This article reviews various models used to determine a country’s exchange rate with another country and focuses on a unique exchange rate environment that existed in Argentina between 2011 and 2016. In particular, the article examines the relationship between a managed official exchange rate and an alternative rate. The analysis follows the two exchange rates from a period when the official rate was highly managed to a period following the lifting of restrictions on the official exchange rate. This article finds that the alternative exchange rate, determined by the relative prices of eight stocks simultaneously traded in Argentina and the United States, serves as a good proxy for a market rate.
The first two sections provide an overview of exchange rate theory and exchange rate policy options. The next sections examine the Argentine experience, the method of computing the alternative exchange rate, the influence of the political environment on the official rate, and the effectiveness of the alternative rate as a market proxy. The article concludes by discussing implications for theory and practice and suggesting areas for future investigation.
The Exchange Rate in Theory
An exchange rate is the price of one currency in terms of another. Without government interference the rate is determined by the relative demand and supply of the two currencies. The demand for a foreign currency arises from a demand for goods, services, and financial assets denominated in that currency. If an Argentine company buys equipment priced in United States dollars (USD), the purchase creates a demand for USD in the foreign exchange market. Similarly, the demand for Argentine pesos (ARS) is derived from the global demand for goods, services, and financial assets denominated in ARS.
When the trade of ARS for USD occurs, it simultaneously creates a supply of ARS in the foreign exchange market. In order to obtain the USD required to pay for the equipment purchase, the Argentine company must sell ARS in the foreign exchange market, contributing to the supply of ARS. Therefore, the supply of a foreign currency in the exchange market is determined by the amount of currency that a country injects into the market through transactions.
The law of one price provides a constraint on the exchange rate. After considering transaction costs, an equilibrium exchange rate between two currencies will equate the local prices of the same good in the two countries. For example, if a pair of Levi jeans costs 50 USD in the United States and the exchange rate is 15 ARS to 1 USD, then the jeans price in Argentina should be 750 ARS. If the jeans cost more or less than that in ARS, an entrepreneur could engage in an arbitrage transaction that would earn a guaranteed profit. For example, if the jeans cost 950 ARS in Argentina. The entrepreneur could purchase the jeans in the US, for 50 USD, ship them to Argentina and sell them for 950 ARS. At an exchange rate of 15 ARS to 1 USD, the 950 ARS earned by selling the jeans in Argentina equates to 63.33 USD. If it costs 3.33 USD to ship the jeans from the U.S. to Argentina, the entrepreneur would earn a 10 USD (20 percent) profit, leading to many people wanting to buy many pairs of Levis to export to Argentina.
As similar transactions occur many times, the USD:ARS exchange rate will move to eliminate this arbitrage opportunity. The purchase of the jeans will increase the demand for USD, while simultaneously increasing the supply of ARS. As a result the dollar will appreciate (so that it will buy more ARS), and the ARS will depreciate (buying fewer USD). This process will continue until the local price in both countries is the same after considering transaction costs.
Exchange Rate Policy Options
The two extreme exchange rate policies are floating and fixed rates. A government that takes a complete laissez faire approach allows markets to set the exchange rate. Such a government is following what is known as a floating exchange rate policy. A totally free-floating exchange rate is rare.
In contrast to a floating rate, a government that sets an exchange rate independent of market forces is following a fixed exchange rate regime. For more than 25 years after World War II, most of the world used a foreign exchange system that fixed, or pegged, exchange rates to the USD. Gold was used as an intermediate good, with a country theoretically setting a price for gold that would satisfy the constraint of the law of one price. Thus, if the pegged exchange rate was 15 ARS to 1 USD and the U.S. price of gold was 35 USD per ounce, the price of an ounce of gold in Argentina would be 525 ARS. The Argentine government would be committed to purchasing gold at that price. If the de facto rate deviated from the peg, an arbitrage opportunity would exist and gold would flow between the two countries. By the late 1960s, the official pegs did not reflect accurately the existing supply and demand for currencies, which led to large-scale outflows of gold from many countries to the United States. As a result, by the mid-1970s developing countries became weary of supporting the peg to common currencies. Between 1975 and 1996, the percentage of developing countries, weighted by their relative size, that maintained a fixed rate exchange regime fell from 70 percent to less than 20 percent.
Some countries adopted an exchange rate regime that pegged to a “basket of currencies” rather than to a single currency. Other countries charged central banks and/or “currency boards” with establishing exchange rates that would maintain acceptable levels of foreign currency reserves used to balance temporary disequilibria in foreign trade. A popular strategy in developing countries was to allow a currency’s value to float with varying degrees of restrictions—that is to create a “managed” or “dirty float.” Such “managed floats” are attractive in many developing countries that do not have fully-developed financial systems, where a few large international financial transactions can lead to destabilizing shifts in foreign exchange rates.
