RISK MANAGEMENT MODULE A – Asset Liability Management AND MODULE B – Risk Management

RISK MANAGEMENT MODULE A – Asset Liability

Management AND MODULE B – Risk Management

A PRESENTATION BYK ESWAR MBA XLRI, CAIIB

CHIEF MANAGER, SPBT COLLEGE.

Market

Credit

Operational

BANKS TYPICALLY FACE THREE KINDS OF RISK

• Risk of loss due to unexpected re-pricing of assets owned by the bank, caused by either

– Exchange rate fluctuation

– Interest rate fluctuations

– Market price of investment fluctuations

• Risk of loss due to unexpected borrower default

• Risk of loss due to a sudden reduction in operational margins, caused by either internal or external factors viz Process failure, systems failure, human error, frauds but does not cover reputational risk/strategic risk.

Daily price change (%)

Unexpected price volatility

Time

Time

Default rate (%)

Unexpected defaultAvg. default

Time

Monthly change of revenue to cost (%)

Unexpected low cost utilization

Example

“Stocks”

“Loans with credit rating 3”

“Business unit A”

Type of Risk

The Current Capital Accord• Focused on credit risk but formula based

• Partially amended in 1996 to include market risk

• Operational risk not addressed• Simple in its application• Produced an easily comparable and

verifiable measure of bank’s soundness

Need for a new frame-work• Financial innovation and growing complexity of

transactions• Categorised bank’s assets into one of only four

categories each representing a risk class• Made no allowance for the effect portfolio diversification

• Requirement of more flexible approaches as opposed to “one size fits all” Approach

• Requirement of Risk sensitivity as opposed to a “broad- brush Approach”

• Operational Risk not covered

Basle Accord I & II - Basle Accord I & II - DifferencesDifferences

Talks of Credit Risk onlyTalks of Credit Risk only

Capital Charge for Credit Capital Charge for Credit Risk – 8% Risk – 8%

Does not mention Does not mention separate Capital charge separate Capital charge for Market and for Market and Operational RiskOperational Risk

No mention about market No mention about market DisciplineDiscipline

No effort to quantify No effort to quantify Market and Operational Market and Operational RiskRisk

Talks of Credit, Market Talks of Credit, Market and Operational Risksand Operational Risks

Capital Charge Capital Charge dependant on Risk rating dependant on Risk rating of assetsof assets

Capital Charge to include Capital Charge to include risks arising out of Credit, risks arising out of Credit, Market and Operational Market and Operational risks. Not a broad brush risks. Not a broad brush approachapproach

Quantitative approach for Quantitative approach for calculation of Market and calculation of Market and Operational risks as for Operational risks as for Credit Risk. Credit Risk.

Three pillars of the Basel II framework

– Credit risk

– Operational risk

– Market risk

– Bank’s own capital strategy

– Supervisor’s review

– Enhanced disclosure

Minimum Capital Requirements

Supervisory Review Process Market Discipline

Pillar I – Credit RiskPillar I – Credit Risk

Standardized Approach

Foundation Internal Ratings

Based Approach

Advanced Internal

Ratings BasedApproach

Risk weights are based on assessment by external credit assessment institutions

Banks use internal estimations of probability of default (PD) to calculate risk weights for exposure classes. Other risk components are standardized.

Banks use internal estimations of PD, loss given default (LGD) and exposure at default (EAD) to calculate risk weights for exposure classes

Pillar 1 – Credit Risk stipulates three levels of increasing sophistication. The more sophisticated approaches allow a bank to use its internal models to calculate its regulatory capital. Banks who move up the ladder are rewarded by a reduced capital charge

Increase Sophistication

Reduce Capital requirements

Pillar I – Minimum Capital Pillar I – Minimum Capital RequirementsRequirements

The new Accord maintains the current definition of total capital and the minimum 8% requirement*

Total capital = Tier 1 + Tier 2Tier 1: Shareholders’ equity + disclosed reservesTier 2: Supplementary capital (e.g. undisclosed reserves, provisions)

