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In most developed countries, a substantial part of portfolios invested in financial markets are managed by institutional investors, typically mutual funds, insurance companies, pension funds and hedge funds. Recent decades have witnessed a tremendous increase in the assets under management by institutional investors - in 2019, these assets amounted to USD 52 trillion representing 58% of the global market (see Boston Consulting Group 2020 Report). In view of the size of this industry and its implications for investors, managers and regulators, one of the most important aspects of delegated portfolio management consists in examining the implications of the fee structures and the fund managers’ attitude toward the risk on asset allocation decisions. Moreover, since portfolio managers are rewarded for performance relative to a benchmark, delegation and benchmarking are closely related (see, for example, Leippold and Rohner, 2011). The objective of active portfolio managers is to overperform a relevant benchmark. Ma et al. (2019) documented that for 79% of active US. open-end mutual funds, managers compensation is directly related to fund performance and 78% “disclose the benchmark used to evaluate performance”.
The goal of this paper is to study the impact of different performance-based fee structures as well as manager’s personal stake in the fund on portfolio management in the setting of prospect theory, in a unified and dynamic framework in relation to regulation in force…

English

This paper studies, in a unified and dynamic framework, the impact of fund managers compensation (symmetric and asymmetric fees including a penalty component) as well as their investment in the fund when managers exhibit a loss aversion utility function. Contrary to the vast majority of the existing literature, the benchmark portfolio, relative to which a fund’s performance is measured, is risky. The optimal portfolio value comprises a call option and a term resembling the optimal value when the benchmark is riskless. The proportion invested in the risky security is a speculative position, while the fraction invested in the benchmark contains both a hedging addend and a speculative element. Our model and simulations show that (i) a risky benchmark substantially modifies the manager’s allocation compared to a riskless benchmark; (ii) optimal positions are less risky when the manager is compensated by symmetric fees or faces a penalty; (iii) a relatively large manager’s stake (30%) in the fund considerably reduces her risk-taking behaviour and results in an almost identical terminal portfolio value for the different fees schemes; (iv) optimal weights significantly react to different parameter values; (v) these results may have important implications on regulation.

Français

L’objectif de cet article est d’étudier, dans un cadre unifié et dynamique, l’impact de la rémunération des gestionnaires de fonds (commission de performance symétrique ou non-symétrique avec potentiellement un malus), ainsi que leur propre investissement dans le fond lorsqu’ils sont caractérisés par une fonction d’utilité de type « aversion aux pertes ». Contrairement à la littérature existante, la performance du fond est appréciée par rapport à une référence (un indice, par exemple) risquée. Les principales conclusions de notre modèle et de nos simulations sont les suivantes : (i) une référence risquée modifie sensiblement l’allocation d’actifs ; (ii) les proportions optimales sont moins risquées dans le cas d’une commission de performance symétrique ; (iii) la détention par le gestionnaire d’une part relativement importante (30%) du fonds altère son comportement risqué et permet d’obtenir une valeur terminale du portefeuille quasi-identique quel que soit le type de rémunération ; (iv) les proportions optimales sont sensibles aux variations des valeurs des paramètres ; (v) ces résultats peuvent avoir des conséquences sur la régulation.

Constantin Mellios
Corresponding author: University Paris 1 Panthéon-Sorbonne, PRISM-Sorbonne, 17, place de la Sorbonne, 75231 Paris Cedex 05, France.
Anh Ngoc Lai
University Rennes 1, CREM (Centre for Research in Economics and Management), CNRS, UMR 6211, 35000 Rennes, France.
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