dr. luděk koleček fixed income risk controlling universität passau 06.06.2012

Dr. Luděk Koleček

Fixed Income Risk Controlling

Universität Passau06.06.2012

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2

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45

22

Market Risk Models3

1

Multifactor Risk Model (Wilshire Axiom)

Discussion

Duration

Fixed Income instruments

Agenda


5

5

What are “Fixed Income Instruments”?

INTEREST

Bonds (government bonds, sovereign bonds, municipal bonds, corporate bonds, agency bonds), inflation-linked bonds, etc.

Money market instruments (commercial papers) Asset backed securities ABS (MBS, CDO, CMO,…) Fixed income derivative instruments Swaps, repos,

swaptions, bond futures, interest rate futures, credit default swaps, currency forwards,…


6

6

Interest rates

- Yield, Yield to maturity, bonds pricing

-Yield curves


7

7

German sovereign yield curve (Bloomberg 31/05/2012)


8

8

Duration

-Quantification of price sensitivity to yield

-Macauley Duration: measures weighted average maturity of cash flows

-Modified Duration: is a price sensitivity measure

-Effective Duration: more exact measure of price sensitivity


9

9

Effective duration (option adjused duration)-The yield curve structure is taken into account-The embedded options (optionality) is taken into account: callable bonds, putable bonds, prepayment options

Duration „Versions“

- Modified duration at call, at worst, as maturity- Duration calculation for Inflation-linked bonds („yield beta“)

- Spread duration – sensitivity of a bond price to changes in the spread (credit)

Pure Level (d1) Shift (+/- 100 bp)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 5 10 15 20 25 30

Term (Years)

Yie

ld (%

)

Rising

Falling

Initial Curve

Bullish Curve

Bearish Curve


10

10

Convexity

- Typically the price is a convex function of interest rate changes- Convexity measures the curvature of the price-interest rate

function- Mathematically: it is the 2nd derivation of the price with respect

to interest rate


11

11

Credit spread

- Spread is an amount that is added to the government yield curve to obtain the market price

-Option Adjusted Spread (effective spread) – includes also the bond optionalities

-Spread Duration Sensitivity of a bond price to changes in the spread Principally the same as regular duration. Differences for floating bonds and mortgage back securities

(prepayment)

-Rating


12

12


13

13


14

14

Market Risk

- Ex-post: derived from realized performance figures Volatility (standard deviation of portfolio returns in the

past) Tracking error (standard deviation of relative portfolio

returns, i.e. difference of portfolio and benchmark returns) Historic Portfolio/Benchmark holdings during the evaluation

period (e.g. 3 years)

- Ex-ante: derived from a market model Absolute and relative (volatility and tracking error) Value at Risk - maximal expected loss amount within a

given time horizon in the future Current portfolio/benchmark holdings


15

15

Market Risk – Ex-ante Risk Models

- Time Series Models Forecast of the expected risk on the basis of single security

return time series, like Historical Simulation techniques, Monte-Carlo techniques

higher forecast accuracy no explanation of risk sources high computational effort

- Factor Models Based on factor returns and factor exposures lower forecast accuracy explanation of risk sources available Prespecified factor models vs. Principle component


16

16

Wilshire AXIOM – Multi Factor Model

- A model with pre-specified exposure based on observations in the market between security returns and security characteristics.

- Decomposition of security returns into yield, systematic effects and an idiosyncratic term as

Local security

return Yield return

, , , ,

Yield return Security exposurescomprises both to systematic effesystematic and

idiosyncratic effects,to the extent that

security pricing doesas well

i t i t i j tr y D

Idiosyncratic

Systematic factor effects return

, ,

Systematic effects,cts, e.g., magnitude of

e.g., duration parallel shift in yields

j t i tj

Wilshire AXIOM Global Credit Risk Model


17

17

Term structure factors – shift, twist, butterfly

Pure Level (d1) Shift (+/- 100 bp)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 5 10 15 20 25 30

Term (Years)

Yie

ld (%

)

