Relativity Theory, Money-Time Curvature and Private Capital Pricing

Wonder what relativity theory and money-time curvature have to do with rational pricing of private capital? The two quotes below, freely adapted from the Wikipedia pages about space-time and reference frame, may give a hint.

Careful though. These hopefully entertaining paragraphs introduce notions that are critical to the pricing process (as defined in our previous post).

“Until the beginning of the 20th century, time was believed to be progressing at a fixed pace in all reference frames. However, later experiments revealed that the duration of time therefore varies depending on the reference frames and contracts in higher discount rates of return reference frames. Such time contraction is particularly important in a special relativity theory, the relative valuation theory”.

Rational pricing is an exercise of relative valuation that relies on accurate comparability. In turn, accurate comparability requires a stable reference frame, univocally known ex-ante, realistic and replicable, which applies to all available investment alternatives.

“Reference frames are used to specify the relationship between an observer and the phenomena under observation, implying that the observer is in a stable frame that includes the coordinate time”.

A stable reference frame for relative valuation can only be set by the available risk-free yield curve (or, given the times, the likes). All modern pricing models anchor to the risk-free yield curve the additional risk factors required to price the available investment alternatives.

Coherently, only the duration of the yield curve can be considered as the suitable coordinate time of such reference frame.

What matters to rational investors is how much premium versus risk-free or public markets returns they can expect over the chosen time-horizon and for the amount of capital they decided to put at risk (on the topic see our earlier posts).

To correctly evaluate the premium, two coherently defined amounts invested in different assets have to be compared on the coherent time scale of a stable reference frame.

As recalled in my previous post entitled “Volatility Inhibits PME’s Meaningfulness”, the terms of the challenge for a new method to accurately meet this objective have already been sharply defined.

IRR or public market rates (like in the PME methods) and their implied durations can’t be used for stable reference frames:

  1. From a financial analyst’s perspective, IRRs and public markets rates are not univocally known ex-ante and therefore not replicable and unrealistic;
  2. In relativistic jargon, the use of such rates in the calculation of the duration alters the time-money curvature. In plain financial terms what this means is that, for example, early cash distributions cause an increase in IRR and a decrease in the duration and in the notional capital at work (this is why end-to-end IRRs have low significance).

Using the yield curve as reference frame, the DaRC rises to the challenge of being the methodology that bridges the performance measurement requirements of both private and public capital and allows accurate comparisons.

If calculated for traditional asset classes, duration adjusted returns on capital produce the same results of standard time weighted calculations. If applied to private capital investments, the methodology unambiguously generates results in terms of public market returns plus premium over specified time-horizons.

When time aims at taking its toll, duration can always offer relief.


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