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07.02.2019 | Research Article

Relative performance concerns among investment managers

verfasst von: Mark Whitmeyer

Erschienen in: Annals of Finance | Ausgabe 2/2019

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Abstract

This paper examines the strategic interaction of n portfolio managers with relative performance concerns. We characterize the unique constant Nash equilibrium and derive some compelling results. Surprisingly, in equilibrium, more risk tolerant players do not generally take riskier positions than less risk tolerant players. We derive sufficient conditions under which this relation does hold. We also examine the effects of adding new players to the game on the equilibrium, and look at the equilibrium in the limiting case as the number of players goes to infinity. We show that for a symmetric population, the equilibrium strategy of the players converges pointwise to some limiting equilibrium policy.

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Indeed there is a (slightly irreverent) quote by the topologist R. H. Bing which conveys something similar to what we are saying here: “Dimension 4 is the most difficult dimension. It is too old to spank, the way we might deal with the little dimensions 1, 2, and 3; but it is also too young to reason with, the way we deal with the grown-up dimensions 5 and higher.” Cannon (2011)

Recall that the natural filtration generated by a Brownian motion is \(F^{W}(t)= \sigma \left( \left\{ W_{s} | 0 \le s \le t \right\} \right) \), \(\forall t\in [0,T]\).

Henceforth, we omit the word constant and just write Nash equilibrium.

A portfolio strategy is admissible if it belongs to the set \({\mathcal {P}}\), where \({\mathcal {P}}\) consists of self-financing \({\mathcal {F}}\)-progressively measurable real-valued processes \((\pi _{t})_{t \in [0,T]}\) which satisfy \({\mathbb {E}}\int _{0}^{T}|\pi _{t}|^{2}dt < \infty \).

Detailed in “Appendix A.2”.

In this case, this assumption is without loss of generality.

Including Friend and Blume (1975) and Donkers and van Soest (1999).

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Titel: Relative performance concerns among investment managers
verfasst von: Mark Whitmeyer
Publikationsdatum: 07.02.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Annals of Finance / Ausgabe 2/2019
Print ISSN: 1614-2446
Elektronische ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-019-00343-2

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