Rising

Falling

Initial Curve

Bullish Curve

Bearish Curve

Pure Slope (d2) Shift (+/- 100 bp)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 5 10 15 20 25 30

Term (Years)

Yie

ld (%

)

Bullish Curve

Bearish Curve

Initial Curve

Steepening

Flattening

Pure Curvature (d3) Shift (+/- 100 bp)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 5 10 15 20 25 30

Term (Years)

Yie

ld (%

)

Bullish Curve

Initial Curve

Bearish Curve

Bulging

Saucering


18

18

Estimated yield curve changes with D1, D2 and D3

t

tt

tttt

df

Ftdf

kyD

/1

1

Estimated vs. real yield curve change (GBP 09/2011 - 12/2011)

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 5 10 15 20 25 30 35

Estimated Shift yield curves change BB

1:1 tFD 7/1:2 tt eFD

)7/1()7/(:3 tt etFD


19

19

Wilshire AXIOM – Multi Factor Model (3) - Overview

Multi Factor Model Yield

Term Structure Model

Sector

Quality

Currency

Other Spread (Euro Country, Prepayment, etc.)


20

20

Wilshire AXIOM – Multi Factor Model (2)

Returns to each of the factors are estimated with a two-stage cross-sectional regression

The first stage includes the D1, D2, and D3 factors for all of the currencies as well as the euro spread factors

The second stage estimates the credit factors Regression universe: mainly Merrill Lynch Regression period: 18 month equally weighted daily data

The covariance matrix is built from the daily estimated factor returns.

New matrices are created each month-end. Ex-ante tracking error and risk estimates are determined by

applying the calculated sensitivities to the covariance matrix.

Wilshire AXIOM Global Credit Risk Model – Regression and Covariance Matrix


21

21

Cross Sectional Regression Process

First regression measures Treasury yield curve shifts by regressing local currency returns in excess of yield and convexity effects on D1, D2, and D3 on Treasury bonds for each currency in model:

Second regression measures spread changes by sector and quality buckets by regressing return in excess of yield, convexity, and D1, D2, and D3 on spread durations and elasticities for non-Treasury bonds for each currency in model:


22

22

Specific Risk

The specific risk factor coefficients are obtained through a two-step estimation using the factor return residuals. The basic assumptions about the factor return residuals specific risk from the regression are:

• The residuals follow a normal distribution.• The residuals have no correlation with the factor returns.• The estimated risk is proportional to the spread duration.

Step I : Sector coefficients calibrated with Aaa rated securities.

Step II : Quality coefficients calibrated with non-Aaa rated securities.


23

23

Specific Risk Illustration: Quality Coefficient


24

24

Risk Report

Portfolio Fund 1 Portfolio Database: SIMCORP:DIM

Benchmark Benchmark 1 Base currency: EUR

Portfolio Description Asset type Rating Allocation in %PF BM PF BM PF BM

MkVal MkVal Eff Dur Eff Dur MkVal MkVal% % Contr Contr % %

Portfolio 84 208 4.4 5.0 4.0 6.3 3.8 BBB+ 1.16 0.19 Bond 98.1 100.0 4.1 5.3 AAA 25.6 43.8Benchmark 3,026 5.3 5.4 4.0 7.0 2.7 A+ 0.08 0.06 Future 0.0 0.0 0.3 0.0 AA 12.8 16.4

Option 0.0 0.0 0.0 0.0 A 43.6 30.6FX 0.1 0.0 0.0 0.0 BBB 12.4 7.7Cash 1.9 0.0 0.0 0.0 High Y 4.5 1.4

n.r. 1.2 0.1

Contribution to Effective Duration Hedged Currency weights (%)

