# What all finance professionals need to know about international cost of capital

In his book, “A Theory of Global Capitalism: Production, Class, and State In a Transnational World” published in 2004, the well-known sociologist William I. Robinson documents the how increasing global capital mobility has resulting in a reorganization of production and supply chains across national borders. Most such reorganization seems to have taken place over the last 20-30 years, and appears to be accelerating. This means companies—including their revenues, profits, and cash flows—are increasingly exposed to inter-national risks, suggesting methods of estimating international cost of capital should be developing to keep pace with the increasingly globalized (i.e., international) business environment. And yet, a review of the finance literature suggests that this is not the case. All financial professionals work in a global business environment and, so, need to understand these issues. Please read on!

#### What is international cost of capital?

International cost of capital (ICC)—as its name directly implies—is the international (i.e., cross-border) cost of capital for a specific set of risk sensitivities and exposures influencing the returns of a capital asset or portfolio. Cost of capital can only be defined in a unique, meaningful way as an *opportunity cost* of capital, which means it is equivalent to the expected return on an equivalent set of risk exposures available in the capital markets. **ICC is an international opportunity cost for a capital asset with international risk exposure, which is equivalent to the expected return on an equivalent set of international risk exposures available in international capital markets.**

International capital markets—and related international prices—are not directly observable and must be estimated. For example, individual capital assets (e.g., equity securities of a single company) often trade in multiple capital markets located in different countries, so there is no unique, observable international price of risks inherent in the security. So, **risk prices are only implicit in capital market prices and must therefore be estimated to estimate ICC**.

#### How is ICC estimated?

There are at least 12 methods commonly used to estimate ICC, many of which are based on or derived from the Capital Asset Pricing Model (CAPM).[1] The clearest, most understandable method is referred to as the Global CAPM (GCAPM) method where the expected return for a capital asset is equal to the sum of the global risk-free rate and the asset’s sensitivity to the risk factors impounded in global capital asset portfolio risk premium.

ICC estimation methods other than GCAPM can generally be summarized in terms of multi-factor empirical asset pricing models (MFMs) and sovereign spread premium models (SSMs). MFMs are obtained by estimating the relationship between capital asset returns in a specific country and an arbitrary set of international risk factors, some of which might be capital asset returns from other countries. SSMs are generally derived from the difference between a specific country’s USD-denominated sovereign debt market yields and, in general, US Treasury security yields. **Multi-factor empirical asset pricing models and sovereign spread premium models, although plausible, are ad hoc models that are neither derived from asset pricing theory nor well-supported by empirical evidence. **

#### Why do ICC estimation methods fail?

Modern asset pricing theory suggests that if investors prefer increased return for accepting increased risk, then expected capital asset prices and returns will be characterized by no capital market arbitrage opportunities being available.[2] While GCAPM is, in principle, consistent with no-arbitrage, CAPM (and, so, GCAPM) have long been known to be based on implausible assumptions and to be inconsistent with capital market data.[3] Further, the no-arbitrage condition for an individual capital asset cannot be demonstrated empirically either in GCAPM, MFMs, or SSMs. It follows that **GCAPM, multi-factor empirical models, and sovereign spread models are not appropriate for use in applications where it is necessary to demonstrate consistency of the ICC estimates with modern asset pricing theory.**

#### What other ICC estimation methods exist?

To solve the theoretical and empirical problems inherent in CAPM and its derivative empirical models, no-arbitrage asset pricing theory (APT) and methods were developed in the mid-1970s.[4] **APT can be easily applied to ICC estimation and used to empirically demonstrate no-arbitrage pricing, hedging, and diversification in international capital asset portfolios**.[5]

**Where to learn more about ICC estimation?**

Read carefully the opportunity cost of capital and ICC estimation method examples provided in the references below, downloadable from SSRN.^{5} If needed, please contact me via e-mail and I’ll be pleased to answer any questions!

Malcolm McLelland Ph.D.

mmc@mclelland-palazzi.com.br

São Paulo, Brazil

* Caveats. Please note: (i) views presented above are my own and do not reflect those of others; (ii) like anyone, I’m not infallible and am responsible for any errors; (iii) I greatly appreciate being informed of any significant errors in facts, logic, or inferences and am happy to give credit to anyone doing so; (iv) the above article is subject to revision and correction; and, (v) the article cannot be construed as investment or financial advice and is intended merely for educational purposes. MMc
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[1] Harvey, Campbell, 2005, “12 Ways to Calculate the International Cost of Capital” (October 14, 2005); available online April 2018.

[2] Ross, Stephen. 2004. *Neoclassical Finance* (Princeton University Press, Princeton, New Jersey, USA).

[3] Fernandez, Pablo. 2015. “CAPM: an absurd model” *Business Valuation Review* 18(3): 25-46; and, Fama, Eugene and Kenneth French, 2006. “The Capital Asset Pricing Model: Theory and Evidence” *Journal of Economic Perspectives* 18(3): 25–46.

[4] Ross, Stephen. 1976. “The arbitrage theory of capital asset pricing.” *Journal of Economic Theory* 13: 341-360.

[5] McLelland, Malcolm, 2018, “CAPM Failure in Private Equity Valuation and the Alternative APT Method” (March 8, 2018), available at SSRN; and, McLelland, Malcolm, 2018, “International Cost of Capital Estimation: The No-Arbitrage Method” (May 8, 2018), available at SSRN.