RoyaltyStat Blog

The capital asset pricing model (CAPM) is widely used to calculate the expected return of equity shares, considering their risk relative to a stock market portfolio. The CAPM is ill-suited to valuing assets that lack stock’s spot market price volatility. Thus, we argue that the CAPM should not be used to determine the arm’s length remuneration for the intra-group transfer of intangibles.

The CAPM is postulated in a simple linear fashion:

     (1)     R = μ + β (M – μ)

where R denotes the one-period return of the selected company stock and M denotes the one-period return of the reference (benchmark) stock market index, such as the Standard & Poor’s 500 Index. The intercept μ denotes a country specific default risk-free sovereign interest rate, and the slope β is regarded as an equity risk-coefficient.

The (“capital gain”) stock price return R = LN(P/P(−1)), where P is the selected company stock price; and the market index return M is defined in similar logarithm calculation.

“We shall renounce . . . the subterfuges.”

We suggested on prior blogs that operating assets (measured by property, plant & equipment) are endogenous and that structural equation estimates of return on assets produce biased coefficients. Here, we provide another alternative from biased estimates of return on assets than using exotic algorithms like two-stage least squares.

Economic models must have mathematical beauty; they must be parsimonious!

Paraphrasing Paul Dirac (1955), Physical laws should have mathematical beauty, quoted in Abraham País, Maurice Jacob, David Olive, Michael Atiyah, Paul Dirac (The Man and his Work), Cambridge University Press, 1998, p. 46.

Después de tanto soportar la pena de sentir tu olvido … y si pretendes remover las ruinas que tú mismo hiciste

Cenizas in the poignant voice of Toña La Negra. Classic bolero lyrics by Wello Rivas (1913-1990).

In applying the comparable profits method (CPM) in the U.S. or the “transactional” net margin method (TNMM) in other OECD countries, many transfer pricing analysts assume that the depreciation rate of property, plant, and equipment is the same among the individual comparables and the tested party.

L’un fece il mundo e l’altro l’ha distrutto.

The “return on assets” is an unsatisfactory profit level indicator (PLI) for the “transactional” net margin and comparable profits methods in transfer pricing because (among other major defects) self-developed intangibles are excluded from the assets base denominator. Assets are also composed of heterogeneous balance sheet accounts with different depreciation rates.

Operating assets are “solid, massy, hard” and cannot be moved from one company to another within the same industry (horizontal market consolidation) or across companies in different industries (vertical market consolidation), without a time-consuming assets purchase agreement. Moreover, if the intra-company assets transfers are large, anti-trust regulatory impediments may occur.

The idea that “return on assets” is a superior PLI because of its fluent or gravitation properties is not consistent with reality. This dubious return on assets sobriquet is posited as a matter of faith because to our knowledge economics is devoid of rigorous demonstrations of the conditions required for such gravitation to occur in actual industries dominated by oligopoly groups.

Like other expressions, economic categories reflect reality, and the term royalty isn't an exception.

Michiel de Vaa’s Etymological Dictionary of Latin and the Other Italic Languages (Brill, 2008) has no entry for royalty or its lemma. See his near-neighbor entry (Vaa, pp. 517-518): rego ("to direct, guide, govern"), but the listed cognates don't refer to payments or other economics allusions.

The Oxford English Dictionary, an erudite arbiter of the English language, includes several meanings for royalty (noun (plural royalties)), and attributes its origin from Old French roialté, from roial (regal): 

“The sense ‘royal right (especially over minerals)’ (late 15th century) developed into the sense ‘payment made by a mineral producer to the site owner’ (mid-19th century), which was then transferred to payments for the use of patents, trademarks, and copyrighted materials.”

See the Oxford English Dictionary. Cite: “royalty, n.”

We take another look that computing profit indicators using restricted data samples can lead to unreliable measures of arm’s length taxable income to benchmark controlled inter-group transactions. To produce reliable measures, we must change the pervasive transfer pricing practice of considering three-years of data, and consider as many individual company financial data as available.