Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard...
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Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Tactical Asset Allocation:Putting the Pieces Together
Dr. Bernhard [email protected]
Invesco Asset Management Deutschland GmbH, Frankfurt am Main
The 2nd International R/Rmetrics User and DeveloperWorkshop
29 June – 3 July 2007, Meielisalp, Lake Thune,Switzerland
![Page 2: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/2.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Contents
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
![Page 3: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/3.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
IntroductionOverview
Cash-portfolio with futures strategy.
Long/short positions are allowed.
Should cover the major bond and equity markets.
Should include a protection mechanism.
Fully-hedged against currency risk.
![Page 4: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/4.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
IntroductionThe Pieces and Packages
Forecasting model, e.g. vars and urca
Risk model, e.q. fExtremes and QRMlib
Linear integer program, e.q. glpk
![Page 5: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/5.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisData
Continuous settlement (Wednesdays’ closing prices) of:
Exchange : Instrument DS-Mnemonic Multiple
Equity
CME: S&P 500 ISPCS00 250 USD / IPEUREX: DJ EURO STOXX 50 GEXCS00 10 EUR / IPLIFFE: FTSE 250 LSYCS00 10 GBP / IPOSX: NIKKEI 225 ONACS00 1000 JPY / IP
Bond
CBT: 10 YEAR US T-NOTE CTYCS00 1000 USD / 100 BPEUREX: EURO BUND GGECS00 1000 EUR / 100 BPLIFFE: LONG GILT LIGCS00 1000 GBP / 100 BPTSE: 10 YEAR T-BOND JGBCS00 1000000 JPY / 100 BP
![Page 6: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/6.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisU.S. Equity
800
1200
1600
US
D
2000 2004 2008
Price of Future
−6
−2
24
6
Continuous Returns
Per
cent
2000 2004 2008
−3 −1 0 1 2 3
0.0
0.2
0.4
Density Plot of Returns
N = 2334 Bandwidth = 0.1785
Den
sity
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−3 −1 0 1 2 3
−6
−2
02
4QQ−Plot of Returns
Normal Quantiles
Ord
ered
Dat
a
![Page 7: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/7.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisEurobloc Equity
2000
4000
EU
R
2000 2004 2008
Price of Future
−10
−5
05
Continuous Returns
Per
cent
2000 2004 2008
−4 −2 0 2 4
0.00
0.15
0.30
Density Plot of Returns
N = 2356 Bandwidth = 0.2228
Den
sity
●
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−3 −1 0 1 2 3
−6
−2
24
6QQ−Plot of Returns
Normal Quantiles
Ord
ered
Dat
a
![Page 8: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/8.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisU.K. Equity
4000
8000
1200
0
GB
P
2000 2004 2008
Price of Future
−4
−2
02
4
Continuous Returns
Per
cent
2000 2004 2008
−3 −2 −1 0 1 2 3
0.0
0.2
0.4
0.6
Density Plot of Returns
N = 2341 Bandwidth = 0.1347
Den
sity
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Normal Quantiles
Ord
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![Page 9: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/9.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisJapan Equity
8000
1400
020
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JPY
2000 2004 2008
Price of Future
−5
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Continuous Returns
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2000 2004 2008
−4 −2 0 2 4
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Density Plot of Returns
N = 2253 Bandwidth = 0.2463
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Normal Quantiles
Ord
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Dat
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![Page 10: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/10.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisU.S. Bond
9510
511
5
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2000 2004 2008
Price of Future
−3
−2
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Continuous Returns
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2000 2004 2008
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Density Plot of Returns
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−3 −1 0 1 2 3
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Normal Quantiles
Ord
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Dat
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![Page 11: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/11.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisEurobloc Bond
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2000 2004 2008
Price of Future
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2000 2004 2008
−1.0 −0.5 0.0 0.5 1.0
0.0
0.4
0.8
1.2
Density Plot of Returns
N = 2361 Bandwidth = 0.056
Den
sity
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●●●●●●
●
−3 −1 0 1 2 3
−4
−2
02
4QQ−Plot of Returns
Normal Quantiles
Ord
ered
Dat
a
![Page 12: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/12.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisU.K. Bond
100
105
110
115
GB
P
2000 2004 2008
Price of Future
−1
01
23
4
Continuous Returns
Per
cent
2000 2004 2008
−1.0 −0.5 0.0 0.5 1.0
0.0
0.4
0.8
1.2
Density Plot of Returns
N = 2338 Bandwidth = 0.05647
Den
sity
●●●●●●●●●●●●●●●●●●●●●●●●
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●
●
−3 −1 0 1 2 3
05
10QQ−Plot of Returns
Normal Quantiles
Ord
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Dat
a
![Page 13: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/13.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Data AnalysisJapan Bond
130
135
140
145
JPY
2000 2004 2008
Price of Future
−1.
