rmb market risk

7/30/2019 RMB Market Risk

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MANAGING MARKETRISK IN BANKS


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Contents:

Market Risk

Measuring Market Risk

Value at Risk (VaR)

Approaches to VaR

Basel Committee Recommendation

Indian Scenario

Conclusion


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MARKET RISK

The risk that the value of on or off balance sheet positions will beadversely affected by movements inequity, interest rate markets,currency exchange rates and

commodity prices.- BIS


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An illustration: Bharat Bank has raised a capital of Rs.10000

Invests the same in Shares of IBS ltd . Being quoted at Rs.100.

Bharat Bank buys 100 sharesCapital Scenario Investment Asset Value P/L

10000 Scenario-1:Notallowed toborrow

@Rs100 * 100 shares =Rs10000 0

9500 5% drop in shareprice

@Rs.95 * 100Shares

=Rs.9500 (-)500

Comments:The loss has directly affected the capital due to movement in marketprice

10000 Scenario-2:Allowed to borrow

9 times thecapital

Capital =10000+Borrowings=90000

Total=1,00,000

=Rs100000 0

@Rs100*1000 shares =Rs100000 0

5000 5% drop in shareprice

@Rs.95 * 1000Shares

=Rs95000 (-)5000

Comments:The loss has affected the capital by 50%.(Transaction and borrowingcosts not taken into account in order to facilitate easy understanding)


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Market Risks in BanksType of

MarketRisks

Sub-Types What is it?

Market Risk Risk of adverse deviations of the mark-to-market value of the trading portfolio,due to market movements, during theperiod required to liquidate the

transactionsLiquidationRisk

AssetLiquidityRisk

Refers to a situation where a specificasset faces lack of trading liquidity.

Market

LiquidityRisk

Refers to a situation when there is a

general liquidity crunch in the marketand it affects trading liquidity adversely

Credit andCounterpartyRisk

Refers to the risk on account of defaultof the issuer/obligor or because ofrating migration


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Sources of Market Risk

Related to Interest Rates and orPrices

Interest Rates

Prices of foreign exchange Prices of other financial products

Non-traded Interest Rate Risk It is the direct consequence of banks role as

intermediary Repricing r isk due to change in fixed and

floating rates of its products

Interest rate sensitivity of balance sheet


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Market Risk - Broader types

Market Risks

Specific RiskThe risk of an individual debtor equity security moving bymore than or less than thegeneral market in day-to-daytrading

General RiskThis risk corresponds to the fraction ofmarket risk associated with the volatilityof positions or a portfolio that can beexplained in terms of general marketfactors


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Market Risk Measurement

SensitivitySensitivity ismeasured as thechange in themarket value due tounit change in thevariable.Example:Where market value of aportfolio of bonds changes

by Rs100000 for 1%change in rate of interest,interest rate sensitivity ofthe portfolio isRs100000.It gives us a measure ofrisk associated with theportfolio is vis-a-vischange in rate of interest

DownsidePotential

It captures thepossible lossesignoring profitpotential andintegratessensitivity andvolatility with

adverse affect ofuncertainty.Example:Measured by Value atRisk (VaR)


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VaR

VaR is a risk measurement and managementconcept

It statistically estimates the potential loss in aposition over a given holding position at a givenlevel of certainty due to adverse movement inmarket variables such as interest rates, exchangerates, equity prices or commodity prices.

Mostly used for trading portfolios, and also for strategic balance sheet management


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VaR VaR is an estimate of potential loss, always for a given

period, at a given confidence level..Examples:

A VaR of 5p in USD / INR rate for a 30- day period at 95%confidence level means that Rupee is likely to lose 5pin exchange value with 5% probability, or in other

words, Rupee is likely to depreciate by maximum 5p on1.5 days of the period (30*5% ) .

A VaR of Rs. 100,000 at 99% confidence level for oneweek for a investment portfolio of Rs. 1,00,00,000 (1crore) similarly means that the market value of the

portfolio is most likely to drop by maximum Rs.1,00,000 with 1% probability over one week, or , 99%of the time the portfolio will stand at or above itscurrent value.


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VaR The Definition

VaR summarizes the predicted maximumloss (or worst loss) over a target horizonwithin a given confidence interval.

Target horizon means the period till whichthe portfolio is held. Ideally, the holding

period should correspond to the longestperiod needed for an orderly (as opposedto a `fire sale) portfolio liquidation.


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Three crucial concepts in VaR

Confidencecoefficient

(95%, 99% or99.9%)

Holding period

(period overwhich portfoliois assumed to

be heldconstant).

