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**Hedge and mutual funds’ fees and the separation of private investments.**
*(English)*
Zbl 1336.91065

The paper discusses the problem of the interplay between manager’s personal and professional investments. It is focused on a model with two investment opportunities, one accessible to the fund, the other accessible to the manager’s private account. Investment opportunities are constant over time and potentially correlated. The authors consider a fund manager with a constant relative risk aversion and a long horizon, who maximizes expected utility from private wealth. The manager’s optimal investment policies for both hedge and mutual fund managers are found explicitly. The optimal portfolio for the fund entails a constant risky proportion which corresponds to the manager’s own risk aversion for mutual funds. The optimal policy for private wealth is more complex but it is described as well. In summary, it is estabished that neither performance fees nor management fees create the incentive to use private investments to either hedge or augment the fund’s returns. The results of the paper rely on the maximization of the equivalent safe rate for constant relative risk aversion and a long horizon.

Reviewer: Yuliya S. Mishura (Kyïv)

### MSC:

91G10 | Portfolio theory |

### Keywords:

hedge fund; fund manager; fund’s asset; private wealth; expected utility; maximization; high-water mark provision; constant-proportion portfolio; performance and management fees
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\textit{P. Guasoni} and \textit{G. Wang}, Finance Stoch. 19, No. 3, 473--507 (2015; Zbl 1336.91065)

### References:

[1] | Aragon, G., Qian, J.: High-water marks and hedge fund compensation. Working Paper. Available online http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1540205 (2010) · Zbl 1131.91345 |

[2] | Carpenter, J., Does option compensation increase managerial risk appetite?, J. Finance, 55, 2311-2331, (2000) |

[3] | Cvitanić, J.; Karatzas, I.; Davis, M.H.A. (ed.); etal., On portfolio optimization under drawdown constraints, No. 65, 77-88, (1995) |

[4] | Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, 2nd edn. Stochastic Modelling and Applied Probability, vol. 38. Springer, New York (1998) · Zbl 0896.60013 |

[5] | Detemple, J.; Garcia, R.; Rindisbacher, M., Optimal portfolio allocations with hedge funds, (2010) |

[6] | Dumas, B.; Luciano, E., An exact solution to a dynamic portfolio choice problem under transactions costs, J. Finance, 46, 577-595, (1991) |

[7] | Dybvig, P.; Rogers, L.; Back, K., Portfolio turnpikes, Rev. Financ. Stud., 12, 165-195, (1999) |

[8] | Elie, R.; Touzi, N., Optimal lifetime consumption and investment under a drawdown constraint, Finance Stoch., 12, 299-330, (2008) · Zbl 1164.91011 |

[9] | Gerhold, S.; Guasoni, P.; Muhle-Karbe, J.; Schachermayer, W., Transaction costs, trading volume, and the liquidity premium, Finance Stoch., 18, 1-37, (2014) · Zbl 1305.91218 |

[10] | Getmansky, M.; Lo, A.; Makarov, I., An econometric model of serial correlation and illiquidity in hedge fund returns, J. Financ. Econ., 74, 529-609, (2004) |

[11] | Grossman, S.; Zhou, Z., Optimal investment strategies for controlling drawdowns, Math. Finance, 3, 241-276, (1993) · Zbl 0884.90031 |

[12] | Guasoni, P.; Obłój, J., The incentives of hedge fund fees and high-water marks, Math. Finance, (2013) · Zbl 1348.91254 |

[13] | Guasoni, P.; Robertson, S., Portfolios and risk premia for the long run, Ann. Appl. Probab., 22, 239-284, (2012) · Zbl 1247.91172 |

[14] | Janeček, K.; Sîrbu, M., Optimal investment with high-watermark performance fee, SIAM J. Control Optim., 50, 790-819, (2012) · Zbl 1248.91092 |

[15] | Leland, H.; Szego, G. (ed.); Shell, K. (ed.), On turnpike portfolios, 24-33, (1972), Amsterdam |

[16] | Merton, R.C.; Samuelson, P.A., Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods, J. Financ. Econ., 1, 67-94, (1974) · Zbl 1131.91345 |

[17] | Panageas, S.; Westerfield, M., High-water marks: high risk appetites? convex compensation, long horizons, and portfolio choice, J. Finance, 64, 1-36, (2009) |

[18] | Ross, S., Compensation, incentives, and the duality of risk aversion and riskiness, J. Finance, 59, 207-225, (2004) |

[19] | Samuelson, P.A.; Merton, R.C., Generalized Mean-variance tradeoffs for best perturbation corrections to approximate portfolio decisions, J. Finance, 29, 27-40, (1974) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.