a SCB shall not be less than such percentage not exceeding 40 per
cent of its total DTL in India as on the last Friday of the second preceding fortnight as the
Reserve Bank may, by notification in the Official Gazette, specify from time to time.
SCBs can participate in the Marginal Standing Facility (MSF) scheme introduced by Reserve
Bank of India. Under this facility, the eligible entities may borrow overnight, up to one per
cent of their respective NDTL outstanding at the end of the second preceding fortnight.
Every SCB has to maintain in India assets as detailed below:-
Cash
Gold valued at a price not exceeding the current market price
Investment in the following instruments which will be referred to as "Statutory
Liquidity Ratio (SLR) securities" – T-Bills, SDLs, dated securities, etc.
Encumbered SLR securities shall not be included for the purpose of computing the
percentage specified.
Procedure for Computation of SLR
SCBs are required to include inter-bank term deposits / term borrowing liabilities of all
maturities in ‘Liabilities to the Banking System’. Similarly, banks should include their inter-
bank assets of term deposits and term lending of all maturities in ‘Assets with the Banking
System’ for computation of NDTL for SLR purpose.
Penalties:
Same as in case of non maintenance of CRR, however in case of SLR the bank needs to
maintain 100% SLR requirement as prescribed by RBI.
Return in Form VIII (SLR)
Banks should submit to the Reserve Bank before 20th day of every month, a return in Form
VIII showing the amounts of SLR held on alternate Fridays during immediate preceding
month with particulars of their DTL in India held on such Fridays
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4. Asset-Liability Management
Asset Liability Management is the heart of every system particularly of Banks and Financial
Institutions. We define “Asset Liability Management is the process of decision making to
control risks of existence, stability and growth of a system through the dynamic balancing of
its assets and liabilities.
Importance of Asset Liability Management:
In a deregulated environment since 1999, Indian banks are free to determine their own
interest rates on deposits and advances in both domestic and foreign currencies on a dynamic
basis. To decide a priori the impact of positive or negative changes on existing interest rate
along with the target value of change there is a need to do sensitivity analysis of interest rate
with respect to profitability, interest spread, and long-term viability. This scenario gives rise
to the basic risks outlined as follows:
1. Interest rate risk: It is the risk of having a negative impact on bank’s future earnings
and on the market value of its equity due to changes in interest rate.
2. Liquidity risk: It is the risk of having insufficient liquid assets to meet the liabilities at
a given time.
3. Forex risk: It is the risk of having losses in foreign exchange assets and liabilities due
to changes in exchange rates among multi-currencies under consideration.
In order to address various financial risks and take proactive steps banks are required to
introduce effective risk management systems in place.
Asset Liability Management is concerned with risk management and it provides a
comprehensive and dynamic framework for measuring, monitoring and managing associated
risks. Asset Liability Management enforces the best practices of risk management to fulfill
business and strategic objectives of the organization. ALM provides best strategies for
managing funds of public for best returns and targets towards increasing the market value of
equity
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Classification of Assets and Liabilities:
For Asset Liability Management purpose the assets and liabilities are classified into different
time periods popularly called as time or maturity buckets, depending on maturity profile and
interest rate sensitivity. As per RBI guidelines issued for ALM implementation for Banks in
1999, there are 8 time buckets T-1 to T-8 classified respectively as follows:
i) 1 to 14 days
ii) 15 to 28 days
iii) 29 days and upto 3 months
iv) Over 3 months and upto 6 months
v) Over 6 months and upto 1 year
vi) Over 1 year and upto 3 years
vii) Over 3 years and upto 5 years
viii) Over 5 years
Having regard to the international best practices, the level of sophistication of banks in India
and the need for a sharper assessment of the efficacy of liquidity management, RBI has
amended the bucketing structure as follows
I. 1 day
II. 2 to 7 days
III. 8 to 14 days
IV. 15 to 28 days
V. 29 days and up to 3 months
VI. Over 3 months and up to 6 months
VII. Over 6 months and up to 1 year
VIII. Over 1 year and up to 3 years
IX. Over 3 years and up to 5 years
X. Over 5 years
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Asset Liability Management Committee (ALCO):
ALM is an integrated activity requiring consolidated information from various sources and
departments of an organization. The first step of the ALM process is to constitute a
committee known as Asset Liability Committee (ALCO).
The ALCO should generally have at least 4 members and a maximum of 8 members
consisting of the bank's senior management from various departments including Chairman &
Managing Director (CMD). It should be responsible for setting business policies, periodic
review and ensuring adherence to the limits set by the Board as well as for deciding the next
business strategy of the bank. The diagram below indicates the structure of ALCO and flow
of reporting to the Board of Directors.
ALM involves viewing the balance sheet as a complex interest rate arbitrage where funds are
obtained from several sources with varying interest rates and employed in a wide variety of
assets at rates high enough to cover interest paid on the liabilities and the operating expenses
to produce profits.
The structure of ALCO with selected executive members from various departments is shown
in the figure below:
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The important functions of ALCO are:
• Define business policies and strategies
• Review economic scenario
• Articulate the interest rate view
• Price assets and Liabilities
• Establish investment policy guidelines
• Examine loan portfolio
• Measure liquidity risk, interest rate risk and FOREX risk particularly
• Review performance of the bank
• Involve in budgeting/planning
• Report, reviews, and developments at regular intervals to CMD, Management Committee
(Supervisory Authority of ALCO) and to the Board
Since ALCO is the driving force of the Bank, the co-ordination and dedication of its
members, factual criticisms, use of analytical models and corrective risk measures, periodic
reviews, support of real time triggers etc. help in the healthy growth of the organization.
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4.1 Asset Liability Management Models:
Analytical models are very important for ALM analysis and scientific decision making.
The basic models
(i) GAP Analysis Model
(ii) Duration GAP Analysis (DGAP) Model
(iii) Scenario Analysis Model
(iv) Value at Risk (VaR) Model
(v) Stochastic Programming (SP) Model
Gap Analysis (GAP) Model:
GAP model for asset liability management is concerned with measuring interest rate risk by
finding the pattern of the net interest income over a given period of time. In this model the
assets and liabilities are classified into different time periods (buckets) based on maturity
pattern.
Gap is defined as the difference between Rate Sensitive Assets (RSA) and Rate Sensitive
Liabilities (RSL).
GAP = RSA – RSL
Gap may be (i) Positive Gap where GAP > 0 and (ii) Negative Gap where GAP < 0 with
following general characteristics, (iii) Gap being zero is the equilibrium state.
Advantages of GAP Model:
Simple to analyze
Easy to implement.
Helps in Future analysis on Interest rate risk.
Helps in Projecting NII for further analysis.
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Disadvantages of GAP Model:
Ignores the time value of assets and liabilities.
Does not consider the embedded options like premature withdrawal of deposits and
prepayment of loans.
Example: Let us consider an XYZ Bank for which the maturity pattern of Assets and
Liabilities as on a particular date, say 31.03.2004 is given in the table No.1 below
Here Rs.705.55 crores in the deposit liability of column-2 means that as on March 31, 2004
the bank is liable to repay this amount including the interest during the next 14 days on
account of deposit received by the bank till date. Similarly Rs.376.05 crores in the loans and
advances asset of column-5 indicates that as on March 31, 2004 the bank is expected to get
back this amount during the next 14 days of the loans and advance that it has given till date.
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The results obtained using the formulas stated above are shown in Table No.2:
Observations: From the above results in Table No.2, GAP amount in col 4 is negative till 3-5
years period and positive for the last period, which means XYZ Bank can be grouped as
Liability Sensitive. Long-term assets are funded with Short-term liabilities, and bank will
benefit as Net interest income increases with decrease in interest rates as shown in col 7 for
an example of decrease in rate of interest of 0.25%. Cumulative GAP amount in col 5 is also
negative for all time periods. Gap Ratio in col 6 is between 0.30 and 0.92 up to “3-5 years
period” indicating inflows are always less than outflows and for the last time period inflows
are double than the outflows.
