Please explain this question especially the part of misestimation of portfolio risk.
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The question is asking you to discuss how Smith’s stated expectation would be affected by the performance-based fee structure identified by Porter, particularly in relation to estimated portfolio risk.
Performance-Based Fee Structure: This fee structure means that the manager’s compensation is tied to the performance of the portfolio. If the portfolio performs well, the manager earns a higher fee; if it performs poorly, the fee is lower. This structure is often used to align the interests of the manager with those of the investor, as the manager is incentivized to maximize returns.
Misestimation of Portfolio Risk: This refers to the possibility that under a performance-based fee structure, the estimation of portfolio risk might be inaccurate or flawed. This misestimation arises because performance-based fees tend to alter the distribution of returns in a way that affects risk perception.
Symmetrical vs. Asymmetrical Return Distributions: Under a symmetrical fee structure, the manager’s compensation is directly linked to both positive and negative performance outcomes of the portfolio. In contrast, a performance-based fee structure often leads to asymmetrical return distributions. This means that while the upside potential is capped (because the manager only benefits from a portion of the gains), the downside risk is not similarly constrained (the manager may not suffer proportionately from losses).
Effect on Portfolio Risk Estimation: Due to the asymmetrical nature of performance-based fee structures, the variability of returns on the upside is reduced (since the manager only receives a portion of the gains), while the downside risk remains largely unchanged (as the manager still bears the full brunt of losses). When calculating risk metrics, such as standard deviation, using a return series affected by this fee structure, it can lead to an underestimation of downside risk. This is because the reduction in variability on the upside can skew the overall risk estimate downwards, making it seem lower than it actually is.