Sector risk (government by country) Effective Duration contribution by sector

%Edur Contr

Sdur Contr

%Edur Contr

Sdur Contr

PF(24) 27.5 1.6 1.6 PF(1) 1.1 0.1 0.1BM 56.4 3.5 3.5 BM 2.9 0.2 0.2PF(1) 0.6 0.0 0.0 PF(3) 4.2 0.3 0.3BM 0.0 0.0 0.0 BM 3.6 0.2 0.2PF(13) 7.7 0.3 0.3 PF(2) 2.4 0.2 0.2BM 8.0 0.4 0.4 BM 17.1 1.0 1.0PF(1) 1.3 0.1 0.1 PF(8) 9.7 0.4 0.4BM 3.0 0.1 0.1 BM 7.2 0.4 0.4PF(3) 2.1 0.2 0.2 PF(1) 0.2 0.0 0.0BM 1.0 0.0 0.0 BM 15.6 1.0 1.0PF(6) 4.1 0.6 0.6 PF(13) 14.5 0.8 0.8BM 3.0 0.2 0.2 BM 13.1 0.8 0.8PF(27) 8.0 0.3 0.3 PF(2) 1.3 0.0 0.0BM 6.7 0.3 0.3 BM 0.1 0.0 0.0PF 0.0 0.0 0.0 PF(2) 1.0 0.1 0.1BM 1.4 0.1 0.1 BM 4.6 0.3 0.3PF(39) 16.5 0.4 0.6 PF(1) 1.3 0.1 0.1BM 8.1 0.3 0.4 BM 0.3 0.0 0.0PF(38) 8.6 0.0 0.3 PF(6) 4.1 0.6 0.6BM 0.1 0.0 0.0 BM 3.0 0.2 0.2PF(11) 2.4 0.0 0.0 PF(9) 3.6 0.0 0.2BM 0.0 0.0 0.0 BM 3.9 0.0 0.2PF(26) 18.3 0.6 0.7BM 12.2 0.5 0.5PF(9) 1.1 0.0 0.1BM 0.0 0.0 0.0PF(10) 1.8 0.3 0.3BM 0.0 0.0 0.0

Risk (ex-ante) Wilshire Axiom Multi-Factor Model

Factor Risk

Duration Term Sector Quality Other spread Currency CovarianceSpecific Risk

TE Risk Decomposition in time Total Risk and Effective Duration in time

Comments

Risk Report 30/03/2012

MarketValue

Gov

Default prob(%)

SprDur

EffDur

BE

Gov AT

Yield toMat

AvgLife

AvgCpon

% n.r.Rating

Avg

No. ofinvestm

ents

Disclaimer: All details and information contained in this report have been carefully investigated and checked by IDS GmbH – Analysis and Reporting Services (IDS), however IDS does not assume liability for the accuracy and/or completeness of the content. The content of the report must be considered confidential. The design of the report is subject to copyright ©.

245

41.2 (15%) 60.0 (5%)

395.228.1 28.1 70.4

47.8

260

20111230

-558.9 -521.9

313.0

42.7 (2%) 60.8 (2%)

65.631.8 24.6

20120330

105.4 261.3 280.7 386.9 340.2

47.1

444.6

7.6 (0%)-125.2 -102.7

1 Day VaR (95%) in tsd 92 175

Ris

kD

ec

om

po

sit

ion

13.1 9.0

89.8

0.088.9 268.1

-684.14.8 9.8 4.8 9.8

77.5 340.0380.7

332.9

19.7 18.3

449.2457.9 484.2

Total

90.3 11.4 359.4

Tracking Error (in bps) Total Risk PF (in bps)

97.1 (85%) 254.4 (95%) 277.4 (98%) 382.1 (98%)

2012033020120330 20111230

0.0-651.9

7.6 (0%)

Total Risk BM (in bps)

332.8 (100%)

450.0464.043.5

340.1 (100%)