Duration Gap Analysis (DGAP) Model:
Duration is defined as the weighted average maturity of a resource (asset or liability) where
the net present values (NPV) of cash flows are used as weights. We use the notation DA to
mean Duration of Assets and DL to mean Duration of liabilities.
Example-1: Duration of a 3-year loan with 12% as rate of simple interest and having market
value is Rs.700 is calculated as follows:
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Duration=Total Cumulative Returns/Market Value (MV) of loan=1883.04/700 = 2.69 yrs
Duration Gap (DG): A method to quantify interest rate risk involving a comparison of the
potential changes in value of assets and liabilities that are affected by interest rate fluctuations
over all relevant intervals. The duration of each asset or liability defines an interval that is
assessed first.
DG = DA – (u*DL) --- (1)
Where u = TL / TA; TL = Total Liabilities excluding Equity, TA = Total Assets
Example: Find the Duration Gap (DG) for the following assets and liabilities of an
organization, if the value unit is Rupees (INR) and duration is in years.
* computed as in example-1.
Here Total Assets (TA) = 100 + 700 + 200 = 1000 and
Total Liabilities (TL) = 620 + 300 = 920 (Without Equity)
DA = Weighted average of Duration of all Assets
= [Σ MV(Ai) x DAi ] / TA for i = 1 to m; where Ai is the i th asset out of m assets
= [700*2.69+200*4.99] /1000
= 2.88 yrs
DL = Weighted average of Duration of Liabilities
= [Σ MV(Lj) x DLj ] / TL for j = 1 to n; where Lj is the j th liability out of n liabilities
= [620*1+300*2.81] /920
= 1.59 yrs
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Duration GAP (DG) = DA- [TL/TA] DL = 2.88 - 1.59 [920/1000] = 1.42 years
Duration gap (DGAP) models focus on the market value of equity. Duration gap analysis
compares the duration of assets with duration of liabilities and calculates the market value of
equity when interest rate fluctuates.
First an interest rate forecast is prepared and it estimates the market value of assets, liabilities
and equity. Then the weighted average duration of assets and weighted average duration of
liabilities is estimated. From this duration gap is calculated. Now with fluctuations in
forecasted interest rates the changes in market value of equity is calculated.
Based on Duration Gap value i.e. positive, negative or zero with changes in interest rates net
interest income is also effectively calculated.
Duration analysis is useful in assessing the impact of interest-rate changes on market value of
equity i.e. asset liability structure.
Advantages:
Duration Gap analysis serves as a strategic planning tool for evaluating and
controlling the interest rate risk.
Duration Gap analysis improves on the maturity gap and cumulative gap models by
taking into account the timing and market value of cash flows rather than horizon
maturity.
Offers flexibility in spread management.
Instead of changing the maturity structure of assets and liabilities duration gap
analysis puts emphasis on change of mix of assets or liabilities whichever is feasible.
Disadvantages:
Requires extensive data on specific characteristics and current market pricing
schedules of the financial instruments.
Requires a high degree of analytical expertise regarding issues such as the term
structure of interest rates and yield curve dynamics.
21
Value at Risk (VaR) Model:
VaR is a method to quantify the risk associated with each asset and liability which in turn can
be aggregated to arrive at a value for all the assets and liabilities of an organization. It
involves computation of the mean (μ), standard deviation (σ), specification of confidence
level (ρ), and the range based on the specific probability distribution function. The volatility
of the return for an asset or liability is computed as follows:
Volatility = Standard Deviation (SD) / Mean x100
V = σ / μ x 100 --- (1)
VaR helps to estimate the possible loss for each asset and liability.
Example:
(1) For single asset or liability:
Suppose a bank deploys Rs.200 Crore in securities and the volatility is 10%. Then we have to
find out the daily volatility (VD) to know the Value at Risk on a given day. For this we use
the formula as given below:
Volatility A = Volatility D√t
Or VA = VD x √t --- (2)
So, 10 = VD x √250, Assuming 250 working days are there in a year
∴ VD = 10 / √250 = 0.63%
Value at Risk (VaR) for a given confidence level , say, 68% and Standard deviation of 1 is
calculated as below:
VaR = Value of Asset x Daily Volatility --- (3)
∴VaR = 200 x 1 x 0.63% = 1.26 Crores assuming normal distribution.
And Value at Risk with 95% confidence that has Standard Deviation of 2 is:
∴VaR = 200 x 2 x 0.63% = 2.72 Crores.
(2) For Multiple assets or liabilities: Here we consider two cases as below:
(a) Two assets or liabilities:
Value at Risk is a function of volatility, which depends on the volatilities of individual assets.
Let A1 and A2 be the two assets and ρ (A1, A2) be the correlation between them.
If variance is given for individual assets, we have to calculate Standard Deviation from that
and to derive Correlation between them use the following formula given below:
ρ (A1,A2) = Covariance (A1,A2) / √ [ var(A1) x var(A2) ] ---(4)
variance of (A1, A2) = var (A1) + var (A2) + 2 x Covariance(A1,A2) ---(5)
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Example:
If we invest Rs.200 Crores each in two assets A1 and A2 with given below details:
Variance of A1 = 81, Variance of A2 = 36 and correlation ρ(A1,A2) = 0.25 then calculate
Value at Risk for each asset.
Solution:
Standard Deviation of A1 = √81 = 9
Standard Deviation of A2 = √36 = 6
Covariance of (A1,A2) = ρ(A1,A2) x √[var(A1) x var(A2)]
= 0.25 x √81 x √36 = 0.25 x 9 x 6
= 13.5
variance of (A1,A2) = var(A1) + var(A2) + 2 x Covariance(A1,A2)
= 81 + 36 + 2 x 13.5
= 144
Standard Deviation of (A1, A2) = √144 = 12
If these assets are invested for two years Daily volatility will be 0.45%, if the rate of return
which is 10% decreases to 8% then computation of minimum and maximum loss on both
assets with a confidence level of 95% will be as given below:
Range of return: when confidence level is 95% and SD is 2 then maximum rate of return will
be 10.90 and minimum return will be 9.10. Then the minimum loss will be Rs.2.2 Crores and
maximum loss will be Rs.5.8 Crores.
(b) When more than two assets or liabilities are considered:
Let A1, A2 an be the n assets. There are nc2 = n (n-1)/2 number of correlations between them
which can be represented by a matrix [ρ(Ai,Aj)] where i, j ranges between 1 to n. It is a
square matrix of order n. From which one can derive covariance and standard deviation for
calculating Value at Risk.
Uses of VaR:
Translates portfolio exposures into potential profit and loss
Aggregates and reports multi-product, multi-market exposures into one number
Uses risk factors and correlations to create a risk weighted index
Monitors VaR limits
Meets external risk management disclosure and expectations.
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5. Capital Adequacy
Capital Adequacy is a measure to check the stability of an institution to withstand financial
shocks due to exposures into various risks. Banks maintain a prescribed minimum capital in
the form of ‘Capital to Risk Adequacy Ratio (CRAR)’ in order to cover the aforesaid risks.
Reserve Bank of India decided in April 1992 to introduce a risk asset ratio system for banks
(including foreign banks) in India as a capital adequacy measure.
The Basle Committee on Banking Supervision (BCBS)’s ‘New Framework on Capital
Adequacy (NCAF) takes into account the elements of credit, market & operational risk in
various types of assets in the balance sheet as well as off-balance sheet business and also to
strengthen the capital base of banks. The Revised Framework consists of three-mutually
reinforcing Pillars, viz. minimum capital requirements, supervisory review of capital
adequacy, and market discipline. The BCBS recommends 3 distinct Pillars viz, Pillar 1,2 & 3
for computing the minimum Capital Charge, Supervisory Review and Market Discipline
respectively.
