Bank Treasury

8/13/2019 Bank Treasury

1/61

1

TABLE OF CONTENTS

Sr.no. Particulars Page

No.

I Executive Summary 2

1Introduction to Treasury Management 3

2 The Federal Bank - An Overview5

2.1 The Federal Bank - Treasury Department6

3 Cash Credit Ratio & Statutory Liquidity Ratio

8

4 Asset Liability Management12

4.1 Models of ALM16

5 Capital Adequacy23

5.1 Calculation of Capital Charge (Market Risk)27

5.2 Pillar II : SREP39

5.3 Pillar III : Market Discipline41

6 Internal Model Approach (IMA)42

7 Value at Risk (VaR)45

7.1 VaR Parameters47

7.2 VaR Models49

7.3 Interpretation of VaR52

7.4 Backtesting of VaR 56

7.5 Expected Shortfalls58

8 Learnings and Shortfalls59

9 References61


2/61

2

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 Ri sk management in Banks with a

special focus on Market Risk-valuation and computation of capital charge,Asset-L iabil ity

Management and also a brief overview of the r isk management guideli nes laid down by

RBI.

The project also involves the study of the responsibilities of the Banks 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 Banks 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.


3/61

3

1. Introduction to Treasury ManagementIn general terms and from the perspective of commercial banking, treasury refers to the fund

and revenue in the banks 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, anddeployed 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 theright 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.


4/61

4

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.


5/61

5

2. The Federal Bank LtdAn OverviewFederal 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 whichare 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


6/61

6

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


7/61

7

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 interbankcontracts

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.


8/61

8

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 bankdeposits, 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 recurringdeposits, 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, billspayable, 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


9/61

9

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 AcceptanceFacility (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 liabilitiesof 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.


10/61

10

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 shouldconvert 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.


11/61

11

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


12/61

12

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 tocontrol 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 banks futu re earningsand 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 ata given time.

3. Forex risk: It is the risk of having losses in foreign exchange assets and liabilities dueto 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


13/61

13

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 yearsvii) 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 dayII. 2 to 7 daysIII. 8 to 14 daysIV. 15 to 28 daysV. 29 days and up to 3 monthsVI. Over 3 months and up to 6 monthsVII. Over 6 months and up to 1 yearVIII. Over 1 year and up to 3 yearsIX. Over 3 years and up to 5 yearsX. Over 5 years


14/61

14

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 nextbusiness 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:


15/61

15

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, periodicreviews, support of real time triggers etc. help in the healthy growth of the organization.


16/61

16

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 = RSARSL

Gap may be (i) Positive Gap where GAP > 0 and (ii) Negative Gap where GAP < 0 withfollowing 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.


17/61

17

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.


18/61

18

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 yearsperiod 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 tomean 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:


19/61

19

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

= [ 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

= [ 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


20/61

20

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 andcontrolling the interest rate risk.

Duration Gap analysis improves on the maturity gap and cumulative gap models bytaking 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 pricingschedules of the financial instruments.

Requires a high degree of analytical expertise regarding issues such as the termstructure of interest rates and yield curve dynamics.


21/61

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 (), standard deviation (), specification of confidence

level (), and the range based on the specific probabilitydistribution function. The volatilityof the return for an asset or liability is computed as follows:

Volatility = Standard Deviation (SD) / Mean x100

V = / 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 Dt

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 (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:

(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)


22/61

22

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 (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) = (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 [(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.


23/61

23

5. Capital AdequacyCapital 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


24/61

24

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 capitalmeasurement.

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.


25/61

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 reserves2.

Reserves representing surplus arising out of sale proceeds of assets

3. Innovative perpetual debt instruments (IPDI) & Perpetual Non-Cumulative PreferenceShares (PNCPS)

For foreign banks in India

1. Interest-free funds from Head Office kept in a separate account2. Statutory reserves kept in Indian books3. 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 aseparate account and which is not eligible for repatriation so long as the bank functions

in India.

