Dr. Luděk Koleček
Fixed Income Risk Controlling
Universität Passau
06.06.2012
2
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Agenda
1
2
2
3
4
5
Fixed Income instruments
Duration
Market Risk Models
Multifactor Risk Model (Wilshire Axiom)
Discussion
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What are “Fixed Income Instruments”?
 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,…
INTEREST
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Interest rates
- Yield, Yield to maturity, bonds pricing
-Yield curves
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7
German sovereign yield curve (Bloomberg 31/05/2012)
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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
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9
Effective duration (option adjused
duration)
7.0
Bearish Curve
6.0
Rising
5.0
Yield (%)
-The yield curve structure is taken into
account
-The embedded options (optionality) is
taken into account: callable bonds,
putable bonds, prepayment options
Pure Level (d1) Shift (+/- 100 bp)
Falling
4.0
Initial Curve
3.0
Bullish Curve
2.0
1.0
0
Duration „Versions“
5
10
15
20
25
30
Term (Years)
-
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)
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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
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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
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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
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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
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Wilshire AXIOM – Multi Factor Model
Wilshire AXIOM Global Credit Risk 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
ri ,t 
Yield return
y i ,t
Yield return
comprises both
systematic and
idiosyncratic effects,
to the extent that
security pricing does
as well
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Idiosyncratic
return
Systematic factor effects

j
Di , j ,t
Security exposures
to systematic effects,
e.g., duration

 j ,t

 i ,t
Systematic effects,
e.g., magnitude of
parallel shift in yields
16
17
Term structure factors – shift, twist, butterfly
Pure Level (d1) Shift (+/- 100 bp)
Pure Slope (d2) Shift (+/- 100 bp)
7.0
7.0
Bearish Curve
Bearish Curve
6.0
6.0
Steepening
5.0
Flattening
Rising
Falling
Yield (%)
Yield (%)
5.0
4.0
Initial Curve
4.0
Initial Curve
Bullish Curve
3.0
3.0
Bullish Curve
2.0
2.0
1.0
1.0
0
5
10
15
20
25
0
30
5
10
15
20
25
30
Term (Years)
Term (Years)
Pure Curvature (d3) Shift (+/- 100 bp)
7.0
Bearish Curve
6.0
Bulging
Yield (%)
5.0
Saucering
4.0
Initial Curve
3.0
Bullish Curve
2.0
1.0
0
5
10
15
20
25
30
Term (Years)
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Estimated yield curve changes with D1, D2
and D3
f  d t  F

1
D

1 y / k
 f d
t
t
t
D1 : Ft  1
t
t
D3 :
t
D 2 : Ft  1  e t / 7
Ft  (t / 7)  e (1t / 7 )
t
Estimated vs. real yield curve change (GBP 09/2011 - 12/2011)
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
0
5
10
15
Estimated Shift
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20
25
30
35
yield curves change BB
18
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Wilshire AXIOM – Multi Factor Model (3) - Overview
Multi Factor Model