Total Capital

Market Risk The risk of losses in trading positions when prices move adversely

Credit Risk The risk of loss arising from default by a creditor or counterparty

Operational Risk The risk of loss resulting from inadequate or failed internal processes, people and systems or from external events

Total capitalCredit risk + Market risk + Operational risk

= Bank’s capital ratio (minimum 9%)

* The revisions affect the denominator of the capital ratio - with more sophisticated measures for credit risk, and introducing an explicit capital charge for operational risk

Internal Ratings Based Approach

• Exposures in five categories because of different risk characteristics– Sovereigns– Banks– Corporates– Retail– NPA

Pillar I – Credit RiskPillar I – Credit Risk

Standardized Approach

Foundation Internal Ratings

Based Approach

Advanced Internal

Ratings BasedApproach

Risk weights are based on assessment by external credit assessment institutions

Banks use internal estimations of probability of default (PD) to calculate risk weights for exposure classes. Other risk components are standardized.

Banks use internal estimations of PD, loss given default (LGD) and exposure at default (EAD) to calculate risk weights for exposure classes

Pillar 1 – Credit Risk stipulates three levels of increasing sophistication. The more sophisticated approaches allow a bank to use its internal models to calculate its regulatory capital. Banks who move up the ladder are rewarded by a reduced capital charge

Increase Sophistication

Reduce Capital requirements

Capital Requirement – What New?

FrameworkFramework

Claims on Banks is 20% subject to the fact that CRAR of borrowing Bank is 9 % and above. And it is scheduled Bank.

Claims on corporates

Credit Credit assessment assessment by domestic by domestic rating rating agenciesagencies

AAAAAA AAAA AA BBBBBB BB BB and and belowbelow

UnratUnrateded

Risk weightRisk weight 20%20% 30%30% 50%50% 100%100% 150%150% 100%100%

Unrated exposure of Rs.50(Rs.10 crores) will attract 150% risk weight.

Mapping process – draft guidelines

Short term ratingsShort term ratings Risk Risk weightsweights

CARECARE CRISILCRISIL FITCHFITCH ICRAICRAPR1+PR1+ P1+P1+ F1+F1+ A1+A1+ 20%20%PR1PR1 P1P1 F1F1 A1A1 30%30%PR2PR2 P2P2 F2F2 A2A2 50%50%PR3PR3 P3P3 F3F3 A3A3 100%100%

PR4/PR5PR4/PR5 P4/P5P4/P5 B/C/DB/C/D AR/A5AR/A5 150%150%UNRATEDUNRATED UNRATEDUNRATED UNRATEUNRATE

DDUNRATEUNRATE

DD100%100%

Retail Portfolio - Criteria• Orientation criterion - exposure to individual person or

persons or to a small business.

• Product criterion - revolving credit, line of credit, personal term loan and lease small business facilities and commitments.

• Granularity criterion- regulatory retail portfolio is sufficiently diversified to a degree that reduces the risk in the portfolio – no aggregate exposure to one counterpart can exceed 0.2% of the overall regulatory retail portfolio

• Low value of individual exposures- the maximum aggregate retail exposure to one counterpart cannot exceed an absolute threshold of euro 1 million.( Rs. 5 Crores for our Bank)

• Turnover Rs.50 Crores.(AVERAGE FOR LAST 3 YEARS)

Capital charge for Credit risk contd…

• Past due loans– The unsecured portion of any loan that is past due for

more than 90 days, net of specific provisions, to be given higher risk weight

– 150% if specific provision <20% o/s– 100% if provision >or= 20%– if provision = or > 50% with supervisory discretion for 50%

weight– 100% if provision > or = 15% if fully secured

Exclusion in Regulatory Retail.

