Expected Market Returns Thursday 25 October 2012, EM Lyon 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

Agenda Overview Motivation Risk Horizon Theoretical setup Empirical application Conclusion 2

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

Motivation Estimation of expected returns: standard methods based on realized returns or forward-looking estimates; lack of theoretical foundations 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

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

Risk Horizon  Problems Refinement: Segregate downside risk and upside potential Account for loss aversion Refinement:  Add a (negative) parameter to reflect this distinction  Multiply by negative weighting  6

Theoretical setup   7

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Term structure of interest rates   9

Empirical application   10

Empirical application: calibration 11

Empirical application: calibration 12

Empirical application: Endogenous estimates of market expected returns 13

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

Empirical application: Statistical predictive performance 15

Empirical application: Statistical predictive performance 16

Empirical application: Economic predictive performance 17

Empirical application: Economic predictive performance 18

Extension: Implied market prices of risks   19

Contribution Risk Horizon characterization of investors’ behavior Deal with moments of higher order in an equilibrium asset pricing framework Intuitive link between the term structure of interest rates, the expected market portfolio and market-wide preferences for asymmetric and fat-tail risks Delivers endogenous estimates of time-varying market expected return 20

Conclusion and future research   21