Yield

Term Structure Model

Sector

Quality

Currency

Other Spread (Euro
Country, Prepayment,
etc.)
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Wilshire AXIOM – Multi Factor Model (2)
Wilshire AXIOM Global Credit Risk Model – Regression and Covariance Matrix
 Returns to each of the factors are estimated with a two-stage crosssectional 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.
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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:
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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.
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Specific Risk Illustration: Quality Coefficient
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Risk Report
produced by: IDS GmbH
17/04/2012
Ludek Kolecek
++49 89 3800 15139
Risk Report 30/03/2012
Fund 1
Benchmark 1
Portfolio
Benchmark
Portfolio Description
84
SIMCORP:DIM
Base currency:
EUR
Asset type
No. of
Market
investm
Value
ents
Portfolio
Benchmark
Portfolio Database:
208
3,026
Eff
Dur
Spr
Dur
Avg
Cpon
Avg
Life
Yield to
Mat
Rating
Avg
% n.r.
Default
prob(%)
4.4
5.3
5.0
5.4
4.0
4.0
6.3
7.0
3.8
2.7
BBB+
A+
1.16
0.08
0.19
0.06
Rating Allocation in %
PF
MkVal
%
98.1
0.0
0.0
0.1
1.9
Bond
Future
Option
FX
Cash
BM
MkVal
%
100.0
0.0
0.0
0.0
0.0
PF
Eff Dur
Contr
4.1
0.3
0.0
0.0
0.0
Contribution to Effective Duration
BM
Eff Dur
Contr
5.3
0.0
0.0
0.0
0.0
PF
MkVal
%
25.6
12.8
43.6
12.4
4.5
1.2
AAA
AA
A
BBB
High Y
n.r.
BM
MkVal
%
43.8
16.4
30.6
7.7
1.4
0.1
Hedged Currency weights (%)
1.4
PF
BM
80
0.9
1.0
99.5
100
PF
BM
1.2
1.2
0.8
60
0.8
0.6
0.6
0.6
40
0.3
0.4
20
0.2
0.0
0.5
0.0
0
<1Y
1-3Y
3-5Y
5-7Y
7-10Y
10-20Y
>20Y
Sector risk (government by country)
%
Gov
Gov
PF(24)
BM
Gov_Relat Gov_Relat PF(1)
_Oth
BM
Gov_Relat Agenc
PF(13)
BM
Gov_Relat Local_Auth PF(1)
BM
Gov_Relat Sov
PF(3)
BM
Gov_Relat Supra
PF(6)
BM
Corp
Ind
PF(27)
BM
Corp
Util
PF
BM
Corp
Fin
PF(39)
BM
Sec
ABS
PF(38)
BM
Sec
CMBS
PF(11)
BM
Sec
Covered
PF(26)
BM
Sec
CMO
PF(9)
BM
Cash
Cash
PF(10)
BM
27.5
56.4
0.6
0.0
7.7
8.0
1.3
3.0
2.1
1.0
4.1
3.0
8.0
6.7
0.0
1.4
16.5
8.1
8.6
0.1
2.4
0.0
18.3
12.2
1.1
0.0
1.8
0.0
Edur
Contr
1.6
3.5
0.0
0.0
0.3
0.4
0.1
0.1
0.2
0.0
0.6
0.2
0.3
0.3
0.0
0.1
0.4
0.3
0.0
0.0
0.0
0.0
0.6
0.5
0.0
0.0
0.3
0.0
EUR
Other
Effective Duration contribution by sector
Sdur
Contr
1.6
3.5
0.0
0.0
0.3
0.4
0.1
0.1
0.2
0.0
0.6
0.2
0.3
0.3
0.0
0.1
0.6
0.4
0.3
0.0
0.0
0.0
0.7
0.5
0.1
0.0
0.3
0.0
Edur
Contr
0.1
0.2
0.3
0.2
0.2
1.0
0.4
0.4
0.0
1.0
0.8
0.8
0.0
0.0
0.1
0.3
0.1
0.0
0.6
0.2
0.0
0.0
%
AT
BE
DE
ES
FR
IT
LU
NL
PL
YY
Other
PF(1)
BM
PF(3)
BM
PF(2)
BM
PF(8)
BM
PF(1)
BM
PF(13)
BM
PF(2)
BM
PF(2)
BM
PF(1)
BM
PF(6)
BM
PF(9)
BM
1.1
2.9
4.2
3.6
2.4
17.1
9.7
7.2
0.2
15.6
14.5
13.1
1.3
0.1
1.0
4.6
1.3
0.3
4.1
3.0
3.6
3.9
Sdur
Contr
0.1
0.2
0.3
0.2
0.2
1.0
0.4
0.4
0.0
1.0
0.8
0.8
0.0
0.0
0.1
0.3
0.1
0.0
0.6
0.2
0.2
0.2
Gov
PF
BM
Gov_Relat_Oth
Agenc
Local_Auth
Sov
Supra
Ind
Util
Fin
ABS
CMBS
Covered
CMO
Cash
0
0.5
1
1.5
2
2.5
3
3.5
4
Risk (ex-ante) Wilshire Axiom Multi-Factor Model
Tracking Error (in bps)
Risk
Decomposition
Total
Factor Risk
Duration
Term
Sector
Quality
Other spread
Currency
Covariance
Specific Risk
Total Risk PF (in bps)
Total Risk BM (in bps)
20120330
20111230
20120330
20111230
20120330
20111230
105.4
97.1 (85%)
90.3
89.8
28.1
13.1
88.9
4.8
-125.2
41.2 (15%)
261.3
254.4 (95%)
11.4
47.8
28.1
9.0
268.1
9.8
-102.7
60.0 (5%)
280.7
