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
1.
2.
3.
4.
5.
6.
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)
1.
2.
3.
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)

Ri
f(1/H  Ri)
-
+
1/H  Ri

5
Risk Horizon
Problems
Refinement:

1. Segregate downside risk and
upside potential
2. Account for loss aversion
 Add a (negative) parameter to reflect this distinction
Multiply by negative weighting 
6
Theoretical setup
7
8
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