Historical periodused for

estimating VaRmodel


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Value at Risk:For e.g.., a set of portfolio having acurrent value of say Rs.100,000- canbe described to have a daily value atrisk of Rs. 5000- at a 99% confidencelevel, which means there is a 1/100chance of the loss exceeding Rs.5000/- considering no great paradigmshifts in the underlying factors.It is a probability of occurrence andhence is a statistical measure of riskexposure

Value-at-RiskValue-at-Risk is a measure of Market Risk, which measures the

maximum loss in the market value of a portfolio with a givenconfidence

VaR is denominated in units of a currency or as a percentageof portfolio holdings


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Features of VaR

JP Morgan popularized VaR in1990s

VaR helps the banks to measurerisks in trading portfolios

VaR actually assigns aProbability of happening of loss

VaR quantifies Market Risk

VaR is Prospective


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Advantages of VaRVaR provides an measure of total risk. VaR is usefulfor monitoring and controlling risk within the portfolio.

It is easy to understand and explain the clientele.

It captures an important aspect of risk in a singlenumber

VaR can measure the risk of many types of financial

securities (i.e., stocks, bonds, commodities, foreignexchange, off-balance-sheet derivatives such asfutures, forwards, swaps, and options, and etc.)

It asks the simple question: How bad can things get?


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Weaknesses of VaRApproach

Relies on simplifying statistical assumptions like normaldistribution, etc..

Past may not be a good approximation of future - volatilities andcorrelations can change abruptly

VaR captures end-of-day rates and not intra-day rates which is

important for trading

Does not capture event risk


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Approaches to Calculate

Value at Risk

HistoricalSimulation Method

Monte CarloSimulation

Parametric VaRMethod


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18

0.0.40.30.20.10-0.1-0.2-0.3-0.4-0.5

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

Cumulative Distribution Function of Portfolio Return

p, % return

Probability that % return


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One approach to computing VaR is to assume that the portfoliosreturns are normally distributed. Let the portfolios random rate of

return over a period ofh days be r. Its probability density function is ( )2~ ,r N r

r1.65r

Probability density funct ion

Rate of return, r

2.33r

5 % of areaunder curve

1 % of areaunder curve

VaR with Normally Distributed Portfolio Returns


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This implies that there is a 5 % probability of a returnless thanand a 1 % probability of a return less than

VaR is usually calculated over a measurement horizon ofa small number of days. For this short horizon, aportfolios standard deviation is typically much greaterthan its expected return. Hence, the practice is to ignore

the expected return and set

If this is done, then we have

VaR(p=5 %, h days) =1.65x x(Portfolio Value)VaR(p=1 %, h days) =2.33x x(Portfolio Value)

1.65r

2.33 .r

0.r

=

Computing VaR ..


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An Example:A portfolios 1 day standard deviation is

10%, and its initial value is $1mn.

Then,P = Probabil ity =1%,H = Holding Period = 1 dayS.D = Standard Deviation = 10% = 0.10

VaR(p=1%, h=1 day) = 2.33x(0.10)x1mn= $233,000.

Computing VaR ..


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What should be the time horizon (h days) over which tocalculate VaR? If a FI can measure its risk and change itonce a day, a one-day VaR is most useful. This wouldbe relevant when a FIs portfolio consists of liquidsecurities that can be bought or sold quickly.

However, if a FI holds a portfolio of illiquid assets thatcannot be sold quickly, a longer horizon would berelevant. The FI should choose the VaRs h to be thenumber of days over which it could change its portfolio.

If the return on a portfolio is estimated to have a one-daystandard deviation of, then, assuming the portfolioscomposition stays the same over h days, its h-daystandard deviation can be estimated as

.h

Computing VaR ..

Computing VaR


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Example: A bank holds a $20 m. portfolio of syndicatedloans that would likely take 5 days to arrange for a sale.

The daily standard deviation of the portfolios value is

0.3 %. Therefore,

Suppose a portfolio consists ofn different assets. Itsstandard deviation depends on the standard deviationsand correlations of the individual assets composing theportfolio.

Let i be the proportion of the portfolios total valuethat is invested in asset i, and let i asset is standard

deviation of return. Further, let ij be the correlationbetween the returns on asset i and assetj. Then, theportfolio returns variance is

( )VaR 5%,5 days 1.65x0.003x 5x$20m=$221,371p = =

2

1 1

n n

i j i j ij

i j

= =

=

Computing VaR ..