50.
01.
0
Continuous Returns
Per
cent
2000 2004 2008
−0.5 0.0 0.5
0.0
0.5
1.0
1.5
Density Plot of Returns
N = 2236 Bandwidth = 0.04195
Den
sity
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Normal Quantiles
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Dat
a
![Page 14: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/14.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Forecasting ModelVector Error-correction Model (VECM)
VECM specified in transitory form with one laggeddifference.
Logarithmic transformation applied.
Full sample period from 1999-01-06 until 2008-04-30.
Pseudo ex ante forecasts starting 2002-11-06.
One-step ahead forecasts are obtained from impliedlevel-VAR.
![Page 15: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/15.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Forecasting ModelERS Tests, Equities
variable statistic 1% 5% 10% lags
U.S. level −1.39 −3.48 −2.89 −2.57 8U.S. difference −5.57 −2.57 −1.94 −1.62 8Eurobloc level −1.27 −3.48 −2.89 −2.57 8Eurobloc difference −5.45 −2.57 −1.94 −1.62 8U.K. level −1.29 −3.48 −2.89 −2.57 8U.K. difference −13.50 −2.57 −1.94 −1.62 8Japan level −1.37 −3.48 −2.89 −2.57 8Japan difference −4.81 −2.57 −1.94 −1.62 8
![Page 16: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/16.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Forecasting ModelERS Tests, Bonds
variable statistic 1% 5% 10% lags
U.S. level −1.98 −3.48 −2.89 −2.57 8U.S. difference −6.33 −2.57 −1.94 −1.62 8Eurobloc level −1.46 −3.48 −2.89 −2.57 8Eurobloc difference −15.57 −2.57 −1.94 −1.62 8U.K. level −2.25 −3.48 −2.89 −2.57 8U.K. difference −5.22 −2.57 −1.94 −1.62 8Japan level −1.54 −3.48 −2.89 −2.57 8Japan difference −3.35 −2.57 −1.94 −1.62 8
![Page 17: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/17.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Forecasting ModelKPSS Tests, Equities
variable statistic 1% 5% 10% lags
U.S. level 5.49 0.216 0.146 0.119 8U.S. difference 0.11 0.739 0.463 0.347 8Eurobloc level 4.66 0.216 0.146 0.119 8Eurobloc difference 0.14 0.739 0.463 0.347 8U.K. level 5.51 0.216 0.146 0.119 8U.K. difference 0.15 0.739 0.463 0.347 8Japan level 5.40 0.216 0.146 0.119 8Japan difference 0.13 0.739 0.463 0.347 8
![Page 18: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/18.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Forecasting ModelKPSS Tests, Bonds
variable statistic 1% 5% 10% lags
U.S. level 3.73 0.216 0.146 0.119 8U.S. difference 0.07 0.739 0.463 0.347 8Eurobloc level 2.18 0.216 0.146 0.119 8Eurobloc difference 0.13 0.739 0.463 0.347 8U.K. level 1.45 0.216 0.146 0.119 8U.K. difference 0.05 0.739 0.463 0.347 8Japan level 4.21 0.216 0.146 0.119 8Japan difference 0.12 0.739 0.463 0.347 8
![Page 19: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/19.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Forecasting ModelResults of Trace Test
rank statistic 10% 5% 1%
r ≤ 7 0.39 6.50 8.18 11.65r ≤ 6 6.82 15.66 17.95 23.52r ≤ 5 17.95 28.71 31.52 37.22r ≤ 4 32.91 45.23 48.28 55.43r ≤ 3 54.48 66.49 70.60 78.87r ≤ 2 83.30 85.18 90.39 104.20r ≤ 1 123.52 118.99 124.25 136.06r = 0 177.79 151.38 157.11 168.92
Conclusion: Cointegration rank of r = 2 cannot be rejected.
![Page 20: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/20.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelSettings and Quantitative Risk Measures
Usage of expected shortfall (ES) numbers.
Rolling window of 1000 observations per instrument.
Estimates based on EVT (POT-method).
Backtest period from 04-11-2002 to 29-04-2008.
KISS: No combined GARCH & ES forecast.
Instead, ES of last trading day used as forecast fortoday’s ES.