20111230

produced by: IDS GmbH

17/04/2012

Ludek Kolecek

++49 89 3800 15139

DE

ES

FR

IT

LU

NL

PL

YY

Other

Gov_Relat_Oth

Gov_Relat

AgencGov_Relat

Local_AuthGov_Relat

SovGov_Relat

Supra

Corp

ABSSec

Gov_Relat

IndCorp

UtilCorp

CMOSec

CashCash

CMBSSec

CoveredSec

Fin

0.0

0.3

0.8

0.6

1.2

0.9

0.6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

<1Y 1-3Y 3-5Y 5-7Y 7-10Y 10-20Y >20Y

PFBM

99.5

0.50

20

40

60

80

100

EUR Other

PF

BM

0 0.5 1 1.5 2 2.5 3 3.5 4

Gov

Gov_Relat_Oth

Agenc

Local_Auth

Sov

Supra

Ind

Util

Fin

ABS

CMBS

Covered

CMO

Cash

PF

BM

230

264

298

332

366

400

20110331 20110531 20110729 20110930 20111130 20120131 20120330

TR

in

bp

s

0.00

1.40

2.80

4.20

5.60

7.00

Eff

Du

r

EFF DUR PF EFF DUR BM TR PF TR BM

90

126

162

198

234

270

20110331 20110531 20110729 20110930 20111130 20120131 20120330

TE

in

bp

s

0%

20%

40%

60%

80%

100%

Duration Term Sector Quality OtherSpread Currency SpecificRisk TE


25

25

Risk Report – part 1

Portfolio Fund 1 Portfolio Database: SIMCORP:DIM

Benchmark Benchmark 1 Base currency: EUR

Portfolio Description Asset type Rating Allocation in %PF BM PF BM PF BM

MkVal MkVal Eff Dur Eff Dur MkVal MkVal% % Contr Contr % %

Portfolio 84 208 4.4 5.0 4.0 6.3 3.8 BBB+ 1.16 0.19 Bond 98.1 100.0 4.1 5.3 AAA 25.6 43.8Benchmark 3,026 5.3 5.4 4.0 7.0 2.7 A+ 0.08 0.06 Future 0.0 0.0 0.3 0.0 AA 12.8 16.4

Option 0.0 0.0 0.0 0.0 A 43.6 30.6FX 0.1 0.0 0.0 0.0 BBB 12.4 7.7Cash 1.9 0.0 0.0 0.0 High Y 4.5 1.4

n.r. 1.2 0.1

Contribution to Effective Duration Hedged Currency weights (%)

Risk Report 30/03/2012

MarketValue

Default prob(%)

SprDur

EffDur

Yield toMat

AvgLife

AvgCpon

% n.r.Rating

Avg

No. ofinvestm

ents

produced by: IDS GmbH

17/04/2012

Ludek Kolecek

++49 89 3800 15139

0.0

0.3

0.8

0.6

1.2

0.9

0.6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

<1Y 1-3Y 3-5Y 5-7Y 7-10Y 10-20Y >20Y

PFBM

99.5

0.50

20

40

60

80

100

EUR Other

PF

BM


26

26

Risk Report – part 2

Sector risk (government by country) Effective Duration contribution by sector

%Edur Contr

Sdur Contr

%Edur Contr

Sdur Contr

PF(24) 27.5 1.6 1.6 PF(1) 1.1 0.1 0.1BM 56.4 3.5 3.5 BM 2.9 0.2 0.2PF(1) 0.6 0.0 0.0 PF(3) 4.2 0.3 0.3BM 0.0 0.0 0.0 BM 3.6 0.2 0.2PF(13) 7.7 0.3 0.3 PF(2) 2.4 0.2 0.2BM 8.0 0.4 0.4 BM 17.1 1.0 1.0PF(1) 1.3 0.1 0.1 PF(8) 9.7 0.4 0.4BM 3.0 0.1 0.1 BM 7.2 0.4 0.4PF(3) 2.1 0.2 0.2 PF(1) 0.2 0.0 0.0BM 1.0 0.0 0.0 BM 15.6 1.0 1.0PF(6) 4.1 0.6 0.6 PF(13) 14.5 0.8 0.8BM 3.0 0.2 0.2 BM 13.1 0.8 0.8PF(27) 8.0 0.3 0.3 PF(2) 1.3 0.0 0.0BM 6.7 0.3 0.3 BM 0.1 0.0 0.0PF 0.0 0.0 0.0 PF(2) 1.0 0.1 0.1BM 1.4 0.1 0.1 BM 4.6 0.3 0.3PF(39) 16.5 0.4 0.6 PF(1) 1.3 0.1 0.1BM 8.1 0.3 0.4 BM 0.3 0.0 0.0PF(38) 8.6 0.0 0.3 PF(6) 4.1 0.6 0.6BM 0.1 0.0 0.0 BM 3.0 0.2 0.2PF(11) 2.4 0.0 0.0 PF(9) 3.6 0.0 0.2BM 0.0 0.0 0.0 BM 3.9 0.0 0.2PF(26) 18.3 0.6 0.7BM 12.2 0.5 0.5PF(9) 1.1 0.0 0.1BM 0.0 0.0 0.0PF(10) 1.8 0.3 0.3BM 0.0 0.0 0.0