277.4 (98%)
359.4
395.2
70.4
31.8
313.0
4.8
-558.9
42.7 (2%)
386.9
382.1 (98%)
444.6
457.9
65.6
24.6
77.5
9.8
-521.9
60.8 (2%)
340.2
340.1 (100%)
449.2
484.2
47.1
19.7
380.7
0.0
-684.1
7.6 (0%)
332.9
332.8 (100%)
450.0
464.0
43.5
18.3
340.0
0.0
-651.9
7.6 (0%)
92
175
245
260
1 Day VaR (95%) in tsd
TE Risk Decomposition in time
Total Risk and Effective Duration in time
234
80%
198
60%
162
40%
126
20%
90
0%
20110331
20110531
20110729
20110930
20111130
20120131
EFF DUR BM
TR PF
TR BM
400
7.00
366
5.60
332
4.20
298
2.80
Eff Dur
100%
TR in bps
TE in bps
EFF DUR PF
270
264
1.40
20120330
230
Duration
Term
Sector
Quality
OtherSpread
Currency
SpecificRisk
TE
0.00
20110331
20110531
20110729
20110930
20111130
20120131
20120330
Comments
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 ©.
© IDS GmbH – Analysis and Reporting Services
24
25
Risk Report – part 1
© IDS GmbH – Analysis and Reporting Services
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26
Risk Report – part 2
Sector risk (government by country)
%
Gov
Gov
PF(24)
BM
Gov_Relat Gov_Relat PF(1)
_Oth
BM
Gov_Relat Agenc
PF(13)
BM
Gov_Relat Local_Auth PF(1)
BM
Gov_Relat Sov
PF(3)
BM
Gov_Relat Supra
PF(6)
BM
Corp
Ind
PF(27)
BM
Corp
Util
PF
BM
Corp
Fin
PF(39)
BM
Sec
ABS
PF(38)
BM
Sec
CMBS
PF(11)
BM
Sec
Covered
PF(26)
BM
Sec
CMO
PF(9)
BM
Cash
Cash
PF(10)
BM
27.5
56.4
0.6
0.0
7.7
8.0
1.3
3.0
2.1
1.0
4.1
3.0
8.0
6.7
0.0
1.4
16.5
8.1
8.6
0.1
2.4
0.0
18.3
12.2
1.1
0.0
1.8
0.0
Edur
Contr
1.6
3.5
0.0
0.0
0.3
0.4
0.1
0.1
0.2
0.0
0.6
0.2
0.3
0.3
0.0
0.1
0.4
0.3
0.0
0.0
0.0
0.0
0.6
0.5
0.0
0.0
0.3
0.0
Sdur
Contr
1.6
3.5
0.0
0.0
0.3
0.4
0.1
0.1
0.2
0.0
0.6
0.2
0.3
0.3
0.0
0.1
0.6
0.4
0.3
0.0
0.0
0.0
0.7
0.5
0.1
0.0
0.3
0.0
© IDS GmbH – Analysis and Reporting Services
Effective Duration contribution by sector
%
AT
BE
DE
ES
FR
IT
LU
NL
PL
YY
Other
PF(1)
BM
PF(3)
BM
PF(2)
BM
PF(8)
BM
PF(1)
BM
PF(13)
BM
PF(2)
BM
PF(2)
BM
PF(1)
BM
PF(6)
BM
PF(9)
BM
1.1
2.9
4.2
3.6
2.4
17.1
9.7
7.2
0.2
15.6
14.5
13.1
1.3
0.1
1.0
4.6
1.3
0.3
4.1
3.0
3.6
3.9
Edur
Contr
0.1
0.2
0.3
0.2
0.2
1.0
0.4
0.4
0.0
1.0
0.8
0.8
0.0
0.0
0.1
0.3
0.1
0.0
0.6
0.2
0.0
0.0
Sdur
Contr
0.1
0.2
0.3
0.2
0.2
1.0
0.4
0.4
0.0
1.0
0.8
0.8
0.0
0.0
0.1
0.3
0.1
0.0
0.6
0.2
0.2
0.2
Gov
PF
BM
Gov_Relat_Oth
Agenc
Local_Auth
Sov
Supra
Ind
Util
Fin
ABS
CMBS
Covered
CMO
Cash
0
0.5
1
1.5
2
2.5
3
3.5
4
26
27
Risk report – part 3
Risk (ex-ante) Wilshire Axiom Multi-Factor Model
Tracking Error (in bps)
Risk
Decomposition
Total
Factor Risk
Duration
Term
Sector
Quality
Other spread
Currency
Covariance
Specific Risk
1 Day VaR (95%) in tsd
Total Risk PF (in bps)
Total Risk BM (in bps)
20120330
20111230
20120330
20111230
20120330
20111230
105.4
97.1 (85%)
90.3
89.8
28.1
13.1
88.9
4.8
-125.2
41.2 (15%)
261.3
254.4 (95%)
11.4
47.8
28.1
9.0
268.1
9.8
-102.7
60.0 (5%)
280.7
277.4 (98%)
359.4
395.2
70.4
31.8
313.0
4.8
-558.9
42.7 (2%)
386.9
382.1 (98%)
444.6
457.9
65.6
24.6
77.5
9.8
-521.9
60.8 (2%)
340.2
340.1 (100%)
449.2
484.2
47.1
19.7
380.7
0.0
-684.1
7.6 (0%)
332.9
332.8 (100%)
450.0
464.0
43.5
18.3
340.0
0.0
-651.9
7.6 (0%)
92
175
245
260
TE Risk Decomposition in time
Total Risk and Effective Duration in time
EFF DUR BM
TR PF
TR BM
400
7.00
234
80%
366
5.60
198
60%
332
4.20
162
40%
298
2.80
126
20%
264
1.40
90
20110331
Duration
Eff Dur
100%
TR in bps
TE in bps
EFF DUR PF
270
0%
20110531
Term
20110729
20110930
20111130
20120131
20120330
Sector
Quality
OtherSpread
Currency
SpecificRisk