BASEL REQUIREMENT
MINIMUM CAPITAL REQUIREMENT
Pillar 1
CREDIT RISK OPERATIONAL RISK MARKET RISK
SUPERVISORY REVIEW
Pillar 2
MARKET DISCIPLINE
Pillar 3
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The Standardized Approach is the most widely used approach to compute the capital charge
requirement for Credit, Operational and Market Risks. Having regard to the necessary up-
gradation of risk management framework as also capital efficiency likely to accrue to the
banks by adoption of the advanced approaches envisaged under the Basel II Framework and
the emerging international trend in this regard, it was considered, in July 2009, desirable to
lay down a timeframe for implementation of the advanced approaches in India. This would
enable banks to plan and prepare for their migration to the advanced approaches for
computing capital charge. Keeping in view the likely lead time that may be needed by banks
for creating the requisite technological and the risk management infrastructure, including the
required databases, the MIS and the skill up-gradation, etc., the following time schedule has
been laid down for implementation of the advanced approaches for the regulatory capital
measurement.
Accordingly, the banks were advised to undertake an internal assessment of their
preparedness for migration to advanced approaches, in the light of the criteria envisaged in
the Basel II document, as per the aforesaid time schedule, and take a decision, with the
approval of their Boards, whether they would like to migrate to any of the advanced
approaches.
25
Capital Funds
The RBI prescribes Capital funds are broadly classified as Tier I and Tier II capital. Tier I
capital is basically the quality capital whereas Tier II Capital is just a supplementary capital.
Elements of Tier II capital will be reckoned as capital funds up to a maximum of 100 per cent
of Tier I capital.
Elements of Tier I capital
For Indian banks
1. Paid-up equity capital, statutory reserves, and other disclosed free reserves
2. Reserves representing surplus arising out of sale proceeds of assets
3. Innovative perpetual debt instruments (IPDI) & Perpetual Non-Cumulative Preference
Shares (PNCPS)
For foreign banks in India
1. Interest-free funds from Head Office kept in a separate account
2. Statutory reserves kept in Indian books
3. Interest-free funds remitted from abroad for the purpose of acquisition of property and
held in a separate account
4. Capital reserve representing surplus arising out of sale of assets in India held in a
separate account and which is not eligible for repatriation so long as the bank functions
in India.
Limits on eligible Tier I Capital
1. IPDI’s eligible to be reckoned as Tier I capital, will be limited to 15 percent of total Tier
I capital
2. PNCPS’s along with Innovative Tier I instruments shall not exceed 40 per cent of total
Tier I capital at any point of time
3. Innovative instruments / PNCPS, in excess of the limit shall be eligible for inclusion
under Tier II
26
Elements of Tier II Capital
1. Revaluation Reserves
2. General Provisions and Loss Reserves
3. Hybrid Debt Capital Instruments
4. Subordinated Debt
5. Excess of IPDI’s &PNCPS’s
Limits on Tier II Capital
1. Upper Tier II instruments along with other components of Tier II capital shall not
exceed 100 per cent of Tier I capital
2. Subordinated debt instruments eligible for inclusion in Lower Tier II capital will be
limited to 50 percent of Tier I capital after all deductions
Capital to Risk Weighted Assets Ratio – CRAR are a measure of the amount of a
bank's core capital expressed as a percentage of its risk-weighted asset.
Capital adequacy ratio is defined as
Tier I CRAR = Eligible Tier I capital funds
Credit Risk RWA* + Market Risk RWA +
Operational Risk RWA
Total CRAR = Eligible total capital funds
Credit Risk RWA + Market Risk RWA
+ Operational Risk RWA
27
5.1 Calculation Of Capital Charge (Market Risks) For The Investments Treasury
The focus area of this project work would be primarily about the computation of capital
charge for market risk.
Market risk is defined as the risk of losses in on-balance sheet and off-balance sheet positions
arising from movements in market prices. The market risk positions subject to capital charge
requirement are: The risks pertaining to interest rate related instruments and equities in the
trading book; and
Foreign exchange risk (including open position in precious metals) throughout the bank (both
banking and trading books).
The capital charge for interest rate related instruments and equities would apply to current
market value of these items in bank’s trading book. Since banks are required to maintain
capital for market risks on an ongoing basis, they are required to mark to market their trading
positions on a daily basis. The current market value will be determined as per extant RBI
guidelines.
The minimum capital requirement is expressed in terms of two separately calculated charges:
“Specific Risk” charge for each security, which is designed to protect against an adverse
movement in the price of an individual security owing to factors related to the individual
issuer, both for short (short position is not allowed in India except in derivatives) and long
positions, and “General Market Risk” charge towards interest rate risk in the portfolio,
where long and short positions (which is not allowed in India except in derivatives) in
different securities or instruments can be offset.
For the debt securities held under AFS category, in view of the possible longer holding period
and attendant higher specific risk, the banks shall hold total capital charge for market risk
equal to or greater of:
28
a) Specific risk capital charge, computed notionally for AFS securities treating them as
held under HFT category plus the General Market Risk Capital Charge (as per Table 3
- Part A/C/E as applicable)
b) Alternative total Capital Charge for the AFS category computed notionally by treating
them as held in the banking book ( as computed in accordance with Table 3- Part
B/D/F as applicable)
Trading book for the purpose of capital adequacy will include:
(i) Securities included under the Held for Trading category
(ii) Securities included under the Available for Sale category
(iii) Open gold position limits
(iv) Open foreign exchange position limits
(v) Trading positions in derivatives, and
(vi) Derivatives entered into for hedging trading book exposures.
Banks are required to manage the market risks in their books on an ongoing basis and ensure
that the capital requirements for market risks are being maintained on a continuous basis, i.e.
at the close of each business day. Banks are also required to maintain strict risk management
systems to monitor and control intra-day exposures to market risks.
• Specific Risk
• General Market Risk
Interest Rate Risk
Foreign Exchange Risk
• Specific Risk
• General Market Risk
Equity Risk
29
Specific Market Risk:
The capital charge for specific risk is designed to protect against an adverse movement
in the price of an individual security owing to factors related to the individual issuer.
The risk weights to be used in this calculation must be consistent with those used for
calculating the capital requirements in the banking book. Thus, banks using the standardized
approach for credit risk in the banking book will use the standardized approach risk weights
for counterparty risks in the trading book in a consistent manner.
The specific risk charge where ‘Government’ or ‘Banks’ are counterparties will be as in
Table 3 - Part A/B/C/D as applicable.
The Specific Charge for all the other securities will be determined by the applicable risk
weights assigned to them by the chosen external rating agencies as per Table 3- Part E/ F.
The debt instruments which are eligible for inclusion as regulatory capital for capital
adequacy purposes issued by banks which are meeting the minimum regulatory CRAR
requirement (Tier 2 Bonds) have 9% Specific Risk Capital Charge.
