Extreme Risk, excess return and leverage: the LP formula

Olivier Le Marois (1) , Julia Mikhalevsky (2) , Raphaël Douady (3, 4)

1 fluks
2 FEDERIS Gestion d'Actifs
3 Riskdata
4 CES - Centre d'économie de la Sorbonne

The LP formula is based upon the substitution of the exogenous risk aversion hypothesis by a credit equilibrium hypothesis. This leads to a trade-off between expected blue-sky return – the expected return excluding default scenarios – and extreme risk estimated from scenarios leading to default. An empirical study on the past 90 years shows that this trade-off curve is almost identical across asset classes. In equilibrium, an asset expected blue-sky return is proportional to its contribution to extreme risk. Assuming normal returns, we obtain CAPM as a sub-case of the LP relation. This relationship makes extreme risk underestimation a strong driver of asset price bubbles.

Mots clés: asset allocation; extreme risk; CAPM; risk budgeting; equilibrium

Domaines: Economies et finances; Probabilités [math.PR]

Olivier Le Marois, Julia Mikhalevsky, Raphaël Douady. Extreme Risk, excess return and leverage: the LP formula. 2014. ⟨hal-01151376⟩