07 market risk kp v2

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Market risk

Risk Management courseCorvinus University of Budapest

4th March 2010

Petra Kalfmann, [email protected]

Director


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bankrkpz TANCSADS S OKTATS 2

Market risk

Every asset that has quoted price on themarket (~ traded assets) are exposed tomarket riskMarket risk factors

Interest rates (bond prices)Stock pricesFX rates

Commodity pricesVolatility


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ban

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Int

erestr

ateris

k

00,5 1

1,5 2

2,5 3

3,5 4

4,5 5

2006.12.29

2007.03.01

2007.05.01

2007.07.01

2007.09.01

2007.11.01

2008.01.01

2008.03.01

2008.05.01

2008.07.01

2008.09.01

2008.11.01

2009.01.01

2009.03.01

2009.05.01

2009.07.01

2009.09.01

2009.11.01

2010.01.01

%


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Interest rate risk

Interest rate risk related assets bonds

Relationship between interest rate and bondprice: Duration and ConvexityDuration: sensitivity of bond price on interest rate

movement linear componentConvexity: sensitivity of bond price on interest ratemovement non-linear component

Volatility of shorter maturities is higherLonger the maturity longer the duration higher the effect on bond price

4


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Volatility of interest rates and impact onbond prices

5

-0,10%

-0,05%

0,00%

0,05%

0,10%

0,15%

0,20%

0,25%

-30,00%

-25,00%

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

5,00%

10,00%

15,00%

200

7.

01.

02

200

7.

03.

02

200

7.

05.

02

200

7.

07.

02

200

7.

09.

02

200

7.

11.

02

200

8.

01.

02

200

8.

03.

02

200

8.

05.

02

200

8.

07.

02

200

8.

09.

02

200

8.

11.

02

200

9.

01.

02

200

9.

03.

02

200

9.

05.

02

200

9.

07.

02

200

9.

09.

02

200

9.

11.

02

201

0.

01.

02

change in EUR 3M yield change in 3M bond price based on D&Cx

Characteristics of 1 day

logreturns of 3M yieldsand its effect on priceof 3M zero bond:

1 day r(log)

change in 3M

bond price

average -0,30% 0,0010%

volatility 2,71% 0,0124%

Why logreturn?


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Volatility of interest rates and impact onbond prices

6

Characteristics of 1 day

logreturns of 5Y yieldsand its effect on priceof 5Y zero bond:

1 day r(log)

change in 3M

bond price

average -0,06% 0,0165%

volatility 1,37% 0,2343%-6,00%

-4,00%

-2,00%

0,00%

2,00%

4,00%

6,00%

8,00%

change in EUR 5Y yield change in 5Y bond price based on D&Cx


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Stock price risk

7

0

50

100

150

200

250

300

350

400

450

0

5000

10000

15000

20000

25000

30000

35000

BUX (left) MAX (right)

BUX: stock price index of Budapest Stock ExchangeMAX: price index of long maturity bonds

Characteristics of BUX

and MAX 1 daylogreturns:

BUX MAX

average 0,04% 0,03%



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Characteristics of stock pricemovements

On efficient markets, assuming a huge samplethe daily log returns are

Independent and

Normally distributed

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Independency

9

-15%

-10%

-5%

0%

5%

10%

15%

-15% -10% -5% 0% 5% 10% 15%

r(t)

r(t-1)

BUX

BUX


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Norm

aldis

tribution

0

%

2

%

4

%

6

%

8

%

10

%

12

%

14

%

16

%

-8,0%

-7,5%

-7,0%

-6,5%

-6,0%

-5,5%

-5,0%

-4,5%

-4,0%

-3,5%

-3,0%

-2,5%

-2,0%

-1,5%

-1,0%

-0,5%

0,0%

0,5%

1,0%

1,5%

2,0%

2,5%

3,0%

3,5%4,0%

4,5%

5,0%

5 5%

BUXempiricaldistribution

Normaldistribu

tion


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FX risk

11

Characteristics of EUR

and USD FX rate 1 daylogreturns:

EUR USD

average 0,00% -0,02%


100

150

200

250

300

350

EUR FX

USD FX


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What is the price of risk?

Risk premia: the additional return of a risky asset over the return of therisk-free assetUS data: Roger Ibbotson Rex Sinquefield (1982): Stocks, Bonds, Bills

and Inflation

BUX-MAX

Data as of 1998:T-bills: 3 monthSome above inflation, avg. return is 3.75%

Long term goverment bonds: 200 bp premia(5.75%)US stocks: 700 bp premia (10.75%)Small stocks: additional 200 bp premia (12.75%)

2003 18,9%

2004 31,7%

2005 25,7%

2006 11,1%

2007 -0,5%Avg. 98-07 -2,0%

Avg. risk premia p.a.