Computing VaR


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Example: A portfolio has three assets held in proportions1 = 0.2, 2 = 0.5, and 3 = 0.3. The assetsh-day

standard deviations are 1 = 0.3, 2 = 0.2, and 3 = 0.4.Their correlations are 12 = 0.1, 13 = 0.6, 23 = -0.1.The portfol ios h-day return variance is then

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( )( )( )( )( ) ( )( )( ) ( )( )

2

1 1

2 2 2 2 2 2

1 1 2 2 3 3 1 2 1 2 12

1 3 1 3 13 2 3 2 3 23

2 2 2 2 2 2

2

2 2

.2 .3 .5 .2 .3 .4 2 .2 .5 .3 .2 .1

2 .2 .3 .3 .4 .6 2 .5 .3 .2 .4 .1

= 0.03544

n n

i j i j ij

i j

= =

=

= + + +

+ +

= + + ++ +

Computing VaR ..

C ti V R


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Then, the portfolio returns standard deviation is

If the three-asset portfolio was initially worth $50m, then, forexample,

VaR(p=5%, h days) =1.65x0.188 x$50 m = $15.5 m.

Under the approach outlined thus far, implementing VaR fora portfolio of many different assets requires estimates ofeach asset returns standard deviation and the correlationsbetween all of the assets returns.

A consulting firm, RiskMetrics, provides daily estimatesof standard deviations and correlations for different types ofassets in many different countries. Of course, an individualFI could compute these estimates on its own usinghistorical data.

0.03544 0.188 = =

Computing VaR ..


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The historic or back simulation approach uses thehistorical returns on the individual assets contained inthe FIs current portfolio.

It then simulates what would have been the losses onthe current portfolio if this portfolio had been heldduring the historical period, say the last 250 or 500trading days.

Specifically, this approach involves the followingsteps:

VaR Using Back Simulation

C ti V R Hi t i B k Si l ti A h


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1.Consider each of the asset/liability positions in the FIs current portfolio.

Suppose, as before, that there are n different assets and i is theproport ion of the port fol ios total value that is invested in asset i.Obtaindata on the returns of these assets and liabilities for, say, the last500 trading days.

2.Let rit is the return on asset/liability i on prior day t. Then if the portfoliohad been held on that day, its return would have been

3 Next, rank the port folio returns, Rt, for previous t = 1, , 500 daysfrom the lowest return to the highest. Let R5 be the fifth worstreturn over the last 500 days and let R25 be the 25

th worst return over

the last 500 days. Most likely, both of these returns are negative(losses).

4 Then we would compute VaR as;

1

n

t i it

i

R r

=

=

( ) ( )

( ) ( )

25

5

VaR 5%,1 day x portfolio value

VaR 1%,1 day x portfolio value

p R

p R

= =

= =

Computing VaR .. Historic or Back Simulation Approach

C ti V R Hi t i B k Si l ti A h


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A similar procedure using historical returns over, say,h=5 day intervals could be used to calculate

VaR(p, h=5 days).

The advantage of this historical simulation approach is that ituses the sample frequency (histogram) of actual returns.There is evidence that empirical distributions of asset returns

display large losses more frequently than would be predictedby the thin-tailed normal distribution, and the back simulationmethod could account for this.

One disadvantage is that the historical period may not berepresentative of the near future. It may have been anunusually quiet (low volatility) period, and volatility is now likelyto be greater. One correction for this is to give more recentobservations a greater weight.

Computing VaR .. Historic or Back Simulation Approach..


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VaR is the basis for setting minimum capital (net worth) requirements

for large international banks.

In 1996, an amendment to the 1988 Basel Capital Accord created arule for bank capital requirements to cover their liquid securities (non-loan) portfolios, so-called trading accounts:

Required capital for day t+1 =

where SRt

is additional capital to cover idiosyncratic risks. Theterms in brackets are the banks current VaR estimate and anaverage of VaR estimates over the last 60 days.

The multiplier St depends on the accuracy of the banks VaR model.

( ) ( )59

0

max VaR 1%,10days , VaR 1%,10days60

tt t i t

i

Sp p SR

=

= = +

Risk-Based Capital Requirements Using VaR


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St is computed by back-testingthe banks VaR model estimates overthe last 250 days. If the banks daily trading portfolio losses

exceeded VaR(p=1%, h= 1 day) on x days over the last 250 days,

then

Thus, a bank with a less accurate internal VaR model has ahigher multiplier, St , and must have more capital .

3 if 4

3.4 if 5

3.5 if 6

3.65 if 7

3.75 if 8

3.85 if 9

4 if 10

t

x

x

x

S x

x

x

x

=

=

= = =

=


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HistoricalSimulationMethod

1. Focuses more on the historicalaspects of the financial instruments

2. It considers the actual historical ratesand revalues the positions for eachchange in the market

3. It calculates the change in the value

of a position using the actualhistorical movements of theunderlying asset(s) but starting formthe current value of the asset

4. It does not need a variance /covariance matrix.

5. No need to make any explicitassumptions


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MonteCarloSimulation

1. Relies on estimation of VaR by

simulating random scenarios andrevaluing positions in the portfolio

2. It is appropriate for both linear andnon- linear derivative instruments.

3. It calculates the change in the valueof a of a portfolio using a sample ofrandomly generated price structures,correlations between risk factors andthe volatility of these factors.