Specific risk charges for various kinds of exposures viz;
1) Central, State and Foreign Central Governments’ bonds (T-Bills)
2) Banks’ Bonds (CODs)
3) Corporate Bonds and Securitised debt (Debentures)
30
Table 3 – Part A: Specific Risk Capital Charge for Sovereign securities issued by Indian and
Foreign Sovereigns – Held by banks under HFT Category
Sr.No. Nature of investment Maturity
Specific risk capital
(as a % of
exposure)
A Indian Central Government and State Governments
1 Investment in Central Government and State
Government Securities All 0.0
2 Investments in other approved securities guaranteed
by Central Government All 0.0
3 Investments in other approved securities guaranteed
by State Government
6 months or
less 0.28
6-24 months 1.13
< 24 months 1.8
4
Investment in other securities where payment of
interest and repayment of principal are guaranteed
by Central Government
All 0.0
5
Investments in other securities where payment of
interest and repayment of principal are guaranteed
by State Government
6 months or
less 0.28
6-24 months 1.13
More than
24 months 1.8
B Foreign Central Governments
1 AAA to AA All 0.00
2 A to BBB
6 months or
less 0.28
6-24 months 1.13
More than
24 months 1.8
3 BB to B All 9.00
4 Below B All 13.50
31
Table 3 - Part B: Capital Charge for securities issued by Indian and Foreign Sovereigns –
Held by Banks under AFS Category
Sr.No. Nature of investment Maturity
Total Capital
Charge (as a
% of exposure)
A Indian Central Government and State Governments
1 Investment in Government Securities All 0.0
2 Investments in other approved securities guaranteed by
Central Government All 0.0
3 Investments in other approved securities guaranteed by
State Government All 1.8
4
Investment in other securities where payment of
interest and repayment of principal are guaranteed by
Central Government
All 0.0
5
Investments in other securities where payment of
interest and repayment of principal are guaranteed by
State Government
All 1.8
B Foreign Central Governments
1 AAA to AA All 0.00
2 A All 1.80
3 BBB All 4.50
4 BB to B All 9.00
5 Below B All 13.50
Unrated All 13.50
32
Table 3 - Part C: Specific Risk Capital Charge issued by Scheduled Banks meeting minimum
CRAR requirements – Held by Banks under HFT Category
Sr.No. Nature of investment Residual
Maturity
Specific risk
capital (as a
% of
exposure)
1
Claims on banks, including investment in securities
which are guaranteed by banks as to payment of interest
and repayment of principal provided the counterparty
bank is meeting the minimum regulatory CRAR
requirement.
6 months or
less 0.28
6 to 24
months 1.13
exceeding
24 months 1.8
Table 3- Part D: Alternative Capital Charge – for Bonds issued by Scheduled Banks meeting
minimum CRAR requirements- Held By Banks under AFS Category
Sr.No. Nature of investment Residual
Maturity
Total
Capital
Charge (as
a % of
exposure)
1
Claims on banks, including investment in securities
which are guaranteed by banks as to payment of interest
and repayment of principal provided the counterparty
bank is meeting the minimum regulatory CRAR
requirement.
All 1.8
33
Table 3: Part E: Specific Risk Capital charge for Corporate Bonds (other than Bank Bonds) –
Held By Banks under HFT Category.
Long term ratings
of chosen credit
rating agencies
operating in India
Residual
Maturity
Specific
Risk
Capital
Charge
AAA to BBB
< 6 months 1.8
6-24
months 2.7
>24 months 4.5
BBB All 9
BB & Below All 13.5
34
Table 3 - Part F: Capital charge for Corporate Bonds (other than Bank Bonds) – Held By
Banks under AFS Category.
Long term ratings of
chosen credit rating
agencies operating in
India
Total
Capital
Charge
AAA 1.8
AA 2.7
A 4.5
BBB 9
BB & Below 13.5
Unrated 13.5
The above table illustrates the amount of ‘Specific Risk Capital Charge for Sovereign
securities issued by Indian and foreign sovereigns – Held by banks under several categories’.
Depending on the banks nature of investment into specific instruments, the total capital
charge would be a weighted sum of individual instruments multiplied by specific risk capital
charge. Similarly, RBI prescribes specific risk capital charge in the AFS category as well.
General Market Risk
The capital requirements for general market risk are designed to capture the risk of loss
arising from changes in market interest rates.
Methodologies
Standard Method
Maturity Method
Modified Duration
Internal Methods
35
The standardized methods there are two principal methods of measuring market risk, a
“maturity” method and a “duration” method. As “duration” method is a more accurate
method of measuring interest rate risk, it has been decided to adopt standardised duration
method to arrive at the capital charge. Accordingly, banks are required to measure the general
market risk charge by calculating the price sensitivity (modified duration) of each position
separately.
Under this method, the mechanics are as follows:
Calculate the price sensitivity (modified duration) of each instrument
Duration (Macaulay duration) measures the price volatility of fixed income securities. It is
often used in the comparison of the interest rate risk between securities with different
coupons and different maturities. It is the weighted average of the present value of all the
cash flows associated with a fixed income security. It is expressed in years. The duration of a
fixed income security is always shorter than its term to maturity, except in the case of zero
coupon securities where they are the same.
Macaulay duration = PVCF x t
PVCF
The modified duration or volatility of an interest bearing security is its Macaulay duration
divided by one plus the coupon rate of the security. It represents the percentage change in a
securities' price for a 100 basis points change in yield. It is generally accurate for only small
changes in the yield.
MD = - dP x 1
dY P
The weighted duration is computed by multiplying the modified duration of the security with
the market exposure. The capital charge for general market risk would be the product of the
weighted duration and the assumed change in yield as explained below.
36
The assumed change in yield to the modified duration of each instrument between 0.6 and 1.0
percentage points depending on the maturity of the instrument
Slot the resulting capital charge measures into a maturity ladder with the fifteen time
bands as set out.
Subject long and short positions (short position is not allowed in India except in
derivatives) in each time band to a 5% vertical disallowance designed to capture basis
risk
Carry forward the net positions in each time-band for horizontal offsetting subject to
the disallowances set out.
37
Computation of Capital Charge
38
Proforma of consolidated calculation of Capital Charge for Market Risk
The following table shows the CRAR of Federal bank for 2012-13 which is maintained at
16.64% .
Capital 2011-12 2010-11 Growth
Equity Capital 171.05 171.05
Net Worth 5706.33 5108.66 11.70%
Capital Adequacy Ratio 16.64 16.79
Tier 1
Tier 2
15.86 15.63
0.78 1.16
This means that 16.64% of the Bank’s total Capital is maintained for the purpose of Capital
Adequacy. We can look at the glass half empty or half full. One that the bank is very
conservative in their approach and they are not capitalizing on their opportunity i.e.
misallocating the capital as a result. Second, the bank is well prepared to withstand huge
financial shocks due to the high CRAR maintained.
39
5.2 Pillar II- Supervisory Review and Evaluation Process (SREP)
The objective of the SRP is to ensure that banks have adequate capital to support all the risks
in their business as also to encourage them to develop and use better risk management
techniques for monitoring and managing their risks. This in turn would require a well-defined
internal assessment process within banks through which they assure the RBI that adequate
capital is indeed held towards the various risks to which they are exposed. The process of
assurance could also involve an active dialogue between the bank and the RBI so that, when
warranted, appropriate intervention could be made to either reduce the risk exposure of the
bank or augment / restore its capital. Thus, ICAAP (Internal Capital Adequacy Assessment
Process) is an important component of the SRP.
The main aspects to be addressed under the SRP, and therefore, under the ICAAP, would
include:
(a) the risks that are not fully captured by the minimum capital ratio prescribed under Pillar 1
(b) the risks that are not at all taken into account by the Pillar 1
(c) the factors external to the bank.
Since the capital adequacy ratio prescribed by the RBI under the Pillar 1 of the Framework is
only the regulatory minimum level, addressing only the three specified risks (viz., credit,
market and operational risks), holding additional capital might be necessary for banks, on
account of both – the possibility of some under-estimation of risks under the Pillar 1 and the
actual risk exposure of a bank vis-à-vis the quality of its risk management architecture.
Illustratively, some of the risks that the banks are generally exposed to but which are not
captured or not fully captured in the regulatory CRAR would include:
(a) Interest rate risk in the banking book;
(b) Credit concentration risk;
(c) Liquidity risk;
(d) Settlement risk;
(e) Reputational risk;
(f) Strategic risk;
(g) Risk of under-estimation of credit risk under the Standardised approach;
(h) “Model risk” i.e., the risk of under-estimation of credit risk under the IRB approaches;
(i) Risk of weakness in the credit-risk mitigants;
(j) Residual risk of securitisation, etc.