Gov

BE

Gov AT

DE

ES

FR

IT

LU

NL

PL

YY

Other

Gov_Relat_Oth

Gov_Relat

AgencGov_Relat

Local_AuthGov_Relat

SovGov_Relat

Supra

Corp

ABSSec

Gov_Relat

IndCorp

UtilCorp

CMOSec

CashCash

CMBSSec

CoveredSec

Fin

0 0.5 1 1.5 2 2.5 3 3.5 4

Gov

Gov_Relat_Oth

Agenc

Local_Auth

Sov

Supra

Ind

Util

Fin

ABS

CMBS

Covered

CMO

Cash

PF

BM


27

27

Risk report – part 3

Risk (ex-ante) Wilshire Axiom Multi-Factor Model

Factor Risk

Duration Term Sector Quality Other spread Currency CovarianceSpecific Risk

TE Risk Decomposition in time Total Risk and Effective Duration in time

245

41.2 (15%) 60.0 (5%)

395.228.1 28.1 70.4

47.8

260

20111230

-558.9 -521.9

313.0

42.7 (2%) 60.8 (2%)

65.631.8 24.6

20120330

105.4 261.3 280.7 386.9 340.2

47.1

444.6

7.6 (0%)-125.2 -102.7

1 Day VaR (95%) in tsd 92 175

Ris

kD

eco

mp

osi

tio

n

13.1 9.0

89.8

0.088.9 268.1

-684.14.8 9.8 4.8 9.8

77.5 340.0380.7

332.9

19.7 18.3

449.2457.9 484.2

Total

90.3 11.4 359.4

Tracking Error (in bps) Total Risk PF (in bps)

97.1 (85%) 254.4 (95%) 277.4 (98%) 382.1 (98%)

2012033020120330 20111230

0.0-651.9

7.6 (0%)

Total Risk BM (in bps)

332.8 (100%)450.0464.043.5

340.1 (100%)

20111230

230

264

298

332

366

400

20110331 20110531 20110729 20110930 20111130 20120131 20120330

TR

in

bp

s

0.00

1.40

2.80

4.20

5.60

7.00

Eff

Du

r

EFF DUR PF EFF DUR BM TR PF TR BM

90

126

162

198

234

270

20110331 20110531 20110729 20110930 20111130 20120131 20120330

TE

in

bp

s

0%

20%

40%

60%

80%

100%

Duration Term Sector Quality OtherSpread Currency SpecificRisk TE


28

28

Performance Attribution – part 1

Portfolio 2.66%Benchmark 1.96%

Active 0.71%

81 228 4.8 5.5 4.6 6.7 4.2 A-2,996 5.2 5.3 4.1 6.9 3.0 A+

? ?

