Some Unpleasant Total Return Arithmetic

Setting total return targets (TR) is tempting. It sells because humans hate variance but love targets. A target return looks like control. Combining target returns with a confidence corridor, that is, a promise that annual excess returns will stay within a narrow band (e.g., ± 3%) around the target (e.g., 4%) most of the time, looks like discipline. A calendar year looks like a horizon. None of these are economics; they are psychology and reporting conventions, conflating measurement with control. The goal of this short note is not to moralize about optimism. It is to do the unpleasant arithmetic that converts a verbal TR objective into an implied Sharpe ratio requirement. Once that conversion is made, most “TR” claims can be recognized for what they imply: an attempt to smuggle a hedge-fund-like promise into a long-only balanced wrapper.