TE
© IDS GmbH – Analysis and Reporting Services
230
0.00
20110331
20110531
20110729
20110930
20111130
20120131
20120330
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Performance Attribution – part 1
produced by: IDS GmbH
05/03/2012
Ludek Kolecek
++49 89 3800 15139
Performance Attribution 30/12/2011 - 31/01/2012 (linked on-change)
Market Value
Return
Fund 1
Benchmark 1
Portfolio
Benchmark
2.66%
1.96%
0.71%
Active
Descriptive Summary
31/01/2012
Market
Value (mio)
No. of
investments
Eff
Dur
Spr
Dur
Avg
Cpon
Avg
Life
Yield to
Mat
Rating
Avg
Portfolio
Benchmark
81
228
2,996
4.8
5.2
5.5
5.3
4.6
4.1
6.7
6.9
4.2
3.0
AA+
Yield
Currency
?
Total
Model
Return
Selection /
Interaction /
Hedge costs
Performance
?
(%)
Effective
Duration
Term
Structure
Sector
Quality
Other
Factors
Portfolio
Benchmark
-0.56
-0.70
0.60
0.76
0.60
0.39
0.16
0.09
1.24
1.02
0.50
0.39
0.00
0.00
2.52
1.94
0.15
0.01
Active
0.14
-0.16
0.21
0.06
0.22
0.11
0.00
0.57
0.13
0.80
Total
2.66
1.96
0.71
0.71
0.70
0.57
0.60
0.50
0.40
0.30
0.20
0.22
0.21
in %
0.14
0.06
0.10
0.13
0.11
0.00
0.00
-0.10
-0.20
-0.16
-0.30
© IDS GmbH – Analysis and Reporting Services
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Performance Attribution – part 2
Attribution detail
Government yield curves changes
0.25
Currency
Active exp.*
Return (%)
Effect
Top 3 contributors
0.20
United Kingdom
0.15
0.00
0.70
0.00
-0.85
0.00
0.00
0.00
-0.03
0.00
United States
0.85
-0.83
0.00
Australia
0.00
2.80
0.00
Euro
0.10
Denmark
yields
0.05
0.00
-0.05
0
5
10
15
20
25
30
-0.10
-0.15
Bottom 2 contributors
-0.20
-0.25
-0.30
years
EUR 12/11 - 01/12
Effective Duration
Sector
source: IDS
AUD 12/11 - 01/12
Active exp.*
Return (%)
Effect
Top 3 contributors
Euro
0.18
0.10
Euro Bank/Finance
0.15
0.60
0.09
United Kingdom Bank/Finance
0.06
0.42
0.02
Euro Supranational
0.24
0.09
0.01
0.02
0.48
0.01
-0.20
0.09
-0.02
0.09
-0.17
-0.01
-0.11
0.04
-0.01
0.02
-0.06
0.00
0.14
United States Finance
United Kingdom
0.07
0.03
0.00
Bottom 4 contributors
Denmark
0.00
-0.38
0.00
Euro Agency
Bottom 2 contributors
Australia Agency
Australia
0.09
-0.02
0.00
Euro Corporate/Industrial
United States
0.04
-0.04
0.00
United Kingdom Corporate/Industrial
Return (%)
Effect
0.70
-0.13
Active exp.*
Return (%)
Euro Mortgage
-0.08
Term Structure
Active exp.*
Top 5 contributors
USD 12/11 - 01/12
Effect
Quality
Top 4 contributors
Active exp.*
Return (%)
Effect
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
-0.21
0.02
0.00
Euro A
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
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
Euro Country: Portugal
-0.01
-4.23
0.03
Euro Country: Austria
-0.19
-0.06
0.02
-0.61
0.83
0.02
Yield
PF
BM
Active
Top 3 contributors
Other Factors
Active exp.*
Return (%)
Effect
United Kingdom
0.06
0.00
0.06
Euro Country: Italy
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
Euro Country: Netherlands
-0.11
0.03
-0.01
Euro Country: Finland
-0.06
0.05
0.00
No negative contributors
* as of beginning of reporting period
© IDS GmbH – Analysis and Reporting Services
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Für weitere Informationen wenden Sie sich bitte an:
Dr. Luděk Koleček
+49 89 3800 15139
Ludek.kolecek@InvestmentDataServices.com
IDS GmbH – Analysis and Reporting Services
Königinstraße 28
80802 München
www.InvestmentDataServices.com
© IDS GmbH – Analysis and Reporting Services
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