• Mortgage loans to the extent they qualify for treatment as claims secured by residential property: Margin 25% : RW upto Rs.20 lakhs :50% and Rs.20 lakh and above 75% Margin less than 25% RW 100%

• Consumer credit, credit card exposure etc. RW125%• Capital market exposure and NBFCs RW125%• Commercial Real Estate : RW 150%• Staff loans: 20% if covered by superanuation funds or

mortgage.• Other staff loans : 75% RW

Operational Risk

• Explicit charge on capital• Basic Indicator approach – 15% of gross

income • Gross income = net interest income plus net

non interest income

GROSS INCOME

• GROSS INCOME = NET PFORIT+ PROVISIONS+OPERATING EXPENSES-PROFIT ON SALE OF INVSTEMENT-INCOME FROM INSURANCE-EXTRA ORDINARY ITEM OF INCOME+ LOSS ON SALE OF INVESTMENT

Operational RiskStandardised Approach- Capital charge is calculated as a simple

summation of capital charges across 8 business lines

Business linesBusiness lines % of gross income% of gross income

Corporate financeCorporate finance 1818Trading & salesTrading & sales 1818Retail BankingRetail Banking 1212Commercial BankingCommercial Banking 1515Payment & SettlementPayment & Settlement 1818Agency ServicesAgency Services 1515Asset ManagementAsset Management 1212Retail BrokerageRetail Brokerage 1212

• CREDIT RISK MITIGATION• HAIR CUT TO EXPOSURE• HAIR CUT TO FINANCIAL COLLATETAL.

• Q. Net Interest Margin NIM is defined as• a. Net interest income divided by total earning assets.• b. Interest income –interest expenses.• c. total interest income divided by total assets.• d. None of above.• • Q..Ratio of share holders funds to total assets is called as• a. Debt equity ratio.• b. TOL/TNW ratio.• c. Economic equity ratio.• d. No ne of above.

• Q The institution is in a position to benefit from rising interest rates

when assets are ……………than liabilities.• Lower.• Greater• Equal • Half.• Q. The liquidity risk arising out of unanticipated withdrawal or non

renewal of deposits is called as • a. Funding Risk.• b. Time risk.• c. Market Risk• d. Operational risk.

• • Q. The liquidity risk arising out of non receipt of expected in flow of

funds due to accounts turning as NPA is known as• a. Time Risk.• b. Call Risk.• c. Operational Risk.• d. Funding risk.• • Q. The liquidity risk arising out of crystallization of liabilities and

conversion of non fund based limits to fund based limits is known as :• a. Call risk.• b. Time risk.• c. Operational risk.• d. Market risk.•

• • Q. Stock approach of measuring and managing liquidity risk and funding

requirements is based on• a. level of assets and liabilities and balance sheet exposure on a

particular date.• b. based on stocks pledged to Bank in Cash Credit Account• c. Stock of Investments of bank.• d. None of above.• • Q. Flow approach to measuring and managing liquidity consist of• a. Measuring and managing net funding requirements.• b. Managing market access.• c. Contingency planning.• d. All the above.

• • Q. Under gap method the net funding requirement is calculated

based on • a. residual maturities of assets and liabilities.• b. Actual maturities of assets and liabilities • c. Both the above.• d. None of above.• • Q. Cash inflows arise from mainly:• a. Maturing assets.• b. Maturing liabilities.• c. Maturing off balance sheet exposure.• d. Maturing time deposits.

• • q. Cash outflows arise out of mainly.• a. Maturing liabilities.• b. Maturing assets.• c. Maturing T Bills.• d. Maturing CPs.• • Q. Different between the cash in flow and cash out flow will result

into……….. if the cash inflows are lower than the cash outflows:• a. deficit.• c. Surplus • d. None of above.• e. No impact.

• • Q. If there is significant deficit observed say after 30 days period the

option available for bank is to• a. acquire an asset maturing on that day.• b. renew or roll over a 30 day liability.• c. Acquire a liability maturing after 30 days.• d. None of above.• • Q. In the year 2007 RBI has for the purpose of measurement of liquidity

risk split the first time bucket of 1-14 days in its structural liquidity in• a. Four time buckets.• b. Three time buckets• c. Five time buckets.• d. None of above.

• Q the net cumulative negative mismatch during the next day, 2-7 days, 8-14 days and 15-28 days buckets should not exceed

• a.5%,10%, 15% and 20% of cumulative cash inflows in respective time bucket.

• b. 20%,15%,10% and 5% of cumulative cash inflows.• c.10%,5%,25% and 30% of cumulative cash inflows.• Q. Frequency of structural liquidity position is• a. fortnightly • b. Weekly.• c. Monthly• d. Quarterly.

