Pseudo-naïve approaches to investment performance measurement

This paper makes use of Magni’s (2013. Insurance Mathematics and Economics, 53, 747-756) Average Interest Rate (AIR) in order to find a performance index which does not depend on the valuation rate (i.e., benchmark return). To this end, we distort the AIR by dropping the discount factors in the formula. The resulting modified AIR (MAIR) is the ratio of overall (undiscounted) return to overall (undiscounted) capital. While seemingly a na¨ive metric, we show that it is a genuinely internal metric, capable of capturing an investment’s economic profitability, as long as it is compared with an appropriate cutoff rate which adequately takes account of the opportunity cost of capital. The not-so na¨ive MAIR is then extended to several different capital bases; the result is that other well-known (allegedly na¨ive) metrics, such as cash multiple, undiscounted profitability, Modified Dietz and Simple Dietz return are given economic significance: each such metric is a (pseudo-na¨ive) performance index that correctly expresses the investment’s amount of return per unit of a specific capital: overall capital, initial investment, total cash outflow, average cash outflow).