Limits on eligible Tier I Capital

1. IPDIs eligible to be reckoned as Tier I capital, will be limited to 15 percent of total TierI capital

2. PNCPSs along with Innovative Tier I instruments shall not exceed 40 per cent of totalTier I capital at any point of time

3. Innovative instruments / PNCPS, in excess of the limit shall be eligible for inclusionunder Tier II


26/61


27/61

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 banks 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:


28/61

28

a) Specific risk capital charge, computed notionally for AFS securities treating them asheld 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 treatingthem 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


29/61

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 riskweights 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)


30/61

30

Table 3Part A: Specific Risk Capital Charge for Sovereign securities issued by Indian and

Foreign SovereignsHeld 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

1Investment in Central Government and State

Government SecuritiesAll 0.0

2Investments in other approved securities guaranteed

by Central GovernmentAll 0.0

3Investments 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

less0.28

6-24 months 1.13

More than

24 months1.8

B Foreign Central Governments

1 AAA to AA All 0.00

2 A to BBB

6 months or

less0.28

6-24 months 1.13

More than

24 months1.8

3 BB to B All 9.00

4 Below B All 13.50


31/61

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

2Investments in other approved securities guaranteed by

Central GovernmentAll 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


32/61

32

Table 3 - Part C: Specific Risk Capital Charge issued by Scheduled Banks meeting minimum

CRAR requirementsHeld 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

less0.28

6 to 24

months1.13

exceeding

24 months1.8

Table 3- Part D: Alternative Capital Chargefor Bonds issued by Scheduled Banks meeting

minimum CRAR requirements- Held By Banks under AFS Category

Sr.No. Nature of investmentResidual

Maturity

Total

Capital

Charge (as

a % of

exposure)

1

Claims on banks, including investment in securitieswhich 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


33/61

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

months2.7

>24 months 4.5

BBB All 9

BB & Below All 13.5


34/61

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 sovereignsHeld bybanks 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


35/61

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.


36/61

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 timebands as set out.

Subject long and short positions (short position is not allowed in India except inderivatives) 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 tothe disallowances set out.


37/61

37

Computation of Capital Charge


38/61

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 Banks 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.


39/61

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 boththe possibility of some under-estimation of risks under the Pillar 1 and the

actual risk exposure of a bank vis--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.


40/61


41/61

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)


42/61

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 determiningthe 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;


43/61

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 hedgingtrading 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 banks 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


44/61

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.


45/61

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 pricingand 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 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-)*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


46/61

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 wont exceed a particular amount.

The relationship between probability level p and confidence level is described as =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 () and the current MTM position (W). The volatility is estimated

implicitly from option pricing or through statistical models (). 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 = WT

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.


47/61

47

7.1 VaR PARAMETERS

1. CONFIDENCE LEVELTo 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 confidencelevel 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. HORIZONIt 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 xN

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.


48/61


49/61

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) VarianceCo 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 1.65below the mean

(2.33will 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 *

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,

Where, is the correlation co-efficient between the 2 assets.


50/61

50

Advantages:

The VarianceCovariance 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


51/61

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- 5 thpercentile 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.


52/61

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


53/61

53

1. Model Building Approach (MBA): The MBA uses Variance of the returns for thepurpose 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 VaRs 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

where = correlation coefficient between the 2 securities.

01020304050

607080

Frequency

Returns

Histogram

Frequency

5% Probablity of Loss

more than Rs. 32.01


54/61

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

-8

2.02

33

56

-

1.53

00

-6

1.

960253

-

.

-

0.93186

9

-3

0.65

9999

-2

0.38

132

6

-

.

0.16360258

10.3

01

2

0.1133

62

3

0.98520513

1.2590

265

5

1.5329

01

.

2.0806

52

8

2.35

5

2

2

9

2.628

102

.

1

13.1

61

53

1

23.500128r

Frequency

Returns

Geetanjali Vs Dollar

Frequency


55/61

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

01020304050607080

-68.69357885

-58.98104187

-49.26850489

-39.55596792

-29.84343094

-20.13089397

-10.41835699

-0.705820013

9.006716963

18.71925394

28.43179092

38.14432789

47.85686487

57.56940184

67.28193882

76.9944758

86.70701277

96.41954975

106.1320867

ore

Freque

ncy

Returns

CIL Vs NTPC

Frequency


56/61

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 committeehas 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


57/61

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 banks 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 dataor errors in the model programming.

2. Model accuracy needs improvement, exceptions occur because the model does notaccurately describe risks.

3.Intraday trading activity, the exceptions occur due to trading activity i.e. the VaR isbased on static portfolios.

4. Bad luck, the exceptions occur market conditions (volatility and correlations amongfinancial instruments) significantly varied from the accepted norms.


58/61

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


59/61

59

8. Learning and LimitationsDue 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 undertaken2. 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 riskoversight 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 forvarious 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


60/61

Documents

Bank Treasury