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Risk Models and Methodologies for Asset Managers

Risk Models and Methodologies for Asset Managers. Laurence Wormald UK Risk Director StatPro Group. Overview. Risk Models and Methodologies for Asset Managers Differing Approaches to Risk Differing Risk Models Variance Models vs VaR Decomposition of Risk New Investment Asset Classes

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Risk Models and Methodologies for Asset Managers

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  1. Risk Models and Methodologies for Asset Managers Laurence Wormald UK Risk Director StatPro Group

  2. Overview Risk Models and Methodologies for Asset Managers • Differing Approaches to Risk • Differing Risk Models • Variance Models vs VaR • Decomposition of Risk • New Investment Asset Classes • Regulatory Issues • Bridging the Gap

  3. Approaches to Risk • Banks • Risk as a hedging problem • Control losses • Portfolio insurance • Asset Managers • Risk as a diversification problem • Control volatility • “Risk is good”

  4. Risk Modelling • Banks • Estimate of probability of loss • Left-hand tail of expected return distribution • Parametric or non-parametric methodology • Asset Managers • Estimate of dispersion (inverse measure of diversification) – volatility or tracking error • Statistic for entire expected return distribution • Parametric methodology

  5. Estimation of Risk Models • Ideally – model the entire Expected Distribution of Returns • Historically – need to simplify • Covariance Matrix-based models (Markowitz) • Based on assumed M-V form of investor utility • Reduces the portfolio risk to a linear algebraic problem • Historically a tremendous advantage • Ignores effects of all higher moments • Originally used with historical covariances • Rests on firm theoretical grounds if either: • Investors really do exhibit quadratic (symmetric) utility • Returns are really multivariate normal

  6. Factor Risk Models • Linear Factor Models as models of Variance • Intuitively appealing to market professionals • We believe in “driving forces” in most securities markets • We would like to know how to “neutralise” certain factor risks • LFM allow construction of factor-mimicking portfolios (factor portfolio of trades) • In Practise • All assumptions are routinely violated • Factors are different for each asset class • “Transient” Factors are invoked to explain residuals • Ever more elaborate estimation methods are proposed (Stroyny, diBartolomeo et al) • Not suitable for derivatives

  7. Value at Risk • Conventional VaR • Simplicity of expression appeals to non-mathematicians (business types, regulators, marketeers) • A fractile of the EDR rather than a dispersion measure • Consistent interpretation regardless of shape of EDR • Widely used in swaps and options markets • May be applied across asset classes and for all new types of securities • Easy to calculate if entire EDR is available • Not easily related to supposed portfolio risk factors

  8. Other VaR measures • Conditional VaR (Expected Shortfall) • Combination fractile and dispersion measure • One of a class of lower partial moment measures • Reveals the nature of the tail • More suitable than VaR for stress testing • Improvement on VaR in that CVaR is subadditive and coherent (Artzner, Acerbi) • CVaR frontiers are properly convex

  9. VaR Models • Parametric • May be simply derived from LFM • If fitted to historical data, entail sample selection bias • Linear or quadratic (delta-gamma) VaR measures • Other modelling assumptions require Monte Carlo methods • All subject to model risk • Historical Simulation • Entails sample selection bias • Can avoid most other assumptions • Extreme Value Theory • Special Parametric form of Tail for Stress Testing

  10. Risk Decomposition • Performance Attribution has provided great insights into investment • Can we do the same for risk? • Marginal Risk • Measures the rate of change of portfolio risk for a small trade in a given security. May be represented as a vector for a given set of securities • Can be estimated in TE or VaR terms • Trade may be financed from cash, from the rest of the portfolio, or from the benchmark • Simply derived algebraically for LFM • May be calculated by brute-force methods for VaR

  11. Risk Decomposition • Component Risk • Measures the fraction of the portfolio risk which can be attributed to the current holding of a particular security • We would like this to be additive, so as to aggregate CR to any sub-portfolio • Simply derived algebraically for LFM in terms of the Marginal Risk vector • May be calculated for VaR (Garman, Hallerbach) - expressed in terms of the Marginal VaR vector • Attribution to factors is heavily dependent on the estimation method (Scowcroft et al) • Does not provide all that performance attribution does, but vital information for the manager