40
It is, therefore, only appropriate that the banks make their own assessment of their various
risk exposures, through a well-defined internal process, and maintain an adequate capital
cushion for such risks.
Banks were advised to develop and put in place, with the approval of their Boards, an ICAAP
commensurate with their size, level of complexity, risk profile and scope of operations. The
ICAAP, which would be in addition to a bank’s calculation of regulatory capital requirements
under Pillar 1, has been operationalised with effect from March 31, 2008 by the foreign banks
and the Indian banks with operational presence outside India, and from March 31, 2009 by all
other commercial banks, excluding the Local Area Banks and Regional Rural banks.
The ICAAP Document would be a comprehensive Paper furnishing detailed information on
the ongoing assessment of the bank’s entire spectrum of risks, how the bank intends to
mitigate those risks and how much current and future capital is necessary for the bank,
reckoning other mitigating factors. The purpose of the ICAAP document is to apprise the
Board of the bank on these aspects as also to explain to the RBI the bank’s internal capital
adequacy assessment process and the banks’ approach to capital management. The ICAAP
could also be based on the existing internal documentation of the bank. The ICAAP
document should, inter alia, include the capital adequacy assessment and projections of
capital requirement for the ensuing year, along with the plans and strategies for meeting the
capital requirement.
The ICAAP Document should contain the following sections:
I. Executive Summary
II. Background
III. Summary of current and projected financial and capital positions
IV. Capital Adequacy
V. Key sensitivities and future scenarios
VI. Aggregation and diversification
VII. Testing and adoption of the ICAAP
VIII. Use of the ICAAP within the bank
41
5.3 Pillar III- Market Discipline
The purpose of Market discipline in the Revised Framework is to complement the minimum
capital requirements ( Pillar I and the supervisory review process detailed under Pillar 2).
The aim is to encourage market discipline by developing a set of disclosure requirements
which will allow market participants to assess key pieces of information on the scope of
application, capital, risk exposures, risk assessment processes, and hence the capital adequacy
of the institution.
It facilitates assessment of the bank by others including investors, analysts, customers, other
banks and rating agencies which leads to good corporate governance.
Operates by requiring institutions to disclose details on the scope of application, capital, risk
exposures, risk assessment processes and the capital adequacy of the institution
Qualitative disclosures providing a summary of the general risk management objectives and
policies which can be made annually
The following sections are the disclosure requirements under Pillar 3.
Scope of Application
Capital Structure
Capital Adequacy
Credit Risk: General Disclosures for All Banks
Credit Risk: Disclosures for Portfolios Subject to the Standardised Approach
Credit Risk Mitigation: Disclosures for Standardised Approaches
Securitization Exposures: Disclosure for Standardised Approach
Market Risk in Trading Book
Operational Risk
Interest Rate Risk in the Banking Book (IRRBB)
42
6. Internal Models Approach (IMA)
Basel II Framework offers a choice between two broad methodologies in measuring market
risks for the purpose of capital adequacy. One methodology is to measure market risks in a
standardised manner as per the Standardised Measurement Method (SMM) which is being
used by banks in India since March 31, 2005. The alternative methodology known as Internal
Models Approach (IMA) is also available which allows banks to use risk measures derived
from their own internal market risk management models. The permissible models under IMA
are the ones which calculate a value-at-risk (VaR)-based measure of exposure to market risk.
VaR-based models could be used to calculate measures of both general market risk and
specific risk. As compared to the SMM, IMA is considered to be more risk sensitive and
aligns the capital charge for market risk more closely to the actual losses likely to be faced by
banks due to movements in the market risk factors. The alternative method, viz., the IMA
envisages use of banks’ own internal market risk management models for deriving risk
measures for determining regulatory capital requirements for market risk, after the internal
models have been approved by the supervisor. Compared to the SMM, the IMA is considered
to be more risk sensitive and aligns the capital charge for market risk more closely to the
actual losses likely to be incurred by banks due to movements in the market risk factors. With
a view, therefore, to provide a wider choice to banks in selecting a method for determining
the regulatory capital requirement for their market risk exposure, it was decided to introduce
the IMA in India.
Under the IMA, the capital requirement for market risk will consist of the following two
components, based on VaR measure:
a) General Market Risk Charge;
b) Specific Risk Charge [including Incremental Risks Charge (IRC) for interest rate
instruments]
The guidelines for the IMA will be applicable to:
a) The risks pertaining to interest rate-related instruments and equities in the trading book;
b) Exchange rate risk (including open position in gold) throughout the bank, that is, both in
the banking book and trading book;
43
[In the case of foreign currency instruments, including derivatives, in addition to the
exchange rate risk, the interest rate risk and equity price risk, as applicable, will also have to
be captured]; and
c) The risks relating to investments in mutual funds kept in trading book.
At present, the SMM is applicable to both Held-For-Trading (HFT) and Available for Sale
(AFS) portfolios. Generally, the positions held in the AFS are more illiquid and the market
prices for them may not be available or may be available with a very low frequency due to
low trading volumes. Therefore, it would not be feasible to compute meaningful VaR
measures for AFS portfolios. Accordingly, the “trading book” for the purpose of these
guidelines will consist of only Held-For-Trading (HFT) portfolio, which will also include
trading positions in derivatives and the derivatives transactions entered into for hedging
trading book exposures. The AFS portfolio should continue to be under SMM for
computation of capital charge for market risk.
Combination of SMM and IMA
The internal models approach will in principle require banks to have an integrated risk
measurement system that captures the broad risk factor categories (i.e. interest rates,
exchange rates (which may include gold), equity prices, with related options volatilities being
included in each risk factor category. However, if a bank’s exposure to a particular risk factor
is insignificant, it may request, in its letter of intent, exemption from application of standards
of these guidelines for that risk factor. For such factors RBI, may allow banks to use the
SMM for calculation of capital. However, banks which start to use models for one or more
risk factor categories will, over time, be expected to extend the models to all their market
risks. A bank which has developed one or more models will no longer be able to revert to
measuring the risk measured by those models according to the SMM (unless, of course, RBI
withdraws approval for that model). However, pending further experience regarding the
process of changing to a models-based approach, no specific time limit will be set for banks
now which use a combination of internal models and the SMM to move completely to IMA.
The conditions mentioned below will apply to banks using such combinations.
Banks can adopt the IMA for one or more of the broad risk factors and remain on SMM for
other risk factors. However, each broad risk factor category must be assessed using a single
approach (either internal models or the standardised approach), i.e. no combination of the two
methods will in principle be permitted within a risk category or across banks’ different
44
entities for the same type of risk. This flexibility will be subject to explicit approval of RBI
and will be reviewed regularly to ensure that there is no cherry-picking between SMM and
IMA within a risk factor category. Banks should progressively adopt IMA for all broad risk
factors so as to achieve integrated risk measurement system. In this regard, banks have to
produce before RBI a credible plan for extending IMA to entire spectrum of market risk
exposure.
No element of market risk may escape measurement, i.e. the exposure for all the various risk
factors, whether calculated according to the standardised approach or internal models would
have to be captured;
The capital charges assessed under the standardised approach and under the internal models
approach are to be aggregated according to simple summation.
45
7. Value at Risk (VaR)
VaR (Value-at-Risk) was introduced precisely with the purpose of providing a one
dimensional approximation of the infinitely dimensional risk. It provides an integrated way to
deal with different markets and different risks and to combine all of the factors into a single
number which is a good indicator of the overall risk level. The common measure used to
express market risk is ‘value-at-risk’ (VaR). The Table below shows the evolution of various
risk measurement tools that has been put forth to the financial world over the years.