The Argentine Experience
Over the last three decades, Argentina has employed many different exchange rate regimes. As detailed in the International Financial Law Review, in October 2011, Argentina adopted comprehensive controls on flows of foreign currencies and required approval by the Argentine Tax Authority for “foreign exchange transactions involving payments of imports and services, and…the purchase of foreign currency by Argentine residents for travel and tourism purposes.” As noted in a 2016 World Bank Group working paper the “restrictions were put in place to limit capital flight and exchange rate depreciation and [to] protect reserve levels.” Furthermore, in response to the restrictions, “[a] de-facto dual exchange rate regime emerged” in 2011. While there were multiple alternatives to the official rate, one rate, known as the “paralelo” or “blue dollar” rate, became so widely used that it was reported in major Argentine newspapers on a daily basis. In fact, the exchange rate data for both the official and blue dollar rates used in this article were obtained from Ámbito.com (the website for a major Argentine financial newspaper). 
In December 2015, the Argentine government removed most of the controls on the Argentine peso, however the blue dollar rate continued to exist. The next section of this article discusses the method of determining the blue dollar rate.
The Method of Computing the Blue Dollar
The blue dollar rate was calculated every twenty minutes by computing an average differential in the price of eight major stocks traded on both the U.S. and Argentine markets. When computing the average differential, the component firms were weighted equally.
The eight companies were:
Banco Macro, S.A.
BBVA Banco Frances, S.A.
Grupo Financiero Galicia, S.A.
Pampa Energía, S.A.
Petrobras Argentina, S.A.
Petroleo Brasileiro, S.A.
Telecom Argentina, S.A.
The Politics of the Argentine Exchange Rate
On October 25, 2015, Argentina held a general election that resulted in the need for a presidential runoff between Daniel Scioli (the Peronista candidate) and Mauricio Macri (a more pro-market candidate). The need for a runoff was unexpected as, prior to October 25, many polls in Argentina were predicting a clear victory for Daniel Scioli. That second election was held on November 22, 2015, and resulted in a victory for Mauricio Macri, who had campaigned on a platform that included removing the cap on the Argentine peso.
Data indicate that the changing political environment had an influence on the differential between the official and blue dollar exchange rates. From October 23 (the last trading day prior to the initial election) to November 23 (the first day after the final election) both the official and blue rates fluctuated, as the likelihood of a Macri victory increased. During that one month period, the official rate to buy USD went from 9.48 ARS per USD to 9.635 (depreciating just over 1.6 percent), while the blue dollar buy rate went from 15.90 ARS per USD to 15.04 (appreciating just over 6 percent). On December 16, 2015, less than a week after taking office, Macri announced the removal of the cap on the official exchange rate, and on December 17, the official rate began to float.
The Blue Dollar as a Market Proxy
As Exhibit 1 demonstrates, the removal of the cap produced a dramatic movement of the official exchange rate toward the blue rate. On December 16, 2015, prior to the removal of restrictions, the official buy rate was 9.79 ARS per USD, while the blue dollar buy rate was 14.42 ARS per USD—a differential of 4.63 ARS per USD (over 47 percent). On the first day after the removal of restrictions (December 17, 2015), the official buy rate immediately converged to the blue dollar rate, depreciating over 40 percent to 13.75 ARS per USD. On the same day, the blue dollar buy rate appreciated slightly to 14.21 ARS per USD—cutting the differential between the two rates by 90 percent. The differential remained low over the remainder of the period examined.
In order to investigate the relative behavior of the two exchange rates more fully, we analyzed the changes in the exchange rates over three 34 trading-day windows. One window encompasses the trading days between the initial election on October 25, 2015 and the lifting of the cap on December 17, 2015. The others consist of the 34 trading days prior to October 25 and the 34 trading days following December 16. Thus, our study, in total, encompassed a 102 trading-day window, beginning on September 7, 2015, and concluding on February 4, 2016.
Our analysis indicates that despite being based on only eight stocks, the blue dollar rate served as a strong proxy of the eventual floating exchange rate. As Exhibit 2 shows, the average differential between the official and blue dollar rates fell from 6.30 ARS per USD in the pre-election period, to 5.35 in the transitional period, to 0.54 in the 34 trading-day period following the removal of the cap. Reviewing the data in another way, the average differential represented 67.2 percent of the official buy rate in the pre-election period, 55.7 percent of the official buy rate in the transitional period, but only 4 percent in the floating period. In addition, the final differential of 0.54 ARS per USD translates to less than 4 cents, which should be within the bounds of transaction costs.
The vast majority of the decline in the differential was due to the change in the official exchange rate. From December 16 to February 4, the official rate depreciated 43.1 percent, while the blue rate depreciated 2.9 percent. Most of the change occurred on the day the official rate began to float. From December 16 to December 17, the official rate depreciated 40.4 percent, while the blue rate actually appreciated 1.5 percent. This trend also is visible in the graph presented in Exhibit 1.
