Abstract
In this paper, we investigate how the combination of investment choices and weak assumptions regarding utility maximization implicitly define a risk-adjusted performance measure (RAPM). An investment choice comprises how an investment is funded, its risk and return attributes, and its financial instrument and market. Our framework demonstrates that a RAPM has many equivalent forms for a given investment choice, but an investor's risk aversion doesn't affect RAPM selection, i.e., the shape of utility function is irrelevant to RAPM selection, and investors with different funding types should use different RAPMs even if they have the same expected utility. We derive some new RAPMs, and our results provide some context for - and we highlight some implicit assumptions behind - several existing RAPMs such as the Sharpe, Information, Treynor, and the Conditional Sharpe ratios.
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