  12. New Investment Asset Classes • Structured Products vs Hedge Funds • Both now available to certain asset managers and pension funds • Both present problems to LFM-based risk management • SP – the banker’s approach • SP allow the buyer to take a view on a specific scenario while limiting downside • May be index-based, capturing systematic risk only • Credit Derivatives: now appearing in many “boring” fixed income portfolios • Explicit optionality and variable leverage • Can be engineered to defeat historical simulation VaR • Hedge Funds – the asset manager’s approach • HF allow the manager much more freedom to pursue alpha • Downside may not be controlled • Unknown leverage • Implicit optionality

  13. Regulatory Issues • New emphasis on regulations based on quantitative risk measures • Supplement to traditional allocation limits • Regulators have focused on downside and ruin • Regulators’ mission is to avoid mis-selling of funds • Product regulations on funds containing derivatives (FDI) via VaR-based approach, inspired by capital adequacy provisions of Basel II • UCITS III – in force Jan 2007 • Sophisticated UCITS = UCITS which may use FDI for investment purposes, particularly UCITS which employ leverage in their use of FDI and/or use OTC derivatives. • Daily VaR, Stress Testing and Model Testing • Now considered part of “best practise” by some regulators?

  14. Bridging the Gap • AMs like to use LFM for portfolio construction • Ubiquitous “factor alpha” models • Investors and regulators are interested in the impact on VaR • How do factor risks relate to VaR? – Marginal Factor VaR • From the LFM, generate the factor portfolio of trades associated with the factor of interest • Unit exposure to Fi, neutral to all other Fj, risk-minimised • Apply this trade to the Marginal VaR vector to obtain the Factor Marginal VaR for this factor • Allows VaR-based comparison of factor effects on portfolio

  15. Conclusions • Alternative Investments, especially Hedge Funds and Structured Products, are changing the rules for risk analysis • Regulators are taking a strong interest in the downside and in stress testing • Traditional mandates may be unaffected – for now • Need for more work in bridging the gap between LFM and VaR approaches

  16. References • Acerbi, C, 2002, “Spectral Measures of Risk: a coherent representation of subjective risk aversion”, Journal of Banking and Finance, 26, 1505-1518 • Artzner, P, F Delbaen, J-M Eber and D Heath, 1999, “Coherent Measures of Risk”, Mathematical Finance, 9, 203-228 • Asgharian, H, 2004, “A Comparative Analysis of Ability of Mimicking Portfolios in Representing the Background Factors”, Working Papers 2004:10, Lund University • Carroll, R B, T Perry, H Yang and A Ho, 2001, “A new approach to component VaR”, Journal of Risk, Volume 3 / Number 3, Spring • DiBartolomeo, D, and S Warrick, 2005, “Making covariance-based portfolio risk models sensistive to the rate at which markets reflect new information” in Linear Factor Models in Finance, Elsevier Finance. • Giacometti, R, and S O Lozza, 2004,”Risk Measures for Asset Allocation Models” in Risk Measures for the 21st Century, Wiley Finance • Hallerbach, W G, 1999 & 2003, "Decomposing Portfolio Value at Risk: A General Analysis", Discussion paper & Journal of Risk, Vol 5, No 2. • Garman, M B, 1997, "Taking VAR to pieces", Risk Vol 10, No 10. • Grinold, R, and R Kahn, 1999, Active Portfolio Management, 2nd Edition, (New York: McGraw Hill) • Satchell, S E, and L Shi, 2005, "Further Results on Tracking Error, concerning Stochastic Weights and Higher Moments", Working paper. • Scherer, B, 2004, Portfolio Construction and Risk Budgeting, Risk Books. • Scowcroft, A, and J Sefton, 2005, in Linear Factor Models in Finance, Elsevier Finance. • Stroyny, A L, 2005, "Estimating a combined linear factor model" in Linear Factor Models in Finance, Elsevier Finance.

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