-0.56 0.60 0.60 0.16 1.24 0.50 0.00 2.52 0.15 2.66-0.70 0.76 0.39 0.09 1.02 0.39 0.00 1.94 0.01 1.960.14 -0.16 0.21 0.06 0.22 0.11 0.00 0.57 0.13 0.71

produced by: IDS GmbH05/03/2012

Ludek Kolecek++49 89 3800 15139

Yield toMat

RatingAvg

MarketValue (mio)

No. ofinvestments

EffDur

SprDur

Performance Attribution 30/12/2011 - 31/01/2012 (linked on-change)

BenchmarkPortfolio

AvgCpon

Descriptive Summary31/01/2012

TotalModelReturn

Fund 1

AvgLife

Market Value Return

Benchmark 1

TermStructure

Sector Quality YieldOther

FactorsCurrency

PortfolioBenchmark

Active

TotalPerformance

(%)

Selection /Interaction /Hedge costs

EffectiveDuration

0.11

0.00

0.71

0.130.14

-0.16

0.21

0.06

0.22

0.57

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

in %


29

29

Performance Attribution – part 2Currency Active exp.* Return (%) Effect

Top 3 contributors

United Kingdom 0.00 0.70 0.00

Euro -0.85 0.00 0.00

Denmark 0.00 -0.03 0.00

Bottom 2 contributors

United States 0.85 -0.83 0.00

Australia 0.00 2.80 0.00

Sector Active exp.* Return (%) Effect

Top 5 contributors

Euro Mortgage 0.70 0.18 0.10

Euro Bank/Finance 0.15 0.60 0.09

Effective Duration Active exp.* Return (%) Effect United Kingdom Bank/Finance 0.06 0.42 0.02

Top 3 contributors Euro Supranational 0.24 0.09 0.01

Euro -0.08 -0.13 0.14 United States Finance 0.02 0.48 0.01

United Kingdom 0.07 0.03 0.00 Bottom 4 contributors

Denmark 0.00 -0.38 0.00 Euro Agency -0.20 0.09 -0.02

Bottom 2 contributors Australia Agency 0.09 -0.17 -0.01

Australia 0.09 -0.02 0.00 Euro Corporate/Industrial -0.11 0.04 -0.01

United States 0.04 -0.04 0.00 United Kingdom Corporate/Industrial 0.02 -0.06 0.00

Term Structure Active exp.* Return (%) Effect Quality Active exp.* Return (%) Effect

Top 4 contributors Top 3 contributors

D3 Australia 0.08 0.17 0.01 United Kingdom Baa 0.08 0.30 0.02

D3 United States 0.04 0.21 0.01 Euro Baa 0.03 0.37 0.02

D3 Denmark 0.00 0.23 0.00 United States A 0.08 0.19 0.01

D2 Denmark 0.00 0.07 0.00 Bottom 1 contributor

Euro A -0.21 0.02 0.00

Bottom 5 contributors

D3 Euro 0.61 0.22 -0.11

D2 Euro -0.44 -0.05 -0.05

D2 Australia 0.06 -0.29 -0.02 Other Factors Active exp.* Return (%) Effect

D3 United Kingdom 0.07 -0.05 0.00 Top 5 contributors

D2 United States 0.01 -0.10 0.00 Euro Country: Belgium -0.22 0.34 0.12

Euro Country: Spain -0.37 0.38 0.05

Yield PF BM Active Euro Country: Portugal -0.01 -4.23 0.03

Top 3 contributors Euro Country: Austria -0.19 -0.06 0.02

United Kingdom 0.06 0.00 0.06 Euro Country: Italy -0.61 0.83 0.02

Euro 0.42 0.39 0.03 Bottom 3 contributors

United States 0.01 0.00 0.01 Euro Country: France -1.18 0.02 -0.02

No negative contributors Euro Country: Netherlands -0.11 0.03 -0.01

Euro Country: Finland -0.06 0.05 0.00

* as of beginning of reporting period

Attribution detail

Government yield curves changes

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15 20 25 30

years

yie

lds

EUR 12/11 - 01/12 AUD 12/11 - 01/12 USD 12/11 - 01/12

source: IDS


30

30

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IDS GmbH – Analysis and Reporting Services

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+49 89 3800 [email protected]

dr. luděk koleček fixed income risk controlling universität passau 06.06.2012

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