“The greatest benefit of VAR lies in the imposition of a structured methodology
for critically thinking about risk. Institutions that go through the process of
computing their VAR are forced to confront their exposure to financial risks and
to set up a proper risk management function. Thus the process of getting to VAR
may be as important as the number itself.” -Philippe Jorion
Value-at-Risk (VaR) has been widely promoted by regulatory authorities as a way of
monitoring and managing market risk and as a basis for setting regulatory minimum capital
standards. The VAR revolution started in 1993 when it was endorsed by the Group of Thirty
(G-30) as part of “best practices” for dealing with derivatives. The methodology behind VaR,
however, is not new. It results from a merging of finance theory, which focuses on the pricing
and sensitivity of financial instruments, and statistics, which studies the behavior of the risk
factors. It is an attempt to provide a single number summarizing the total risk in a portfolio of
financial assets. It has become widely used by corporate treasurers and fund managers as well
as by financial institutions. Bank regulators also use VaR in determining the capital a bank is
required to keep for the risks it is bearing.
In its most general form, the Value at Risk measures the potential loss in value of a risky
asset or portfolio over a defined period for a given confidence interval. It is a measure of the
loss (expressed in say rupees crores) on the portfolio that will not be exceeded by the end of
the time period with the specified confidence level. If α is the confidence level and ‘T’ days is
the time period, the calculation of VaR is based on the probability distribution of changes in
the portfolio value over T days. Specifically, VaR is set equal to the loss in the portfolio at the
(1-α)*100 percentile point of the distribution. Thus, if the VaR on an asset is Rs 100 Crores at
a one-week, 95% confidence level, there is a only a 5% chance that the value of the asset will
drop more than Rs 100 Crores over any given week. Thus when applied in case of normal
market risk, VaR indicates the possible maximum loss which will be suffered in a specified
46
period and at a specified confidence level from a fall in the price of security or exchange rate,
given historic data on the price behaviour of the security or assessment of likely future market
movements. It is a probability that specifies that the loss won’t exceed a particular amount.
The relationship between probability level p and confidence level α is described as α=100*(1-
p).VaR is an estimate of the potential loss, always for a given period at a given confidence
level. This concept is applied to calculate risk content of an individual security, foreign
exchange position, equity share or a portfolio of these instruments.
Table 3: Defining Value at risk
The inputs used to calculate VaR for a certain asset are the volatility, time horizon and a
choice of confidence level (α) and the current MTM position (W). The volatility is estimated
implicitly from option pricing or through statistical models (ϭ). In practice, past observations
are often used to estimate the future volatility. The time period (√T) chosen affects both the
measured volatility and therefore also the VaR, where a longer time period gives a higher
volatility measure and hence, a higher VaR.
The chosen confidence interval states how often the loss on the specific asset will be greater
than the VaR. The most commonly used confidence intervals are 95% and 99%. The formula
to calculate VaR for one asset is:
VaR = α ϭ W√T
To calculate the portfolio VaR the formula below is used:
This methodology uses the above formulae in calculating VaR It is also called delta normal
or VAR COVAR or variance method.
47
7.1 VaR PARAMETERS
1. CONFIDENCE LEVEL
To measure VAR, we first need to define two quantitative parameters, the confidence level
and the horizon. It can be seen that higher the confidence level, the greater the VAR
measure. Varying the confidence level provides useful information about the return
distribution and potential extreme losses. It is not clear, however, whether one should stop
at 99%, 99.9%, 99.99% and so on. Each of these values will create an increasingly larger
loss, but less likely. Another problem is that, as increases, the number of occurrences below
VAR shrinks, leading to poor measures of large but unlikely losses. The choice of the
confidence level depends on the use of VAR. For most applications, VAR is simply a
benchmark measure of downside risk. If so, what really matters is of the VAR confidence
level across trading desks or time. The usual recommendation is to pick a confidence level
that is not too high, such as 95 to 99 percent.
2. HORIZON
It is seen that longer the horizon (T), greater the VaR measure. This extrapolation depends
on two factors, the behaviour of the risk factors, and the portfolio positions. To extrapolate
from a one-day horizon to a longer horizon, we need to assume that returns are
independently and identically distributed. This allows us to transform a daily volatility to
multiple-day volatility by multiplication by the square root of time. We also need to assume
that the distribution of daily returns is unchanged for longer horizons, which restricts the
class of distribution to the so-called “stable” family, of which the normal is a member. VaR
has two parameters: the time horizon N, measured in days, and the confidence level X. In
practice, analysts almost invariably set N = 1 in the first instance. This is because there is
not enough data to estimate directly the behavior of market variables over periods of time
longer than I day. The usual assumption is
N-day VaR = 1-day VaR x√ N
This formula is exactly true when the changes in the value of the portfolio on successive days
have independent identical normal distributions with mean zero. In other cases its is an
approximation.
48
The Basel committee for Banking Supervision recommends calculation of capital for trading
book using VaR measure with N=10 & X=99%. This means that it focuses on revaluation
losses over a 10 day period which is expected to exceed only 1% of the times. The capital it
requires the bank to hold is k times this VaR measure. The multiplier k varies from bank-to-
bank basis and RBI recommends that it must be atleast 3. Federal Bank uses this VaR
multiplier and subsequently increases the value for higher level of exceptions as explained
under Back Testing.
Given the way a 10-day VaR is calculated, this minimum capital level is 3 x √10 = 9.49
times the 1-day 99% VaR.
If so, we have
VaR (T days) = VaR (1 day) * √T
This requires
(1) The distribution to be invariant to the horizon (i.e., the same, as for the normal),
(2) The distribution to be the same for various horizons (i.e., no time decay in
variances), and
(3) VaR can be extended from a 1 day horizon to days by multiplication by the square root of
time.
This adjustment is valid with i.e. returns that have a normal distribution. The choice of the
horizon also depends on the characteristics of the portfolio. If the positions change quickly, or
if exposures (e.g., option deltas) change as underlying prices change, increasing the horizon
will create “slippage” in the VaR measure. Again, the choice of the horizon depends on the
use of VaR. If the purpose is to provide an accurate benchmark measure of downside risk, the
horizon should be relatively short, ideally less than the average period for major portfolio
rebalancing. In contrast, if the VaR number is being used to decide how much capital to set
aside to avoid bankruptcy, then a long horizon is advisable. Typically, banks measure P&L on
a daily basis, and corporate on a longer interval (ranging from daily to monthly). This interval
is the minimum horizon for VaR.
49
7.2 VaR Models
Essentially there are three VaR models ,i.e. Parametric ,Non Parametric and Semi Parametric
Models .While Historic Simulation method comes under Non Parametric method ,the
Variance –Co variance method , Risk Metrics( Delta Normal Method) ,GARCH etc models
comes in Parametric models . Extreme Value Theory, Quasi Maximum GARCH comes under
the Semi Parametric model types. Although there are numerous methods of calculating VaR,
the 3 main methods are Historic Simulation Method, Variance – co variance method and
Monte Carlo simulation method are the most popular.
(A) Variance –Co Variance Method
The simplest possible VaR method is the normal (covariance) method. This is a parametric
method, based on the assumption that the returns are normally distributed. Historical data is
used to measure the major parameters: means, standard deviations, correlations. The overall
distribution of the market parameters is constructed from this data. Using the risk mapping
technique, the distribution of the profits and losses over the time horizon (typically one day)
can be found. When the market value of the portfolio is a linear function of the underlying
parameters, the distribution of the profits is normal as well.
Therefore, the 5% quantile corresponding to VaR can be calculated at 1.65ϭ· below the mean
(2.33ϭ will give the 1% level).
For example, consider the returns of Nifty Index Fund, which is Normally distributed over
the Horizon. The average return of the fund is 8% with a standard deviation of 4%. The 99%
VaR for the portfolio can be computed as 99%VaR= -Z * ϭ
i.e -2.33 * 4= -9.32%. This means that, 99% of the times, the portfolio would give a returns
of more than -9.32%. However, 1% of the times, the losses would exceed 9.32%.
