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Georges Hübner Deloitte Chair of Portfolio Management and Performance, HEC-University of Liège

Risk Horizon and Expected Market Returns. Georges Hübner Deloitte Chair of Portfolio Management and Performance, HEC-University of Liège Associate Professor of Finance, Maastricht University Chief Scientific Officer, Gambit Financial Solutions Thomas Lejeune

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Georges Hübner Deloitte Chair of Portfolio Management and Performance, HEC-University of Liège

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  1. Risk Horizon and Expected Market Returns Georges Hübner Deloitte Chair of Portfolio Management and Performance, HEC-University of Liège Associate Professor of Finance, Maastricht University Chief Scientific Officer, Gambit Financial Solutions Thomas Lejeune FNRS Fellow, HEC-University of Liège Thursday 25 October 2012, EM Lyon

  2. Agenda • Overview • Motivation • Risk Horizon • Theoretical setup • Empirical application • Conclusion 2

  3. Overview • Development of an equilibrium asset pricing model • Asymmetric risks • Incomplete information on returns distributions & agents’ utility • Only moments up to order 4 of unconditional distributions are known • A new intuitive risk measure is introduced: Risk Horizon of a security: time required for its mean return to converge around its expectation with a specified tolerance • Starting from this general framework, series of 3 papers (current in red) • Link with the term structure of interest rates estimation of the equilibrium market risk premium; • Derivation of market equilibria equations (HCML, HSML) calibrations and tests of a multi-moment asset pricing model; • Identification of nested utility- or distributions-based models tests of optimal asset allocations. 3

  4. Motivation • Estimationof expectedreturns: standard methodsbased on realizedreturns or forward-lookingestimates; lack of theoreticalfoundations • Weaknesses of CAPM (questionable assumptions, Jensen’s alpha, evidence of multiple sources of risks) • Forces of CAPM (robust equilibrium framework, flexible additional assumptions, empirical adaptation to BTM, size, PE, theoretical adaptation to skewness: Kraus & Litzenberger, 1976) • Critiques to alternative models: • Utility-based models: any assumed relationships between expected utility and moment preferences is theoretically unsound (Brockett & Kahane 1992) • Distribution-based models: diversification is a two-edged sword (Simkowitz & Beedles 1978, Mitton & Vorkink 2007) 4

  5. Risk Horizon f(Ri) f(1/H  Ri)  Ri 1/H  Ri - +  5

  6. Risk Horizon Problems Segregatedownsiderisk and upsidepotential Account for loss aversion Refinement:  Add a (negative) parameter to reflectthis distinction  Multiply by negative weighting  6

  7. Theoretical setup 7

  8. 8

  9. Term structure of interest rates 9

  10. Empirical application 10

  11. Empirical application: calibration 11

  12. Empirical application: calibration 12

  13. Empirical application: Endogenous estimates of market expected returns 13

  14. Empirical application: Statistical predictive performance • Out-of-sample tests alonglines of Rapach & Wohar (2006) and Goyal & Welch (2008) 14

  15. Empirical application: Statistical predictive performance 15

  16. Empirical application: Statistical predictive performance 16

  17. Empirical application: Economic predictive performance 17

  18. Empirical application: Economic predictive performance 18

  19. Extension: Implied market prices of risks 19

  20. Contribution • Risk Horizon characterization of investors’ behavior • Deal withmoments of higherorderin an equilibriumassetpricingframework • Intuitive link between the term structure of interest rates, the expected market portfolio and market-wide preferences for asymmetric and fat-tail risks • Deliversendogenousestimatesof time-varyingmarketexpected return 20

  21. Conclusion and future research 21

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