• • Capital , Reserves and Surplus are slotted in which time bucket in

Structural Liquidity Statement:• Over 5 years.• Over 3 Years.• Over 1 Year.• Over 6 months.• Q. Saving and Current deposit may be treated as volatile portion

upto • a. 10% and 15 % respectively.• b.20% and 30% respectively.• c. 30% and 40% respectively.• d. None of above

• Q. Placement of volatile portion and core portion of Saving and current deposit may be done as under:

• a. volatile portion in day 1 time bucket and core portion in 1-3 year bucket.

• b. Volatile portion in 7 day time bucket and core portion in 5 year bucket.

• c. Volatile portion in 2-7 days time bucket and core portion in 1 year time bucket.

• d. none of above.• • Q. Cash should be shown under which time bucket for inflow:• a. 1 day.• b. 2-7 days.• c. 8-14 days.• d. One year.

• • Q. Investment in shares and mutual fund (open ended) should be

shown in • a. Over 5 year bucket• b. Over 1 year bucket.• c. Over 2 year Bucket.• D. None of above.• • Q. Investment in subsidiaries and joint ventures to be shown• a. In over 5 year bucket.• b. In over 3 year bucket.• c. In over 1 year bucket.• d. None of above.

• • Q. Core portion of Cash credit advances may be shown under

a. 1-3 year time bucket.• b. over 3 year time bucket.• c. Over 5 years time bucket.• d. None of above.• • Q. Term Loans to be shown under:• a. Interest and principal of the loan under residual maturity

bucket.• b. Principal under residual maturity bucket.• c. all in 5 year and above bucket.• d. None of above.

• • Q. Sub Standard loans to be shown under • a. Over one year bucket.• b. Over 2 year bucket.• c. Over 3 years bucket.• d. Over 3-5 year bucket.• • Q. Fixed Assets:• a. Over 5 year bucket.• b. Over 2 year bucket.• c. Over 1 year bucket.• d. none of above.

• Q. The net cumulative negative mismatches

during the day 1, 2-7, 8-14 and 15-28 days buckets if exceed the prudential limits may be financed from market by

• a. Market borrowings ( call /term)• b. Bills discounting• c. Repo• d. All above.

• Q. Market Value of an asset is conceptually equal to • a. Present value of current and future cash flows from that asset and

liability.• b. future value of current and future cash flows from that asset and

liability.• c. None of above.• d. all the above.• • Q. There fore rising interest rates increase the discount rates on those

cash flows and thus• a. Decrease the market value of asset or liability.• b. Increase the market value of asset or liability.• c. No impact is caused.• d. None of above.•

• Q. Falling interest rate decrease the discount rates on these cash flows and thus

• a. Increase the market value of an asset or liability.• c. Decrease the market value of an asset or liability.• d. No Impact.• e. None of above.• • Q. What is basis risk:• a. risk that interest rate of different assets and liabilities may

change in different magnitudes is called basis risk.• b. Risk relating to basis on which loan is sanctioned.• c. Risk related to yield curve.• d. None of above.

• Q. Yield Curve Risk is known as:• a. Risk owing to altering of yields across maturities and its impact

on NII• b. Risk owing to wrong drawing of yield curve by Bank staff.• c. risk of lower current yield .• d. None of above.• • Q. Gap method is basically used for • a. measuring banks interest rate risk exposure.• b. measure maturity mismatch• c. Measure potential losses from off balance sheet exposure.• d. None of above.

