The Mathematics of Return Calculation

Timothy Peterson

Just as Chapter 1 serves as a primer on alternative investments for the performance analyst, the goal of this chapter is to provide sufficient background to the alternative investment manager who may not be well versed in all of the nuances of rate-of-return calculation. An overview of the most commonly used performance calculation methods is presented, along with examples.

Of the methods discussed, two in particular – Modified Dietz and internal rate of return (IRR) – can be very problematic in certain circumstances.

Modified Dietz comes with important caveats. The accuracy of the result is dependent on relatively small capital flows, low volatility and frequent valuations. It also does not appropriately handle cases of extreme leverage. Alternative investment strategies routinely deal in circumstances with large capital flows, volatile returns brought about by high degrees of leverage, and infrequent valuations. These are precisely the circumstances where Modified Dietz fails. The result is that sometimes calculation of return using traditional methods yields results that are either nonsensical at best or impossible to calculate at worst.

IRR has its own issues, and