RISK MANAGEMENT
MODULE A – Asset Liability
Management AND MODULE B – Risk
Management
A PRESENTATION BY
K ESWAR MBA XLRI, CAIIB
CHIEF MANAGER, SPBT COLLEGE.
BANKS TYPICALLY FACE THREE KINDS
OF RISK
Type of Risk
Example
•
Market
Credit
•
•
Operational
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.
“Stocks”
Daily price
change (%)
Unexpected
price volatility
Time
Default
rate (%)
“Loans with credit rating 3”
Unexpected
default
Avg. default
Time
Monthly change
of revenue to cost
(%)
“Business unit A”
Unexpected
low cost
utilization
Time
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 “broadbrush Approach”
• Operational Risk not covered
Basle Accord I & II Differences





Talks of Credit Risk only
Capital Charge for Credit
Risk – 8%
Does
not
mention
separate Capital charge
for
Market
and
Operational Risk
No mention about market
Discipline
No effort to quantify
Market and Operational
Risk




Talks of Credit, Market
and Operational Risks
Capital
Charge
dependant on Risk rating
of assets
Capital Charge to include
risks arising out of Credit,
Market and Operational
risks. Not a broad brush
approach
Quantitative approach for
calculation of Market and
Operational risks as for
Credit Risk.
Three pillars of the Basel II framework
Minimum Capital
Requirements
– Credit risk
– Operational risk
– Market risk
Supervisory
Review Process
– Bank’s own capital
strategy
– Supervisor’s review
Market Discipline
– Enhanced disclosure
Pillar I – Credit Risk
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
Advanced
Internal
Ratings Based
Approach
Foundation Internal
Ratings
Based Approach
Standardized
Approach
Banks use internal estimations of
PD, loss given default (LGD) and
exposure at default (EAD) to
calculate risk weights for exposure
classes
Banks use internal estimations of
probability of default (PD) to calculate risk
weights for exposure classes. Other risk
components are standardized.
Risk weights are based on
assessment by external credit
assessment institutions
Reduce Capital requirements
Pillar I – Minimum Capital
Requirements
The new Accord maintains the current definition of total capital and the minimum 8%
requirement*
Total capital
= Bank’s capital ratio
Credit risk + Market risk + Operational risk (minimum 9%)
Total Capital
Total capital = Tier 1 + Tier 2
Tier 1: Shareholders’ equity + disclosed reserves
Tier 2: Supplementary capital (e.g. undisclosed reserves, provisions)
Credit Risk
The risk of loss arising from default by a creditor or counterparty
Market Risk
The risk of losses in trading positions when prices move adversely
Operational Risk
The risk of loss resulting from inadequate or failed internal processes,
people and systems or from external events
* 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 Risk
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
Advanced
Internal
Ratings Based
Approach
Foundation Internal
Ratings
Based Approach
Standardized
Approach
Banks use internal estimations of
PD, loss given default (LGD) and
exposure at default (EAD) to
calculate risk weights for exposure
classes
Banks use internal estimations of
probability of default (PD) to calculate risk
weights for exposure classes. Other risk
components are standardized.
Risk weights are based on
assessment by external credit
assessment institutions
Reduce Capital requirements
Capital Requirement – What
New?
Framework
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
AAA AA
assessment
by domestic
rating
agencies
A
BBB
BB
Unrat
and
ed
below
Risk weight
50%
100%
150%
20% 30%
100%
Unrated exposure of Rs.50(Rs.10 crores) will attract 150% risk weight.
Mapping process – draft guidelines
Short term ratings
CARE
Risk
weights
CRISIL FITCH ICRA
PR1+
P1+
F1+
A1+
20%
PR1
P1
F1
A1
30%
PR2
P2
F2
A2
50%
PR3
P3
F3
A3
100%
PR4/PR5
P4/P5
B/C/D
AR/A5
150%
UNRATED UNRATE
D
UNRATE
D
100%
UNRATED
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
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 Risk
Standardised Approach- Capital charge is calculated as a simple summation
of capital charges across 8 business lines
Business lines
% of gross income
Corporate finance
18
Trading & sales
18
Retail Banking
12
Commercial Banking
15
Payment & Settlement
18
Agency Services
15
Asset Management
12
Retail Brokerage
12
• 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.
•
•
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•
•
•
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•
•
•
•
•
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.
•
•
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•
•
•
•
•
•
•
•
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.
Market Value with interest at 8%
year
1
2
3
4
5
Total
Discount
Rate =
8%
discount
cashflow
value
8
0.9259
8
0.8573
8
0.7938
8
0.7350
108
0.6806
Present
Value
7.4074
6.8587
6.3507
5.8802
73.5030
100.0000
M arket Price is Rs 100 (Par Value)
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41
Interest Rate
• Suppose that current expectation of yield is
10%. What will be the market price?
Discount
Rate =
year
1
2
3
4
5
Total
cashflow
8
8
8
8
108
10%
discount
value
0.9091
0.8264
0.7513
0.6830
0.6209
Present
Value
7.2727
6.6116
6.0105
5.4641
67.0595
92.4184
Market Price is Rs 92.4148 (less than Par
Value) when current expectation of yield has
gone up.
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42
Interest Rate
• Suppose that current expectation of yield is
6%. What will be the market price?
Discount
Rate =
year
1
2
3
4
5
Total
cashflow
8
8
8
8
108
6%
discount
value
0.9434
0.8900
0.8396
0.7921
0.7473
Present
Value
7.5472
7.1200
6.7170
6.3367
80.7039
108.4247
Market Price is Rs 108.4247 (more than Par
Value) when current expectation of yield has
come down.
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SPBT COLLEGE.
43
•
• 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.
•
•
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•
•
•
•
•
•
•
•
•
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
11.0000%
10.0000%
YTM
9.0000%
8.0000%
7.0000%
6.0000%
5.0000%
0
1
2
3
4
5
6
7
8
9
10
Time Period in Years
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Yield Curve – Parallel Shifts
Yield Curve - Parallel Shifts
10.2500%
9.7500%
9.2500%
YTM
8.7500%
8.2500%
7.7500%
7.2500%
6.7500%
6.2500%
5.7500%
1
2
3
4
5
6
7
8
9
10
Tenor in Years
YC1
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YC-Rate Rise
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YC-Rate Fall
63
Yield Curve – Stiffening &
Flattening
Yield Curve -Stiffening & Flattening
11.0000%
10.0000%
YTM
9.0000%
8.0000%
7.0000%
6.0000%
1
2
3
4
5
6
7
8
9
10
Tenor in Years
YC1
3/16/2016
YC-Stiff
SPBT COLLEGE.
YC-Flat
64
Duration Analysis
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65
DURATION
A 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”
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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.
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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.
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DURATION ANALYSIS – An Example
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%
Year (Y)
(1)
1
2
3
4
5
6
7
8
9
10
Total
PV
P V*Y
(4)=(2*3)
(5)=(1*4)
5.55556
5.55556
5.14403
10.28807
4.76299
14.28898
4.41018
17.64072
4.08350
20.41750
3.78102
22.68611
3.50094
24.50660
3.24161
25.93291
3.00149
27.01344
49.09851 490.98510
86.57984 659.31497
D=
7.61511
Duration is arrived at by dividing total of Col 5 by
total of Col 4.
Discouting Factor is arrived at by "1/(1+r)^n"
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Inflow
(2)
6
6
6
6
6
6
6
6
6
106
DF at 8%
(3)
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
0.54027
0.50025
0.46319
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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.
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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.
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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.
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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.
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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.
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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.
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