• Q. In a given time band a negative or liability sensitive gap occurs when • a. Rate sensitive liabilities exceed rate sensitive assets.• b. Rate sensitive assets exceed rate sensitive liabilities.• c. None of above.• d. All the above.• • Q. with a negative gap , an increase in market interest rates could cause a • a. decline in net interest income.• b. Increase in net interest income.• c. None of above.• d. All above.•

04/24/23 SPBT COLLEGE. 41

Market Value with interest at 8%Discount

Rate = 8%

year cashflowdiscount

valuePresent Value

1 8 0.9259 7.40742 8 0.8573 6.85873 8 0.7938 6.35074 8 0.7350 5.88025 108 0.6806 73.5030

Total 100.0000

Market Price is Rs 100 (Par Value)


Interest Rate • Suppose that current expectation of yield is

10%. What will be the market price?Discount

Rate = 10%


valuePresent Value

1 8 0.9091 7.27272 8 0.8264 6.61163 8 0.7513 6.01054 8 0.6830 5.46415 108 0.6209 67.0595

Total 92.4184Market Price is Rs 92.4148 (less than Par Value) when current expectation of yield has gone up.


Interest Rate • Suppose that current expectation of yield is

6%. What will be the market price?Discount

Rate = 6%


valuePresent Value

1 8 0.9434 7.54722 8 0.8900 7.12003 8 0.8396 6.71704 8 0.7921 6.33675 108 0.7473 80.7039

Total 108.4247Market Price is Rs 108.4247 (more than Par Value) when current expectation of yield has come down.

• • Q. Higher the duration implies that a given change in the level of interest

rates will have • a. larger impact on economic value.• b. smaller impact on economic value.• c. No Impact.• d. None of above.• • Q. Duration will be higher if

a. longer the maturity date or smaller the payments that occur before maturity ( coupon payments)

• b. shorter the maturity and higher the payments that occur before maturity ( coupon payments)

• c. None of above.• d. all the above.

• • Q. One of the strategies for reducing the asset or liability

sensitivity could be :• a. Increase floating rate instruments.• b. Increase fixed rate instruments.• c. None of above.• d. all the above.• • Q. The Duration of Zero coupon bond would be • a. Greater than its maturity.• b. Shorter than its maturity.• c. Equal to its maturity.• d. None of above.

• None of above.• Q. Under Put option the buyer has • a. Right to sell but not obligation to sell• b. Right to buy but not obligation to buy• c. Right to receive interest payments.• d. None of above.• Q. Under Call option the buyer has • a. Right to buy but not obligation to buy• b. right to sell but not obligation to buy• c. None of above.

• ..• • Q. American option • a. Permit the holder to exercise any time before the expiration date.• b. Does not permit to exercise any time before the expiration date.• c. None of above.• d. all above.• • Q. European option means• a. Which permit holder to exercise any time before expiration date.• b. Does not permit holder to exercise any time before expiration date.• c. all above.• d. none of above.

• • Q. In India only • a. European option are allowed.• b. Only American option are allowed.• c. Both are allowed.• d. None are allowed.• • Q. Futures are• a. Over the counter products.• b. Exchange traded.• c. None of above.• d. all the above.

• • Q. Which of the following is true:• a. A swap has invariably two legs of transaction.• b. A swap only one leg of transaction.• c. None of above.• d. All the above.• • Q. Futures are marked to market on • a. Daily basis and margin is adjusted.• b. Weekly basis.• c. Monthly basis.• d. None of above.

• • Q. Short term dynamic liquidity statement relate to• a. monitoring liquidity on dynamic basis over a time horizon of 1-90 days.• b. monitoring liquidity on dynamic basis over a time horizon of 7-90 days.• c. monitoring liquidity on dynamic basis over a time horizon of 28-90 days.• d. None of above.• • Q. In statement of interest rate sensitivity :• a. Only rupee assets and liabilities and off balance sheet positions should

be reported.• b. All assets and liabilities should be reflected.• c. Only foreign currency assets and liabilities should be reflected.• d. None of above.

• • Q. Gap is the difference between• a. Rate Sensitive Assets and Rate Sensitive Liabilities for each time bucket.• b. Rate Sensitive Liabilities and Rate Sensitive Assets for each time

bucket.• c. None of above.• d. all above.• • Q If positive gap of RSA > RSL, Bank will• A.Benefit from rising interest rate.• B.Lose from rising interest rate.• C.None of above.• D.All of above.

• Q. If negative gap of RSL > RSA will benefit from• a. declining interest rate.• b. Rising interest rate.• c. None of above.• d. No impact.• • Q. Capital , Reserves and Surplus are • a. Non interest rate sensitive.• b. Interest Rate Sensitive.• c. None of above.

