Underperformance Fees and Manager’s Portfolio Risk Taking

Gabriele Stabile

doi:10.5430/ijfr.v6n1p79

Abstract

This paper investigates how a manager’s compensation contract where good performance are rewarded and poor performance are penalized impacts on the managerial risk taking propensity. The results of the model indicate that the presence of underperformance penalty has a strong impact on the manager’s investment strategies. As the asset value goes to zero, the optimal proportional portfolio goes to infinity. On the other hand, as the asset value goes to infinity, the optimal proportional portfolio converges to the Merton constant, that is the portfolio the manager chooses if he were trading his own account. In some situations, the manager’s optimal portfolio is below the Merton constant. If the asset value is somewhat below the overperformance region, the manager chooses trading strategies more risky than the Merton constant. Thus, in order to assure that his incentive option will finish in-the-money, the manager increases the investment volatility, but not in the indiscriminate manner as he does in case of absence of underperformance penalty.

Highlights

This paper analyzes the implications of performance fee incentives allowing for both over- and under-performance on manager’s portfolio risk taking
As the asset value goes to zero, the optimal proportional portfolio goes to infinity
As the asset value goes to infinity, the optimal proportional portfolio converges to the Merton constant, that is the portfolio the manager chooses if he were trading his own account

Summary

Introduction

This paper analyzes the implications of performance fee incentives allowing for both over- and under-performance on manager’s portfolio risk taking. In particular we assume that under-performance is rewarded if the managed assets value exceeds the value of an external benchmark, whereas under-performance fee is applied if the asset value goes below a predetermined percentage of the benchmark These incentive scheme considered includes the symmetric performance fee, where over- and under-performance are measured in respect to the same threshold, and the bonus performance fee where no penalty is applied in case of under-performance. Carpenter (2000) examines the manager’s trading behavior in case the manager is compensated with a base fee plus a bonus if the asset value ends up above a stochastic benchmark. She finds that in some situations the manager chooses a lower asset volatility than he would if he were investing on his own.

The Model

The Analysis

Illustrative Results and Numerical Examples

Evaluation time t

Conclusions