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Measurement of risk

The easiest way of measuring risk is: volatility (avg. deviationfrom the mean)

Assumption: the return of financial assets has nomaldistribution; in this case we can assume that the statisticsrepresenting the past can give a good foreast for the futureProblems:

Positive and negative deviations from the mean has the same weightwhen calculating the volatilityAbsolute value it is not convenient for ranking investments withoutknowing the return of the investment

1

)( 2

=

n

xx

BUX MAX RMAX

Avg. daily return 0,03% 0,04% 0,04%

Avg. daily volatility 1,70% 0,33% 0,09%

Volatility p.a. 26,82% 5,30% 1,46%


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Measurement of risk

V@R concept: Value atRisk

possible future lossin a given time periodwith a given probability

in normal marketenvironment

15

John Pierpont (J.P.)Morgan (1837-1913)

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V@R concept

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0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Possible future loss at a givenprobability = VAR


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V@R interpretation

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V@R (1 day, 99,9%) = 10 M

Optimistic

99,9% is the probability thatwe may lose less than 10 M

forint tomorrow on a givenfinancial asset/portfolio

Pessimistic0,1% is the probability thatwe may lose more than 10 Mforint tomorrow on a given

financial asset/portfolio


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V@R parameters

Liquidation period: the liquidation period ofthe given financial asset the longer thisperiod the higher the V@R

Confidence interval: depends on the riskappetite of the bank the higher theconfidence interval the higher the V@R

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V@R calculation

VaR = p Position Volatiltiy

p parameter depends on the level of risk(probability)

1-p= 99% p

= - 2,326

1-p= 95% p = - 1,645

Volatility: volatility of the risk factorPosition: value of position today

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V@R of one share

= position valueN: number of sharesS: spot price

P/L =

w: position valuer: return (logarithmic)

SNw =

rwS

SSNSNw =

==

rp wVaR =


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Example

OTPWhat is the VaR of one OTP share?

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OTP


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V@R of more than one risk factor

Portfolio effect => diversificationThe risk of portfolio depends on:

the weight of each element in the portfoliothe risk of each element in the portfoliothe correlation between the returns of the elements of theportfolio

Correlation:Perfect co-movement (1)Perfect adverse movement (-1)Neutral co-movement (0)

22

ijj

i j

iport ww =2

ABBABABBAAAB wwww ++= 2)()(222

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ABBAAB =cov

covariance


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V@R of more than one risk factor

Mapping the portfolio into risk factors:(w1; w2; w3 wn)w

i: weight of risk factor i

Assuming that the risk factors follow normaldistribution:

VAR =p w = =

C is the covariance matrix of the returns of riskfactorsR is the correlation matrix of the returns of riskfactors, r is the volatility vector of returnsw is the weight of each risk factor in the portfolio

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wCwp )()( wRwp

portfolio risk


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Why banks have market risk?

Trading book vs banking bookTrading book was launched in 1996 as

amendment to the capital regulation oncredit risk (so called Basel 1 regulation)Why? Banktrupcy of Barings in 1995

Operational risk: front-office (trading) andback-office (settlement) under the control ofthe same person (Nick Leeson)

Market risk: huge volumes on futuresmarket speculation on short side, butmarket turned to downside !

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Trading book: assets held with trading intent with theaim of reaching short term return

T-bond, T-bills (10-20% of all assets)SharesFX risk in the whole portfolio !

Capital requirement has to be measured and settled

against the riskIn case of market risk capital requirement is necessary tocover the potential future losses ~ V@R

Two measures:

Simple risk weigthsV@R methodologywith scaling factor: multiplier is 3with predefined parameters: 99%, 10 days

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Market risk in the banking book:FX risk: managed under trading book rules

Interest rate risk yes, it must be managed underbanking book as well

Interest rate risk in the banking book: riskarising from the different interest ratecharacteristics of assets and liabilities

Different maturitiesDifferent base ratesDifferent repricing periods

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IR in banking book

Repricing riskYield curve riskBasis riskEmbedded options

Mortgage retail portfolios (refinancing option)Current accounts (no maturity)

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IR in banking book

Repricing GAP

RSA: risk sensitive assetsRSL: risk sensitive liabilitiesNII: change of expected net incomei: expected change in return

Duration GAP

V@R methodsEarnings at RiskEconomic Value of Equity

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ttt RSLRSAGAP = expexp iGAPNII =


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Repricing GAP

Increasing interest

rates

Negative GAPPositive GAP

Decreasing interest

rates


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Value based approach

Measuring interest rate risk sensitivity with well knonw D(mod) and Cx

2*

21 drCxdrD

P

dP +=


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Duration GAP

Considers the risk sensitivity of assets and liabilitiesAssuming that assets and liabilities are bonds (predefined

cash-flows)

( ) DLMVAMVLDADGAP =

( )[ ] MVAiiDGAPEVE += 1

Duration GAP of total bank portfolio:

Assets: D(A)

Market valueof assets:

MVA

Liabilities(deposits,

money marketliab): D(L)

Market value ofliabilities: MVL

Equity: D(E)

EVE=?

DGAPED =)(


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Case study Interest rate risk exposure in the

world nowadays in pictures


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Liquidity risk as market risk

Maturity mismatch between assets andliabilities at banks is natural

Liquidity risk: the bank is not able to fulfill itsliabilities at due date without suffering non

expected lossLiquidity Solvency !

