Dynamic asset allocation with asymmetric payoffs : risk management, financial incentives, and benchmarking

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It is common practice to judge third-party asset managers by looking at their financial performance relative to a benchmark portfolio. For this reason, they often choose to rely on internal risk-management models to control the downside risk of their portfolio relative to the benchmark. Moreover, an increasing number are adopting an incentive-based scheme, by charging an over-performance commission relative to the benchmark. Indeed, including this variable component in their global remuneration allows them to increase their revenue in case of over-performance without any penalty in the event of underperforming the benchmark. However, such practices have recently been at the heart of several polemics: the recent global financial crisis has uncovered some shortcomings in terms of internal risk control as well as excessive risk-taking and compensation levels of several financial players. Nevertheless, it appears that analyzing the impact of these practices remains a relatively new issue in continuous time-dynamic asset allocation theory. This thesis analyses in this theoretical framework the implications of these "benchmarking" practices on the asset manager's investment behavior. The first part examines the properties of the optimal dynamic strategy for the asset manager who is concerned by the difference of return between their portfolio and a fix or stochastic benchmark (over- or under-performance). Several asset manager types are considered, defined by different utility functions and different downside-risk constraints. In particular, the link between investment problems with aversion to under-performance and risk management constraints is shown. In the second part, the case of the asset manager who benefits from an incentive compensation scheme (variable asset management fees, over-performance bonuses or additional commission on asset under management), is investigated. We study how, depending on the choice of financial inventive structure and loss aversion level, the asset manager's strategy differs from that of the investor (or the strategy of the asset manager receiving no incentive remuneration). This study shows that the change in investment behavior of the asset manager can lead to both a reduction in the risk taken relative to the strategy without financial incentives or conversely an increase thereof. Finally we show that the existence of downside risk constraints, imposed on the asset manager or corresponding to their aversion for under-performance, can be beneficial to the investor mandating financial management.

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