In case of two assets, the standard deviation is calculated as follows,
ϭ ϭ
Where, is the correlation co-efficient between the 2 assets.
50
Advantages:
The Variance – Covariance Method is easy to implement because it involves a simple matrix
multiplication. It is also computationally fast, even with a large number of assets, because it
replaces each position by its linear exposure. Portfolios that are linear combinations of
normally distributed risk factors are themselves normally distributed. It only requires the
market values and exposures of current positions, combined with risk data. Also, in many
situations, the delta-normal method provides adequate measurement of market risks. As a
parametric approach, VaR is easily amenable to analysis, since measures of marginal and
incremental risk are a by-product of the VaR computation.
Disadvantages:
A first problem is the existence of fat tails in the distribution of returns on most financial
assets. These fat tails are particularly worrisome precisely because VaR attempts to capture
the behaviour of the portfolio return in the left tail. In this situation, a model based on a
normal distribution would underestimate the proportion of outliers and hence the true Value-
at-Risk.
Another problem is that the method inadequately measures the risk of nonlinear instruments,
such as options or mortgages. Asymmetry in the distribution of options is not captured by the
Variance-Covariance Method.
(B)Historical Simulation Method
The historic simulation method for calculating VaR is the simplest and avoids some of the
pitfalls of the correlation method. Specifically the three main assumptions behind correlation
(normally distributed returns, constant correlations, and constant deltas) are not needed in
this case. It involves using past data in a very direct way as a guide to what might happen in
the future. We apply the current weights to the historical asset returns by going back in time
such as over the last 100 days. A distribution of portfolio returns is obtained. These portfolio
returns are then sorted and depending on the target probability the corresponding quantile of
the distribution is taken. This gives us the 1-day VaR using Historical Simulation method.
Historical simulation calculates potential losses using actual historical returns in the risk
factors and so captures the non-normal distribution of risk factor returns. This means rare
events and crashes can be included in the results. As the risk factor returns used for revaluing
the portfolio are actual past movements, the correlations in the calculation are also actual
51
past correlations. They capture the dynamic nature of correlation as well as scenarios when
the usual correlation relationships break down. Historical VaR
For eg, the Nifty returns of 500 historical days is plotted. The distribution would be most
likely normal. In order to compute, 95%, the least 5% returns of the portfolio is taken. Which
is the 25th
value of the return from the left end- 5th
percentile of the distribution return.
Advantages:
Historical simulation method is relatively simple to implement if the past data is readily
available for estimating Value-at-Risk. It is not necessary that the distribution is linear and
normal as it relies on the actual prices. It does not rely on underlying stochastic structure of
the market or any specific assumptions about valuation models. Historical simulation method
does not rely on valuation models and is not subjected to the risk that the models are wrong.
Disadvantages:
The Historical Simulation method assumes the availability of sufficient historical price data.
This is a drawback because some of the assets may have a short history or in some cases no
history at all. It is also probable that the institution may not store data that much farther into
the past. There is also an assumption that the past represents the immediate future which is
not always true. In case of unanticipated events the VaR calculated may not hold true. The
Historical Simulation method quickly becomes cumbersome for large portfolios with
complicated structures.
52
7.3 Interpretation of VaR
Historical Simulation: The Historical returns of 744 days for a Rs1000 Crore investment in
the index funds of SENSEX and NIFTY were computed. For computing 95% VaR (5%
level of significance), the 5th worst percentile return i.e (5% of 744= 37th worst) value is
taken. Assuming, an average 1 day VaR for SENSEX &NIFTY are -20.1052 and -20.1606
respectively means that, 95% of the times, the losses from the portfolio would be less than
Rs 20.1052 crores for SENSEX and Rs 20.1606 crores for NIFTY. There is 5% of a chance
that the loss might exceed this value. This means that the risk involved in having a portfolio
with an average return of 0.10% as computed would be Rs 20.16 crores.
To compute the 10 day VaR from the 1 day VaR, we simply use the square root rule and
multiply the computed 1 Day VaR by sqrt of 10 i.e
10 day, 95% VaR for SENSEX = 1 day , 95% VaR * sqrt(10) = Rs 63.578 crores
Similarly, the VaR can be computed for US Dollar returns as obtained is Rs -7.699 crores for
a Rs1000 crore investment in the Dollar market.
A combined portfolio VaR is also computed by firstly calculating the total Return on the
portfolio containing Index funds(Nifty+SENSEX) and USD, and then the 95% VaR, the 5th
worst percentile return i.e (5% of 744= 37th worst) value is taken. The average 1 day VaR
for the Portfolio is Rs -32.010199 crores. This means that, 95% of the times, the losses from
the portfolio would be less than Rs 32.010199 crores. There is 5% of a chance that the loss
might exceed this value.
Std Dev MODEL BUILDING HISTORICAL
Nifty 12.01359 -19.82241727 -20.1606
Sensex 11.86539 -19.57789744 -20.1052
USD 5.273917 -8.701963601 -7.69935
Nif+USD 13.66105 -22.54073349
Sen+USD 13.44398 -22.1826
Total PF 18.11964 -31.103 -32.010199
53
1. Model Building Approach (MBA): The MBA uses Variance of the returns for the
purpose of computing the VaR. As we know that the returns are normally distributed,
the probability of a loss being more than the VaR value can be easily computed by
multiplying the standard deviation of the return with the value for Z= 95 % i.e -1.65
(The negative sign indicates the loss in the Left tail of the distribution). The Standard
deviations of the returns of SENSEX, NIFTY, USD and total Portfolio, is calculated.
The individual VaR’s is calculated as,
95% VaR = z * std dev (z= -1.65 for 95% left tail distribution)
Index
Funds USD
Index Funds 1 -
USD 0.01249 1
For calculating the Portfolio VaR, of a portfolio containing two kinds of security (Index funds
& USD), the combined standard deviation for a two-asset portfolio is calculated as
ϭ ϭ
where = correlation coefficient between the 2 securities.
0 10 20 30 40 50 60 70 80
Fre
qu
en
cy
Returns
Histogram
Frequency
5% Probablity of Loss
more than Rs. 32.01
54
The 95 % VaR for a combined NIFTY +USD and SENSEX +USD is computed by the above
mentioned method as Rs -22.54073349 crores and Rs -22.1826 crores respectively. Similarly
the combined Portfolio VaR of Index funds + USD is computed as Rs -31.103 crores. The
results obtained by the 2 methods are as tabled and we see that there is a slight variation in
the values.
Computation of VaR for equity portfolios:
Geetanjali Vs Dollar
Correlation
Geetanjali Dollar
Geetanjali 1 ---
Dollar 0.007396725 1
Std Dev
MODEL
BUILDING HISTORICAL
Geetanjali 18.62620694 -30.73324145 -26.56546009
Dollar 5.564639167 -9.181654626 -6.958062428
PF 19.47906844 -32.14046293 -27.63959236
0
20
40
60
80
100
120
140
-82
.02
73
37
56
-71
.75
34
70
04
-61
.47
96
02
53
-51
.20
57
35
01
-40
.93
18
67
49
-30
.65
79
99
97
-20
.38
41
32
46
-10
.11
02
64
94
0.1
63
60
25
8
10
.43
74
70
1
20
.71
13
37
62
30
.98
52
05
13
41
.25
90
72
65
51
.53
29
40
17
61
.80
68
07
69
72
.08
06
75
2
82
.35
45
42
72
92
.62
84
10
24
10
2.9
02
27
78
11
3.1
76
14
53
12
3.4
50
01
28
Mo
re
Fre
qu
en
cy
Returns
Geetanjali Vs Dollar
Frequency
55
Coal India Vs NTPC
Correlation
CIL NTPC
CIL 1 -
NTPC 0.04262 1
Std Dev
MODEL
BUILDING HISTORICAL
CIL 19.98245163 -32.97104518 -28.9162
NTPC 15.11237807 -24.93542381 -24.1886
PF 24.53452041 -40.48195867 -39.4078
0 10 20 30 40 50 60 70 80
-68
.69
35
78
85
-58
.98
10
41
87
-49
.26
85
04
89
-39
.55
59
67
92
-29
.84
34
30
94
-20
.13
08
93
97
-10
.41
83
56
99
-0.7
05
82
00
13
9.0
06
71
69
63
18
.71
92
53
94
28
.43
17
90
92
38
.14
43
27
89
47
.85
68
64
87
57
.56
94
01
84
67
.28
19
38
82
76
.99
44
75
8
86
.70
70
12
77
96
.41
95
49
75
10
6.1
32
08
67
Mo
re
Fre
qu
en
cy
Returns
CIL Vs NTPC
Frequency
56
7.4 Back Testing of VaR:
Back testing is an important part of VaR model validation which involves comparing the
number of instances when the actual Profit/Loss exceeds the VaR level (called exceptions)
with the number predicted by the model at the chosen level of confidence.