![Page 21: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/21.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelOverview Long-Positions, 99%-Level
Instrument Expected VaR-GPD ES-GPD VaR-NormEquity
U.S. 14 20 6 23Eurobloc 14 12 4 18U.K. 14 21 9 36Japan 14 18 7 28
BondsU.S. 14 17 6 28Eurobloc 14 13 6 25U.K. 14 13 4 21Japan 14 12 3 25
![Page 22: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/22.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.S. Equity: VaR & ES (Long, 99%)
−4
−2
02
4
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.S. Equity
2.0
3.0
4.0
perc
enta
ges
2003 2005 2007
ES (GPD)
6 shortfalls
2.0
2.5
3.0
3.5
perc
enta
ges
2003 2005 2007
VaR (GPD)
20 shortfalls
1.5
2.0
2.5
3.0
3.5
perc
enta
ges
2003 2005 2007
VaR (Normal)
23 shortfalls
![Page 23: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/23.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelEurobloc Equity: VaR & ES (Long, 99%)
−5
05
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Eurobloc Equity
3.0
4.0
5.0
6.0
perc
enta
ges
2003 2005 2007
ES (GPD)
4 shortfalls
2.5
3.5
4.5
perc
enta
ges
2003 2005 2007
VaR (GPD)
12 shortfalls
2.0
3.0
4.0
perc
enta
ges
2003 2005 2007
VaR (Normal)
18 shortfalls
![Page 24: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/24.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.K. Equity: VaR & ES (Long, 99%)
−4
−2
02
4
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.K. Equity
2.6
3.0
3.4
perc
enta
ges
2003 2005 2007
ES (GPD)
9 shortfalls
2.2
2.6
3.0
perc
enta
ges
2003 2005 2007
VaR (GPD)
21 shortfalls
1.7
1.9
2.1
2.3
perc
enta
ges
2003 2005 2007
VaR (Normal)
36 shortfalls
![Page 25: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/25.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelJapan Equity: VaR & ES (Long, 99%)
−6
−2
02
4
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Japan Equity
4.0
4.4
4.8
5.2
perc
enta
ges
2003 2005 2007
ES (GPD)
7 shortfalls
3.0
3.4
3.8
perc
enta
ges
2003 2005 2007
VaR (GPD)
18 shortfalls
2.6
3.0
3.4
3.8
perc
enta
ges
2003 2005 2007
VaR (Normal)
28 shortfalls
![Page 26: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/26.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.S. Bond: VaR & ES (Long, 99%)
−3
−2
−1
01
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.S. Bond
1.2
1.4
1.6
1.8
perc
enta
ges
2003 2005 2007
ES (GPD)
6 shortfalls
0.8
1.0
1.2
1.4
perc
enta
ges
2003 2005 2007
VaR (GPD)
17 shortfalls
0.8
0.9
1.0
1.1
perc
enta
ges
2003 2005 2007
VaR (Normal)
28 shortfalls
![Page 27: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/27.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelEurobloc Bond: VaR & ES (Long, 99%)
−1.
00.
01.
0
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Eurobloc Bond
0.9
1.0
1.1
1.2
perc
enta
ges
2003 2005 2007
ES (GPD)
6 shortfalls
0.65
0.75
0.85
0.95
perc
enta
ges
2003 2005 2007
VaR (GPD)
13 shortfalls
0.60
0.70
0.80
perc
enta
ges
2003 2005 2007
VaR (Normal)
25 shortfalls
![Page 28: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/28.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.K. Bond: VaR & ES (Long, 99%)
−1.
00.
01.
0
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.K. Bond
0.8
1.0
1.2
perc
enta
ges
2003 2005 2007
ES (GPD)
4 shortfalls
0.7
0.8
0.9
1.0
perc
enta
ges
2003 2005 2007
VaR (GPD)
13 shortfalls
0.65
0.75
0.85
0.95
perc
enta
ges
2003 2005 2007
VaR (Normal)
21 shortfalls
![Page 29: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/29.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelJapan Bond: VaR & ES (Long, 99%)
−1.