• • Q. Provisions and inter office adjustments are• a. Rate sensitive.• b. Rate non sensitive.• c. None of above.• d. all of above.• • Q. Current account balance is• a. Rate sensitive.• b. Rate non sensitive.• c. None of above.• d. All of above.

• . Banking Book relates to assets which are• A held till maturity and reflected in Balancesheet at acquisition

cost.• b. held till maturity and reflected in Banking book at market cost.• c. None of above.• d. all of above.• • Q. Trading book includes :• a. assets a which normally not held till maturity and mark to

market system is followed.• b. assets which are held till maturity.• c. assets which are purchased in market.• d. none of above.

• • Q..which book is exposed to market risk.• a. Banking book.• b. trading book• c. None of above.• d. Both a and b.• • Q. Which is true:• a. Risk associated with portfolio is always less than the weighted average

of risks of individual items in portfolio.• b. Risk associated with portfolio is always more than the weighted

average of risks of individual items in portfolio.• c. Risk associated with portfolio is equal to weighted average of risks of

individual items in a portfolio.•

• Q. Daily volatility of stock is 1%. What is 10

day volatility?• a. 3%• b.10%• c.1%• d.4%

• Q. Systemic risk can be diversified • a. True.• b. False• c. Partly true• d. partly false.• • Q. Basel Committee (BCBS) possess formal super

national supervisory authority and its conclusions have legal force:

• a. True.• b. False.

• • q..Bond prices changes can be estimated using modified duration using

following relationship• a. modified duration* yield change.• b. Mculay duration* yield change.• c. Maturity*yield change.• d. None of above.• • Q.VaR is • a. potential worst case loss at a specific confidence level over a certain

period of time.• b. potential worst case loss over indefinite period of time.• c. none of above.•

• • 1 day VaR of portfolio is Rs.5,00,000 with 95% confidence

level in a period of six months ( 125 days) how many times the loss on the portfolio may exceed Rs.5,00,000

• 4 days. B. 5 days. 3. 6 days 4. 7 days.• • Q. RAROC stands for• a. Risk Adjusted Return on capital• b. Risk adjusted return on cost.• c. Return adjusted risk on credit.• D none of above.

• • Q.Credit Default swaps are • a. One of credit derivatives.• b. a kind of Bank guarantee• c. a kind of line of credit.• d. stand by credit.• • Q. The beta factor for calculating operational risk under

standardized approach for retail banking is • a. 12%• b.18%• c.15%• D. None of above.

• • Q. Probability of occurrence =4• Potential financial impact =4• Impact of internal control =0%• • a. What is estimated level of operational risk?• 1. 3• 2. 2• 3 0• 4. 4


Interest Rates

Yield Curve

5.0000%

6.0000%

7.0000%

8.0000%

9.0000%

10.0000%

11.0000%

0 1 2 3 4 5 6 7 8 9 10

Time Period in Years

YTM


Yield Curve – Parallel ShiftsYield Curve - Parallel Shifts

5.7500%

6.2500%

6.7500%

7.2500%

7.7500%

8.2500%

8.7500%

9.2500%

9.7500%

10.2500%

1 2 3 4 5 6 7 8 9 10

Tenor in Years

YTM

YC1 YC-Rate Rise YC-Rate Fall


Yield Curve – Stiffening & Flattening

Yield Curve -Stiffening & Flattening

6.0000%

7.0000%

8.0000%

9.0000%

10.0000%

11.0000%

1 2 3 4 5 6 7 8 9 10Tenor in Years

YTM

YC1 YC-Stiff YC-Flat


Duration Analysis


DURATIONA methodology is required for following purposes: To assess ALM mis-matches between

assets and liabilities To compare two portfolios - Both can be

assets / liabilities or one asset and one liability portfolio

To decide between various options for contracting assets or liabilities

“DURATION ANALYSIS”


DURATION• In financial analysis, any intermittent cash flow

earned from a financial asset is presumed to be reinvested at current interest rates.