For Eg. If a VaR of 10million is calculated at 95% confidence Level, we expect to have
exceptions (losses) exceeding 10 million i.e 5% of the time. If exceptions are occurring with
greater frequency, we are underestimating the actual Risk, and if exceptions are occurring
within the acceptable level, then we are overestimating the actual Risk and misallocating
capital as a result.
Basel Committee rules for Back Testing :
The Basel committee for Banking supervision (BCBS) rules attempts to strike a balance
between Type I error (reject the return which is in the acceptable range) and a Type II error
(accepting the unacceptable/exceptions). The committee recommends the market VaR to be
calculated at 99% confidence level and back tested over the past years. Say at 99%
confidence level we would normally expect to have (over 250 days period 2.5 exceptions) i.e.
1% of 250. In order to compensate for using inaccurate models (skewed data) the committee
has established a scale of the number of exceptions and corresponding increases in the capital
multiplier k.
The bank classifies its back-testing outcomes into the following three zones depending on the
number of exceptions arising from back-testing:
Zone 1 Green: If the back-testing results produce four or fewer exceptions, it falls within the
Green Zone and there may not be any increase in the multiplication factor beyond minimum
three for both VaR and stressed VaR as mentioned in the guidelines.
Zone 2 Yellow: If the back-testing results produce five to nine exceptions, it falls within the
Yellow Zone and there would be an increase in the multiplication factors for both VaR and
stressed VaR as mentioned in the Table below.
Zone 3 Red: If the back-testing results produce ten or more exceptions, it falls within the Red
Zone and the multiplication factors for both VaR and stressed VaR will be increased from
57
three to four. RBI will allow 10 or more exceptions under the most extraordinary
circumstances. RBI may require banks whose model for market risk fall in Red Zone to either
discontinue the model or begin work on improving the model immediately. RBI may also
consider further increase in the capital requirements if the bank is not able to demonstrate that
its models are capturing all market (general market risk and specific risk, if any) risks it is
exposed to.
Zone Number of exceptions Multiplier (k)
Green 0-4 3.00
Yellow 5 3.40
6 3.50
7 3.65
8 3.75
9 3.85
Red 10 or more 4.00
The bank normally recommends a multiplier of k which subsequently increases to 4 based on
the accuracy of the bank’s VaR model. Increase in k significantly increases the amount of
capital the bank must hold and lowers the banks performance measures like ROE.
The penalty (raising the multiplier from 3 to 4) is automatically required for banks with 10 or
more exceptions. The committee suggests 4 categories of causes for the exceptions as
1. The basic integrity of the model is lacking, exceptions occur because of incorrect data
or errors in the model programming.
2. Model accuracy needs improvement, exceptions occur because the model does not
accurately describe risks.
3. Intraday trading activity, the exceptions occur due to trading activity i.e. the VaR is
based on static portfolios.
4. Bad luck, the exceptions occur market conditions (volatility and correlations among
financial instruments) significantly varied from the accepted norms.
58
7.5 Expected shortfall
A major limitation of the VaR measure is that it does tell the investor the amount or
magnitude of the actual loss. VaR only provides the maximum value we can loose for a given
confidence level. The expected shortfall (ES) provide the estimate of the tail loss by
averaging the VaRs for increasing the confidence levels in the tail. Specifically, the tail mask
is divided into n equal slices and the corresponding (n-1) VaRs are computed. For example if
n=5 we construct a table as below based on the normal distributions.
We observe that VaR increases (from difference column) in order to maintain the same
interval mass of 1% because the tail becomes thinner and thinner. The average of the 4
computed VaRs is 2.003 and represents the probability weighted expected loss (ES). Note
that as n increases, the ES will increase and approach the theoretical true loss (2.063 in this
case, the average of the high numbers of VaRs).
Confidence Level VaR Difference
96% 1.7507
97% 1.8808 0.1301
98% 2.0537 0.1729
99% 2.3263 0.2726
Average 2.003
Theoretical true value 2.063
59
8. Learning and Limitations
Due to the increasing importance of market risk management, commercial banks have
integrated market risk identification, measurement, monitoring and control with business
management activities such as strategic planning, business decision-making and financial
budgeting. For this purpose it is imperative that certain measures be taken.
The banks maintain an independent risk monitoring wing (Mid Office) in the Treasury
department which reports directly to the top management through Integrated Risk
Management Department (IRMD) department. This specialized risk department constantly
monitors the trades and deals and verifies and monitors each deal through an online
monitoring system.
The online monitoring system at Federal Bank follows a two-step process, as detailed below:
1. Monitor simultaneously and concurrently all the deals that are undertaken
2. Integrate and process data collected from the various sources and generate daily VaR
so as to effectively manage the risk exposure.
Thus the Mid Officer is a part of the IRMD and performs a role of an independent risk
oversight function. The relevant roles and responsibilities of this Mid Office would be clearly
established and demarcated.
Federal Bank constantly upgrades its Risk identifications and assessment methodologies.
They are on the path of setting up the state of the art, Risk Management Unit. However,
presently they are computing market risk capital through SMM. While Valuation is done
through their software they maintain the Valuation computations in Microsoft Excel for
various scenarios analysis. This indeed calls for high end statistical tools which they are in
process of acquiring for all the analysis. Implementing a specialized software which
streamlines the operations would increase overall efficiency and plug the loopholes, so that
the manual functions will be minimized
The RBI (based on the BASEL framework) has suggested banks to migrate from the
foundation approaches to the advanced methods of risk mitigation such as the Internal
Models approach (IMA) for Market Risk, Internal Rating Based (IRB) approach for Credit
60
Risk and Advanced Management Approach (AMA) for Operational Risk. The migration to
these methods is a slow and a gradual procedure which is the need of the hour for the Bank.
Federal Bank is working towards compliance of Basel III norms as prescribed by RBI,
which is a relatively an efficient practice for overall banking regulation and transparency.
Shortfalls/ Limitations to the Study:
1. Limited disclosure due to the confidential nature of the Treasury department and its
functioning.
2. Short duration of 2 months resulted in limited scope of the study
3. Due to the live nature of the dealing room and the level of secrecy maintained, the
study was limited to more theoretical information.
4. The RBI circulars which was used as a reference contained several sub-reference
circulars which were not easily available
61
9. References
1. RBI Master circulars
Implementation of Internal Models Approach for Market Risk
Cash Reserve Ratio (CRR) and Statutory Liquidity Ratio (SLR)
Asset Liability Management
New Capital Adequacy Framework
2. www.fimmda.org.in
3. www.investopedia.in
4. www.nse.in
5. NCFM reference module on Fixed Income Securities.
6. IDRBT Training Documents of Federal Banks
7. Options, Futures and other income Derivatives – John C Hull
8. Handbook of Treasury Operations-Federal Bank