4. There is a need to make certainassumptions about the marketstructures.


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ParametricVaRMethod

1. It involves the estimation of VaRby using equations that specifyparameters such as volatility,correlations, delta and gamma.

2. It is a deterministic approach

3. It yields usually accurate resultsfor traditional assets and linearderivatives

4. It gives less accurate results fornon-linear derivative products.


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Estimation of VaR The Three Approaches

Methodology Description Applications

Variance/ Covariance(Parametric)

Estimates VaR withequation that specifiesparameters such asVolatility, Correlation,Delta and Gama

Accurate fortraditional assets andlinear derivatives, butless accurate for non-linearDerivatives

Monte CarloSimulation

Estimates VaR bysimulating randomscenarios and revaluingpositions in the portfolio

Appropriate for alltypes of instruments,linear and non-linear

Historical Simulation Estimates VaR byreliving history; takesactual historical ratesand revalues positionsfor each change in the

market


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Back Testing

Is a process where model based VaRis compared with the actualperformance of the portfolio. This iscarried out for evaluating a newmodel or to assess the accuracy of the existing model


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Stress Testing

Stress Testing essentially seeks to determinepossible changes in the market value of aportfolio that could arise due to non-normalmovement in one or more market parameters.

Stress Testing covers many different techniques.Some of important ones are:

1. Simple Sensitivity Test

2. Scenario Analysis

3. Maximum Loss

4. Extreme Value Theory


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The New Basel Capital Accord

Market Risk:

(a) Standardised Method(i) Maturity Method

(ii) Duration Method

(b) Internal Models Method

New Basel Accord II:


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New Basel Accord II:Market Discipline

Disclosure requirements thatallow market participants to

assess key information about abanks risk profile and level ofcapitalisation.

Pillar-III


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Market Risk: Standardized Approach

1. Two alternative approaches

1. Standardized Approach

2. Internal Rating Based (IRB) Approach

2. Standardized Approach

5 distinct sources of market risk are identified viz., interest raterisk, equity position risk, forex risk, commodities risk, optionstrading risk.

3. Illustration of capital charges for interest rate risk

1. Specific interest rate risk (adverse movements in theprice of an individual security owing to factors related toindividual issues)

2. General r isk (arising from movements in market interest

rates).4. Specific interest rate risk.

Three types of securities1. Government

2. Qualifying (securit ies of multi lateral development banks, PSEs,securit ies rated as investment grade by at least 2 rating agencies)

3. Others.


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Market Risk: IRB Approach

1. Concept of Value-at-Risk (VaR)

2. Three crucial concepts in a VaR

(i) Confidence coefficient (95%, 99% or 99.9%)

(ii) Historical period used for estimating VaR model

(iii) Holding period (period over which portfolio is assumed to beheld constant).

A VaR estimate is simply an appropriate percent ile of the banksportfolio loss distr ibution, e.g., If 99% VaR estimate of a bank is Rs.50lakhs, it means that there is only 1% chance that the banks portfolioloss will exceed Rs.50 lakhs.

Basel II proposes a confidence coeffic ient of 99%, a holding period of 10 daysand a historical observation period of at least 1 year.

Capital Requirement (Daily) = Max {Previous day VaR estimate; (Average of VaRof preceding 60 working days) x m}

m (multipl ication factor) = 3 + Minimum value of = 0 (bank performance good)Maximum value of = 1 (poor bank performance)


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Risk Monitoring & Control

Risk Monitoring and Control calls for

implementation of risk and business policiessimultaneously. This is achieved through thefollowing:

1. Policy guidelines limiting roles and authority

2. Limits structure and approval process3. System and procedures to unbundle products

and transactions to capture all r isks

4. Guidelines on portfolio size and mix

5. Defined policy for market to market6. Limit monitoring and reporting

7. Performance Measurement and Resourceallocation


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Managing Market Risk

Board and Senior ManagementOversight

Organizational Structure

Risk Management CommitteeAsset-Liability Committee

Middle Office

Risk Measurement

Interest Rate, Foreign Exchange, Equity


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Managing Market Risk

Risk Measurement

Repricing Gap Models

Measuring Risk to Economic Value Value at Risk

Risk Limits

Gap Limits Factor Sensitivity Limits

rmb market risk

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