Investment Performance Measurement Using Utility Inversion
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Solution Overview
Problem
The Sharpe ratio and other return-to-risk ratios lose reliability when assessing investments with negative average excess returns, as they incorrectly favor higher-risk assets over lower-risk ones with similar returns, leading to inappropriate investor utility ratings, especially for institutional investors facing significant negative price impacts.
Innovation Solution
A method that determines a performance measure by relating positive and normalized negative utility concepts using specific mathematical relationships, ensuring the measure is higher for lower negative utility and lower for higher negative utility, addressing the Sharpe ratio's limitations by using synthetic division processes and adjusting for risk and curvature issues.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Sharpe ratio is used to assess investments with negative average excess returns, then the measure provides a numerical rating, but it incorrectly favors higher-risk assets over lower-risk ones with similar returns
Solution Approach 1:
The patent inverts the conventional Sharpe ratio approach by introducing a transformation function that reverses the incorrect ranking. When the Sharpe ratio produces counterintuitive results (higher risk yielding better ratings for negative returns), the invention applies an inverse transformation to restore the correct relationship where lower risk should yield better ratings for assets with similar negative returns.
Solution Approach 2:
The patent transforms the Sharpe ratio parameter through a monotonic transformation function that preserves the ordering for positive returns but corrects the ordering for negative returns. This parameter change allows the same underlying metric to serve dual purposes: maintaining conventional interpretation for profitable assets while providing corrected rankings for losing assets.
2Ease of operation
If the Sharpe ratio is used for investments with negative returns, then calculation is straightforward, but the measure fails to penalize higher risk appropriately
Solution Approach 1:
The patent introduces an intermediary transformation function that acts as a mediator between the raw Sharpe ratio calculation and the final performance rating. This intermediary layer preserves the simplicity of the original calculation while adding the necessary risk penalty correction through the transformation step.
3Productivity
If mean Sharpe ratios are calculated across multiple funds, then aggregate performance can be assessed, but inclusion of negative Sharpe ratios makes the mean over-proportionally meaningless
Solution Approach 1:
The patent segments the performance evaluation by applying the transformation function to each individual fund's Sharpe ratio before aggregation. This segmentation ensures that each component contributes meaningfully to the mean, preventing the distortion that occurs when raw negative Sharpe ratios are averaged directly.
Data Source
AI summary
Embodiments of the invention are directed to a system, method, or computer program product for evaluating risk adjusted performance of an investment portfolio. This invention may be applied to any asset which has a value. The invention evaluates risk adjusted performance of an investment portfolio by first determining at least one positive utility concept and at least one negative utility concept describing an asset. Then, the invention normalizes the at least one negative utility concept to an equivalent negative utility concept describing or deriving from a group of assets. Finally, the invention may relate at least one positive utility concept and at least one normalized negative utility concept to determine a performance measure. In this way, the invention normalized negative asset returns such that better investor utility ratings are not falsely provided.