5−
0.5
0.5
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Japan Bond
0.8
1.0
1.2
1.4
perc
enta
ges
2003 2005 2007
ES (GPD)
3 shortfalls
0.6
0.8
1.0
perc
enta
ges
2003 2005 2007
VaR (GPD)
12 shortfalls
0.55
0.65
0.75
perc
enta
ges
2003 2005 2007
VaR (Normal)
25 shortfalls
![Page 30: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/30.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelOverview Short-Positions, 99%-Level
Instrument Expected VaR-GPD ES-GPD VaR-NormEquity
U.S. 14 14 8 16Eurobloc 14 13 7 13U.K. 14 24 6 30Japan 14 14 5 14
BondsU.S. 14 21 8 18Eurobloc 14 19 9 16U.K. 14 14 3 13Japan 14 16 5 18
![Page 31: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/31.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.S. Equity: VaR & ES (Short, 99%)
−4
−2
02
4
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.S. Equity
2.0
3.0
4.0
perc
enta
ges
2003 2005 2007
ES (GPD)
8 exceedances
2.0
3.0
4.0
perc
enta
ges
2003 2005 2007
VaR (GPD)
14 exceedances
2.0
2.5
3.0
perc
enta
ges
2003 2005 2007
VaR (Normal)
16 exceedances
![Page 32: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/32.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelEurobloc Equity: VaR & ES (Short, 99%)
−5
05
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Eurobloc Equity
34
56
7
perc
enta
ges
2003 2005 2007
ES (GPD)
7 exceedances
2.0
3.0
4.0
5.0
perc
enta
ges
2003 2005 2007
VaR (GPD)
13 exceedances
2.5
3.5
4.5
perc
enta
ges
2003 2005 2007
VaR (Normal)
13 exceedances
![Page 33: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/33.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.K. Equity: VaR & ES (Short, 99%)
−4
−2
02
4
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.K. Equity
2.6
3.0
3.4
perc
enta
ges
2003 2005 2007
ES (GPD)
6 exceedances
1.8
2.2
2.6
perc
enta
ges
2003 2005 2007
VaR (GPD)
24 exceedances
1.9
2.1
2.3
perc
enta
ges
2003 2005 2007
VaR (Normal)
30 exceedances
![Page 34: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/34.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelJapan Equity: VaR & ES (Short, 99%)
−6
−2
02
4
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Japan Equity
3.0
3.5
4.0
4.5
5.0
perc
enta
ges
2003 2005 2007
ES (GPD)
5 exceedances
2.6
3.0
3.4
3.8
perc
enta
ges
2003 2005 2007
VaR (GPD)
14 exceedances
2.8
3.2
3.6
perc
enta
ges
2003 2005 2007
VaR (Normal)
14 exceedances
![Page 35: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/35.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.S. Bond: VaR & ES (Short, 99%)
−3
−2
−1
01
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.S. Bond
1.05
1.15
1.25
perc
enta
ges
2003 2005 2007
ES (GPD)
8 exceedances
0.80
0.90
1.00
perc
enta
ges
2003 2005 2007
VaR (GPD)
21 exceedances
0.8
0.9
1.0
1.1
perc
enta
ges
2003 2005 2007
VaR (Normal)
18 exceedances
![Page 36: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/36.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelEurobloc Bond: VaR & ES (Short, 99%)
−1.
00.
01.
0
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Eurobloc Bond
0.70
0.80
0.90
perc
enta
ges
2003 2005 2007
ES (GPD)
9 exceedances
0.60
0.70
perc
enta
ges
2003 2005 2007
VaR (GPD)
19 exceedances
0.60
0.70
0.80
perc
enta
ges
2003 2005 2007
VaR (Normal)
16 exceedances
![Page 37: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/37.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelU.K. Bond: VaR & ES (Short, 99%)
−1.
00.
01.
0
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
U.K. Bond
0.9
1.1
1.3
1.5
perc
enta
ges
2003 2005 2007
ES (GPD)
3 exceedances
0.65
0.75
0.85
perc
enta
ges
2003 2005 2007
VaR (GPD)
14 exceedances
0.65
0.75
0.85
0.95
perc
enta
ges
2003 2005 2007
VaR (Normal)
13 exceedances
![Page 38: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/38.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Risk ModelJapan Bond: VaR & ES (Short, 99%)
−1.
5−
0.5
0.5
Con
tinuo
us r
etur
n, p
erce
ntag
es
2003 2005 2007
Japan Bond
0.8
1.0
1.2
1.4
perc
enta
ges
2003 2005 2007
ES (GPD)
5 exceedances
0.6
0.7
0.8
0.9
perc
enta
ges
2003 2005 2007
VaR (GPD)
16 exceedances
0.55
0.65
0.75
perc
enta
ges
2003 2005 2007
VaR (Normal)
18 exceedances
![Page 39: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/39.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Linear integer programTarget function
Maximize:
z =n∑
i=1
|∆pfi |mixi , (1)
whereby |∆pfi | is the absolute expected price change of
the i-th future contract, mi is the correspondingmultiple and xi is the integer number of contracts tobuy or sell.
