Dr. Luděk Koleček Fixed Income Risk Controlling Universität Passau

© IDS GmbH – Analysis and Reporting Services 2 2 Statistics based on legal entities as of May 2011 IDS is a managed service provider operating worldwide 63% Asset Managers 22% Insurance Companies 10% Banks 5% Other Sectors 76% Europe 17% Asia 7% USA 63% Allianz Group 37% Third Party Regions Industry 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

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

© IDS GmbH – Analysis and Reporting Services Market Risk Models 3 1 Multifactor Risk Model (Wilshire Axiom) Discussion Duration Fixed Income instruments Agenda

© IDS GmbH – Analysis and Reporting Services 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,…

© IDS GmbH – Analysis and Reporting Services 6 6 Interest rates - Yield, Yield to maturity, bonds pricing -Yield curves

© IDS GmbH – Analysis and Reporting Services 7 7 German sovereign yield curve (Bloomberg 31/05/2012)

© IDS GmbH – Analysis and Reporting Services 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

© IDS GmbH – Analysis and Reporting Services 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)

© IDS GmbH – Analysis and Reporting Services 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

© IDS GmbH – Analysis and Reporting Services 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

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© IDS GmbH – Analysis and Reporting Services 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

© IDS GmbH – Analysis and Reporting Services 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

© IDS GmbH – Analysis and Reporting Services 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 Wilshire AXIOM Global Credit Risk Model

© IDS GmbH – Analysis and Reporting Services 17 Term structure factors – shift, twist, butterfly

© IDS GmbH – Analysis and Reporting Services 18 Estimated yield curve changes with D1, D2 and D3

© IDS GmbH – Analysis and Reporting Services 19 Wilshire AXIOM – Multi Factor Model (3) - Overview Multi Factor Model  Yield  Term Structure Model  Sector  Quality  Currency  Other Spread (Euro Country, Prepayment, etc.)

© IDS GmbH – Analysis and Reporting Services 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

© IDS GmbH – Analysis and Reporting Services 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:

© IDS GmbH – Analysis and Reporting Services 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.

© IDS GmbH – Analysis and Reporting Services 23 Specific Risk Illustration: Quality Coefficient

© IDS GmbH – Analysis and Reporting Services 24 Risk Report

© IDS GmbH – Analysis and Reporting Services 25 Risk Report – part 1

© IDS GmbH – Analysis and Reporting Services 26 Risk Report – part 2

© IDS GmbH – Analysis and Reporting Services 27 Risk report – part 3

© IDS GmbH – Analysis and Reporting Services 28 Performance Attribution – part 1

© IDS GmbH – Analysis and Reporting Services 29 Performance Attribution – part 2

© IDS GmbH – Analysis and Reporting Services 30 Für weitere Informationen wenden Sie sich bitte an: Dr. Luděk Koleček IDS GmbH – Analysis and Reporting Services Königinstraße München