• Thus, when current interest rates go up, price of a bond falls while the reinvestment income will go up for period to maturity. Thus capital loss and higher income occur together.

• At some point of time in the life of the asset, the capital loss will equal the rise in reinvestment income This point of time is defined as Duration of the Asset.


DURATION• Duration is also termed as effective life of

an asset / liability or as weighted average life.

• Duration can be applied to any asset / liability that is of fixed income type. It cannot be applied to floating rate instruments.

• Duration is a direct outcome of maturity (to term) and interest rates.

• Hence Duration is also viewed as primary measurement of price sensitivity.

• Duration measure (D) is expressed in years.


DURATION ANALYSIS – An Example

Year (Y) Inflow DF at 8% PV PV*Y(1) (2) (3) (4)=(2*3) (5)=(1*4)1 6 0.92593 5.55556 5.555562 6 0.85734 5.14403 10.288073 6 0.79383 4.76299 14.288984 6 0.73503 4.41018 17.640725 6 0.68058 4.08350 20.417506 6 0.63017 3.78102 22.686117 6 0.58349 3.50094 24.506608 6 0.54027 3.24161 25.932919 6 0.50025 3.00149 27.0134410 106 0.46319 49.09851 490.98510

Total 86.57984 659.31497D= 7.61511

Discouting Factor is arrived at by "1/ (1+r)̂ n"

Duration is arrived at by dividing total of Col 5 by total of Col 4.

Calculate Duration of a bond of Rs 100 carrying coupon at 6.00%, payable annually and maturity of 10 years. Principal to be repaid upon maturity. Current expectation of Interest Rate is 8.00%


Duration• Duration in expressed in years and is

comparable across portfolios.• Duration of a Zero Coupon Bond is equal

to its maturity.• Duration is additive. Hence, Duration of a

portfolio is the weighted average duration of all instruments of the portfolio.

• Duration of a coupon paying bond / asset is less than its maturity.

• Longer the maturity of a bond, longer is Duration.

• Duration is inversely related to Coupon.


Duration• Duration is directly related to market

interest rates / Yield.• Higher the frequency of coupons, lower

the Duration.• Duration of a Floating Rate bond is equal

to its interest reset period or the period remaining to next reset of interest.

• For small changes in yield, Duration multiplied by percentage change in yield gives percentage change in price for bonds.


Duration & Price Change• If current price of a bond is Rs 98.50, its Duration

is 2.7613 and yield is likely to change from 6.00% to 5.80%, then the likely price of the bond is computed as under:% change in Price = D*(percentage change in Yield)= 2.7513 * (6.00 - 5.80)= 0.55226%Absolute change in Price = 98.50 * 0.55226%= 0.54398.As Yield has come down, price will increase and therefore, expected bond price will be Rs 99.04398.


Modified Duration• Duration is not preferred to compute price

changes when change in yield is large. For this purpose, Modified Duration (MD) is used.

MD = Duration / (1+Yield)• In our Bond example, D=2.76129 and yield is

6.00%. Therefore, MD = 2.76129/(1+0.06) or 2.60500. Let current market price be Rs 98.50.

• If yield changes from 6.00% to 5.80%, percentage change in price will be 0.52100% and absolute change in price will be 0.51318.

• Hence changed price will be Rs 99.01318.


Duration & Interest Rate Risk• In a bank’s balance sheet, If DA = DL, there

is no IRR faced by the bank. IRR manifests itself if DA > DL or DA < DL, depending on the direction of movement of interest rates.

• Hence, the strategy for containing IRR will be to aim at a mix of assets and liabilities in such a way that their Duration matches.

• Duration Gap is the difference between the Duration of Assets less the effective Duration of Liabilities.


Duration & Interest Rate Risk• If a bank has Asset Duration of 3 years,

Assets of Rs 200 crore and Liabilities (excluding Equity) of Rs 150 crore, the bank should target Liability Duration of 4 years (200*3/150).

• In that case, Duration of Equity will be (3*200) – (4*150) = 0.

• In other words, bank’s net worth is immunized against changes in interest rates.

Documents

RISK MANAGEMENT MODULE A – Asset Liability Management AND MODULE B – Risk Management