1. 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

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
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

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

6. 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

7. Theoretical setup 7

8. 8

9. Term structure of interest rates9

10. Empirical application10

11. Empirical application: calibration11

12. Empirical application: calibration12

13. Empirical application: Endogenous estimates of market expected returns13

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

15. Empirical application: Statistical predictive performance15

16. Empirical application: Statistical predictive performance16

17. Empirical application: Economic predictive performance17

18. Empirical application: Economic predictive performance18

19. Extension: Implied market prices of risks19

20. 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

21. Conclusion and future research21