Why IRR, PME Induce Inaccurate Allocation Decisions

In one of my previous posts, I wrote about the importance of time – of correctly framing time – for purposes of comparability and pricing. The topic is so critical not to require a second round that adds more details and practical implications.

Professor Mandelbrot, in his book “The (mis)Behavior of Markets – A Fractal View of Risk, Ruin, and Reward”, powerfully cristallizes the importance of the concept:

“The prime mover in financial market is not value or price, but price differences; not averaging, but arbitraging. People arbitrage between places and times.”

Professor Mandelbrot had a perspective that was much broader than just the financial markets. But the expression “arbitrage between places and times” perfectly defines any asset allocation and trading decision.

Markets’ volatility deforms (trading) time perception – a fast market is qualified by the (high) volatility of the moment – but ultimately prices and returns are charted over a clock-defined time line.

Returns are function of price and time horizon; prices are a function of value and risk perception vis-à-vis time horizon.

Time is not a function of return – there is realistically nothing you can do about it.

This is true, unless one adopts IRR and PME calculations, accepting the consequences of their unrealistic implications.

• The issues relating to framing time in the IRR context can be easily explained by referring to the well known equation that ties the total-value-versus-paid-in (TVPI) multiple to the IRR of the transaction: TVPI = (1+IRR) ^ (Duration).

1. The equation holds if duration is calculated by discounting cash flows at a rate equal to the IRR – i.e. “time” depends on an uncertain/unknown rate of return.
2. Annualization of IRR data is meaningless as is tying duration to clock-defined time.
3. Duration starts at “time zero”, which is instead only true for secondary transactions paid outright and with no further capital calls.

• The issues relating to framing time using the various versions of the PME methodology are somehow similar to those identified for the IRR.

1. Instead of a single discount rate (the IRR), the implicit duration for the PME methodologies depends on the returns of the reference listed market as of the days in which the cash flows are scheduled.
2. As already addressed in a previous post, volatility may make the results of the PME methodology totally meaningless.

From an arbitrage (i.e. allocation decision) standpoint, the common critical shortcoming of both IRR and PME methods is that the risk premiums calculated are inaccurate and potentially misleading.

There are two main reasons for this:

1. risk premiums are calculated comparing non-homogeneous quantities (i.e. money-weighted data and time weighted data and their variations).
2. they usually refer to non-coherent durations.

To the curious reader I suggest to look for the relevant information in every chart, in the disclosure notes and the appendix in any of the publications issued by any of the industry data and benchmark provider.

In case you do not find them or find a lot of confusion, this is a good sign:

There is a still lot of inefficiency in the industry to profit from.