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Liquidity risk as market risk

Funding liquidity risk: the bank is not able torenew its funds

in required volumeat acceptable price

Asset liquidity risk: the bank is not able to sellits assetsat acceptable price

in acceptable timeframe

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So


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0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

2001. 12.

2002. 12.

2003. 03.

2003. 06.

2003. 09.

2003. 12.

2004. 03.

2004. 06.

2004. 09.

2004. 12.

2005. 03.

2005. 06.

2005. 09.

2005. 12.

2006. 03.

2006. 06.

2006. 09.

2006. 12.

2007. 03.

2007. 06.

2007. 09.

2007. 12.

2008.01.

2008.02.

2008.03.

2008.04.

2008.05.

2008.06.

2008.07.

2008.08.

2008.09.

2008.10.

2008.11.

2008. 12.

2009.01.

2009.02.

2009.03.

gyflhitelek/gyflbettek

Fundingliqu

idityr

isk

ource:H

FSA

EUavera

Loans/Depositsfu

nding

gap


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R lt f f di li idit h li idit f


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Result of funding liquidity gap when liquidity ofmarkets disapper Case study 1

Source: www.bearstearns.com, February, 2008.

17 March 2008: JP


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17 March 2008: JP

Morgan announced theacquistion of BS with

the financial help ofFED

The role of central banks in providing liquidity on


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The role of central banks in providing liquidity onthe market (lender of last resort)

Concerns about credit exposure in financial markets began to surface in the summer of 2007and credit spreads (the cost of credit) increased. The announcement by a major USinvestment bank of difficulties in one of its investment conduits and subsequent similarannouncements by other banks led to a serious disruption in the medium term funding

markets on 9 August 2007. This quickly led to severe restrictions in the liquidity of the shortterm wholesale markets. Despite these restrictions during August and early September 2007Northern Rock continued to fund in the short dated wholesale markets and maintained significantbalances of liquid assets.In the week commencing 10 September 2007, despite the fact that the Company continued toraise funds at shorter durations, the general tightening of longer term liquidity and the closure of

the securitisation and medium term markets meant it was necessary to arrange a facility in casesuch markets failed to reopen.Therefore an approach was made to the Bank of England to provide a loan facility to theGroup. (Annual Report 2007)

Non derivatives CF


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FundingTightening of longer term liquidity and closure ofsecuritisation and medium term financing marketsled to the need to arrange a liquidity support facilityfrom the Bank of England in the second half of 2007The Bank of England loan facilities to NorthernRock as at 31 December 2007 stood at 26.9 billionand have since fallen to around 24 billionFull year net outflow of retail funds of 12.2billion reflects significant withdrawals by retail

depositors during the second half of 2007Level of retail deposits since stabilised and showingsigns of improvement in 2008

www.northernrock.co.uk

Non derivatives CF

bank run


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MARKET RISK

Classification of liquidity risk

ClassificationMaturity liquidity risk: riskarising from maturity mismatch

Withdrawal liquidity risk: riskof withdrawal of huge volumeof deposits before maturity(bank run)Structural liquidity risk: risk

of renewal of funds and theshift in cost of fundsMarket liquidity risk: riskarising from the liquidityproblems of the market(position cannot be closed ingiven timeframe)

MeasurementStatic/dynamic maturitymismatch, limits

Scenario analysis, expertestimation

Increasing risk premium increase in funding cost V@RV@R with longer liquidityhorizon

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Thank you for yourattention!

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Effective and logarithmic interest rate

Effective interest rate is based on thecompounding interest rate calculation

Logarithmic interest rate calculation gives thesame result but on a different scale (likeCelcius and Fahrenheit both measurestemperature but on a different scale)The relationship is as follows (i: log return)

i

eff er =+1 )1ln( effri +=

Eff i d l i h i i


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Effective and logarithmic interest rate

Example

r(eff)1 = 120/100-1 = 20%r(log)1 = ln(120/100) = 18,23%

Logreturn is additive => cumulated logreturn =sum of daily logreturns-4,08% = 18,23% -22,31% !

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t S r eff r log

0 1001 120 20,00% 18,23%

2 96 -20,00% -22,31%

Total -4,00% -4,08%

N l di t b ti


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Normal distrubution

Normal distribution: continuous distribution

Characteristics: average, volatility: N(, )

Standard normal distribution: N(0, 1)Density function of normal distribution

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

-5,0 -4,0 -3,0 -2,0 -1,0 0,0 1,0 2,0 3,0 4,0 5,0

I t t fid i t l f l


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Important confidence intervals of normal

distribution95% one-side confidence interval

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

-5,0 -4,0 -3,0 -2,0 -1,0 0,0 1,0 2,0 3,0 4,0 5,0

5%

95%

-1,645 1,645

Inverted function

I t t fid i t l f l


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Important confidence intervals of normal

distribution99% one-side confidence interval

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

-5,0 -4,0 -3,0 -2,0 -1,0 0,0 1,0 2,0 3,0 4,0 5,0

1%

99%

-2,326 2,326

07 market risk kp v2

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