Currency indexes and consistent currency misvaluation: Illustrations using Big Mac data

A currency misvaluation is implied by a difference between an actual foreign exchange (FX) rate and its intrinsic FX value. The intrinsic FX value between two currencies is based on an economic model, like absolute purchasing power parity (PPP) for example, and is the basis for estimating the currencies’ bilateral misvaluation versus each other. An estimate of a reference currency’s mul­tilateral misvaluation, versus an index basket of other currencies, may then be found using index weights and the index currencies’ estimates of bilateral misvaluation versus the reference currency. A currency’s multilateral misvaluation may be quite different from the currency’s bilateral misvaluation versus another individual currency. For example, the Chinese yuan might be fairly valued versus a currency index, but be undervalued by 8% versus the US dollar.

Published currency indexes, such as the Federal Reserve’s, are widely used in economic and financial research and typically use trade weights. For example, Cline and Williamson (2008) use trade-weighted currency indexes to estimate the Chinese yuan’s multilateral misvaluation. However, trade-weighted currency indexes have two problems. First, in a global economy, weighting an index’s currency positions by trade is less meaningful than weighting by a measure of global economic significance, like GDP (Ho, 2012). Second, because trade-weighted indexes have economy-specific weights, two currencies’ multilateral misvaluation estimates will generally be inconsistent with an estimate of bilateral misvaluation between the two currencies. That is, the Chinese yuan’s multilateral misvaluation estimate versus a Chinese trade-weighted index and the US dollar’s multilateral misvaluation estimate versus a U.S. trade-weighted index will generally be inconsistent with a bilateral misvaluation estimate of the Chinese yuan versus the US dollar.

This article makes two contributions. First, the article clarifies the notion of consistency in currency misvaluation estimates. Second, the article provides instructive empirical illustrations of multilateral misvaluation using some economically-meaningful currency indexes that ensure consistency among currency misvaluation estimates, with weighting by: (1) total GDP; (2) equity market capitalization; and (3) financial wealth. The currency indexes typically yield different multilateral misvaluation estimates for a given currency, and one cannot say which estimate is the best; each index yields multilateral misvaluation estimates that are useful from a particular economic perspective.

There are many economic models of intrinsic FX value, but for illustration purposes the study uses the Economist’s two popular Big Mac methods: (1) The “raw” Big Mac method, which represents the absolute PPP approach to intrinsic FX value; and (2) the Adjusted Big Mac method, which represents the Balassa (1964); Samuelson (1964) approach to intrinsic FX value, where a cross-sectional linear regression is used to adjust PPP deviations for differences in per capita GDP. In principle, bilateral misvaluation estimates of the Adjusted Big Mac method improve on those of the raw Big Mac method.

An equal-weight currency index is easier apply than any of the economically-meaningful indexes, which require data for the weights. Moreover, an equal-weight index yields multilateral misvaluation estimates that closely approximate those based on the Adjusted Big Mac (Balassa-Samuelson) regression residuals (O’Brien and Ruiz de Vargas, 2017). For these reasons, we ask following question: Does an equal-weight index give multilateral misvaluation estimates that also approximate those of the economically-meaningful indexes? Although what constitutes a reasonable approximation depends on the user and the context of the application, the study finds the answer is “not necessarily”. Instead, the approximation’s closeness (or lack thereof) depends on the currency, the index method, and especially the market conditions.

The study’s insights may point financial managers, policy-makers, and researchers to improved applications and new research in the following fields: international capital budgeting (for expansion/contraction of international operations), corporate FX risk management, international portfolio management, cross-border valuation, the economics of international trade and finance, and perhaps others.

 

The full article is published in the current edition of the journal "Research in International Business and Finance" (issue 48 (2019) 464-474).

 

WP Dipl.-Kfm. Santiago Ruiz de Vargas (CVA), Munich, is partner of Noerr LLP, board member of NOERR AG WPG StBG and co-head of the Advisory Services division of the Noerr Group.