Dr. Lud ěk Koleček

1. Dr. Luděk Koleček Fixed Income Risk Controlling Universität Passau 06.06.2012

2. IDS is a managed service provider operating worldwide Regions 76% Europe 17% Asia 7% USA Industry 63% Asset Managers 22% Insurance Companies 10% Banks 5% Other Sectors Structure IDS GmbH – Analysis and Reporting Services • 100% subsidiary of Allianz SE • established in 2001 • headquarter in Munich, branch in Frankfurt/Main • outposts at client sites in Minneapolis, Hong Kong, San Francisco; under evaluation:Milan • More than 250 employees from about 30 nations with sector-specific background 63% Allianz Group 37% Third Party Statistics based on legal entities as of May 2011

3. Asset Managers Banks Institutional Investors Portfolio Manager, Fund Accounting Department, Compliance Officers, Marketing/Sales, Product Specialists, Account Manager, Investment Controlling Compliance Officers, Controller, Custodian Bank/AMC-Controlling, Sales/Account Management COOs/CFOs/CIOs of Insurance Companies, Pension Funds, Corporate Treasury, Foundations IDS provides operational investment controlling services Operational Investment Controlling Services One-stop shop Flexible and high-grade Consistent over all reports Short set-up and processing times Risk Performance Reporting Data Management • Market Risk Measurement • DerivateV / UCITS III-guideline • Market Risk Analysis • Liquidity Reporting • Guarantee Fund Controlling • Performance Measurement • Performance Attribution • Outperformance Fee • Composite Calculation • GIPS Service • Peer Group Analysis • Stock Option Plans • Factsheets • KID • Solvency Reporting • VAG Reporting: Investment Funds §54d VAG • Major Shareholding Reporting • Pension Fund Reporting • Customized Reporting • Fund Data Hub / GroMiKV • Customized Benchmarks • Controlling specific market data (yield and credit curves for long maturities and illiquid markets, inflation rates)

4. Agenda 1 Fixed Income instruments 2 Duration 2 3 Market Risk Models 4 Multifactor Risk Model (Wilshire Axiom) 5 Discussion

5. 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

6. Interest rates • Yield, Yield to maturity, bonds pricing • Yield curves

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

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. 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)

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. 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

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. 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. Wilshire AXIOM Global Credit Risk Model 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

17. Term structure factors – shift, twist, butterfly

18. Estimated yield curve changes with D1, D2 and D3

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. Wilshire AXIOM Global Credit Risk Model – Regression and Covariance Matrix 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.

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. 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. Specific Risk Illustration: Quality Coefficient

24. Risk Report

25. Risk Report – part 1

26. Risk Report – part 2

27. Risk report – part 3

28. Performance Attribution – part 1

29. Performance Attribution – part 2

30. Für weitere Informationen wenden Sie sich bitte an: Dr. Luděk Koleček IDS GmbH – Analysis and Reporting Services Königinstraße 28 80802 München www.InvestmentDataServices.com +49 89 3800 15139 Ludek.kolecek@InvestmentDataServices.com