The expected price changes are denominated in Euro.
![Page 40: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/40.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Linear integer programRestrictions, I
Budget:
w ≥n∑
i=1
pimixi . (2)
whereby w is the portfolio wealth.
Buffer:
p ≥n∑
i=1
pimi rixi , (3)
whereby p assigns the risk buffer and ri is the risk factor.
Equity share:
qa1 ≤1
w
nequity∑j=1
pjmjxj ≤ qa2 , (4)
whereby qa1 and qa2 are the equity bounds.
![Page 41: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/41.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Linear integer programRestrictions, II
Bond share:
qr1 ≤1
w
nbonds∑j=1
pjmjxj ≤ qr2 (5)
whereby qr1 and qr2 are the fixed income bounds.
Shorts:
qs ≥ 1
w
nshort∑j=1
pjmjxj , (6)
whereby qs is the upper bound on short positions.
![Page 42: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/42.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioAssumptions and sample, I
Begin of simulation: 2002-10-30.
End of simulation: 2008-04-23.
Risk-free rate: 1-week Euribor.
Usage of 99% ES-rate derived from GPD-distribution(POT-method).
Scaling of daily ES by√
7.
No transaction costs and fully hedged.
![Page 43: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/43.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioAssumptions and sample, II
Initial wealth, w , 1,000,000 Euro.
Risk buffer: 90% of the highest wealth amount(high-watermark).
Equity share between 10% and 90% of wealth.
Bonds share between 10% and 90%.
Maximal amount of short positions as high as 50% ofwealth.
Only trade if expected return is greater than 200 BPabove 1 week risk-free rate.
![Page 44: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/44.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioPortfolio vs. Cash
1000
000
1400
000
1800
000
EU
R
2003 2004 2005 2006 2007 2008
PortfolioMoney Market
![Page 45: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/45.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioCash rate
020
4060
80
Per
cent
age
2003 2004 2005 2006 2007 2008
![Page 46: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/46.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioEquity Contribution
−60
000
040
000
EU
R
2003 2005 2007
U.S. Equity
−60
000
040
000
EU
R
2003 2005 2007
Eurobloc Equity−
6000
00
4000
0
EU
R
2003 2005 2007
U.K. Equity−
6000
00
4000
0
EU
R
2003 2005 2007
Japan Equity
![Page 47: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/47.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioCumulated Contribution from Equity Futures
U.S. Eurobloc U.K. Japan
0e+
001e
+05
2e+
053e
+05
4e+
05
![Page 48: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/48.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioNumber of Traded Equity Futures
U.S. Eurobloc U.K. Japan
050
010
0015
0020
0025
00
![Page 49: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/49.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioAverage Return from Equity Futures
U.S. Eurobloc U.K. Japan
020
040
060
080
0
![Page 50: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/50.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioBond Contribution
−50
000
5000
EU
R
2003 2005 2007
U.S. Bond
−50
000
5000
EU
R
2003 2005 2007
Eurobloc Bond−
5000
050
00
EU
R
2003 2005 2007
U.K. Bond−
5000
050
00
EU
R
2003 2005 2007
Japan Bond
![Page 51: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/51.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioCumulated Contribution from Bond Futures
U.S. Eurobloc U.K. Japan
050
0010
000
1500
020
000
2500
030
000
![Page 52: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/52.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioNumber of Traded Bond Futures
U.S. Eurobloc U.K. Japan
050
010
0015
0020
0025
00
![Page 53: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/53.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioAverage Return from Bond Futures
U.S. Eurobloc U.K. Japan
020
040
060
080
0
![Page 54: Tactical Asset Allocation: Putting the Pieces Together · Putting the Pieces Together Dr. Bernhard Pfa bernhard_pfaff@fra.invesco.com Invesco Asset Management Deutschland GmbH, Frankfurt](https://reader035.fdocuments.in/reader035/viewer/2022063013/5fcc006b36644c5c5d17f06b/html5/thumbnails/54.jpg)
Tactical AssetAllocation:
Putting the PiecesTogether
Pfaff
Introduction
Data Analysis
Forecasting Model
Risk Model
Linear Program
Simulated Portfolio
Simulated PortfolioPortfolio Characteristics
Sharp ratio: 1.42
Number of futures traded: 5348.
Average return per single future: 155 EUR.
Maximal draw down equities: -66310 EUR.
Maximal draw down bonds: -8939 EUR.
Contribution from tactical allocation: 831985 EUR.
End value of portfolio: 2042979 EUR.