Furthermore, the relative volatility of the differentials also appeared to change with the political and economic environments. As Exhibit 2 shows, in the pre-election period the standard deviation of the average differential was 0.15 ARS per USD. During the uncertainty of the transitional period, the standard deviation rose to 0.49 ARS per USD. During the floating period, the differential stabilized somewhat, with a standard deviation of 0.36 ARS per USD. The increased volatility in the final period relative to the pre-election period may reflect what a Goldman Sachs analyst labeled a “process of price discovery.”
To summarize this section, when the restrictions on the Argentine peso were lifted, the official exchange rate converged within one day to the blue rate, and the differential between the two rates was within the bounds of transaction costs for the remainder of the period examined.
Implications for Theory and Practice
The quick convergence of the official rate to the blue rate provides support for the law of one price. The evidence suggests that employing the law of one price to estimate an exchange rate based on the simultaneous prices of eight stocks on exchanges in two countries worked. The exchange rate determined based on stock prices seems to have reflected the underlying forces that lead to market-driven exchange rates.
Practically speaking, the evidence suggests that a firm can use the law of one price to estimate an appropriate market exchange rate for pricing cross-border transactions in an economy with an artificial exchange rate. Returning to our Levi example, during the controlled period examined in this article, an exporter should have priced the 50 USD jeans at 795 ARS in Argentina (reflecting the blue dollar rate of 15.9 ARS per USD), rather than selling the jeans for the 474 ARS suggested by the official rate of 9.48 ARS per USD.
In addition, analyses based on the law of one price may enable individuals and companies to predict the direction and level of movements in exchange rates for currency speculation purposes. Similarly, the approach could be used by speculators to predict the likely consequences of an eventual deregulation of a fixed exchange rate. The Argentine experience related here shows that, when the cap was removed, the official rate rapidly converged to the blue dollar rate, creating a 40 percent profit opportunity.
Avenues for Future Investigation
The Argentine blue rate demonstrated that the differential prices of a small number of stocks traded at the same time on different markets can be used as an effective proxy for a market exchange rate. These findings may be stronger because the proxy used financial assets. Such assets may have an advantage over tangible assets due to lower transaction costs since financial assets may be transferred electronically. One interesting question for the future is whether basing a proxy on the law of one price is equally effective with financial assets traded on exchanges that are not open simultaneously. For example, would comparing the daily prices of a basket of financial assets in Asia and North America lead to a similarly useful proxy?
 Caramazza, Francesco, and Jahangir Aziz. “Fixed or flexible? Getting the exchange rate right in the 1990s.” International Monetary Fund, (April 1998). Accessed June 25, 2016. http://www.imf.org/external/pubs/ft/issues13/index.htm.
 Abramovich, Fernanda López, and Jorge I Mayora. “Foreign exchange controls in Argentina.” International Financial Law Review, (October 8, 2012). Accessed June 23, 2016. http//www.iflr.com/Article/3099463/Foreign-exchange-controls-in-Argentina.html.
 Coppola, Andrea, Andresa Lagerborg, and Zafer Mustafaoglu. “Estimating an equilibrium exchange rate for the Argentine peso.” World Bank Group Macroeconomics and Fiscal Management Global Practice Group, (May 2016): 2. Accessed June 18, 2016. http://www-wds.worldbank.org/external/default/WDSContentServer/WDSP/IB/2016/05/24/090224b08435dd0a/1_0/Rendered/PDF/Estimating0an00r0the0Argentine0Peso.pdf
 Ámbito.com. 2016. “Ámbito.com Dólar Oficial.” Accessed June 18, 2016. http://www.ambito.com/economia/mercados/monedas/dolar/info/?ric=ARSSCBCRA&desde=01/09/2015&hasta=18/06/2016&pag=1.
 Ámbito.com (2). 2016. “Ámbito.com Dólar Informal.” Accessed June 18, 2016. http://www.ambito.com/economia/mercados/monedas/dolar/info/?ric=ARSB=&desde=01/09/2015&hasta=18/06/2016&pag=5
 Coppola, “Estimating an equilibrium.”
 Herzbach, Jeff. “Inside Argentina’s Blue Dollar Market.” The Argentina Independent, (November 19, 2014). Accessed June 20, 2016. http://www.argentinaindependent.com/currentaffairs/analysis/inside-argentinas-blue-dollar-market/
 For a detailed explanation of how the Blue Dollar rate is computed, see, Dolarblue.net. “Methdology for Calculations.” Dolarblue.net, from Internet Archive. Accessed July 28, 2016. https://web.archive.org/web/20150926023011/http://blog.dolarblue.net/p/calculo.html
 Herzbach, “Inside Argentina’s Blue Dollar.”
 The Economist. “A Big Surprise: The First Round of Voting Shakes Up the Presidential Race,” (October 31, 2015.) Accessed July 5, 2016. www.economist.com/news/americas/21676972-first-round-voting-produces-unexpected-results.
 Watts, Jonathan. “Argentina Elections: Peronist Daniel Scioli Ahead by ‘Wide Margin’.” The Guardian, (October 25, 2015). Accessed June 28, 2016. https://www.theguardian.com/world/2015/oct/25/argentina-presidential-elections-2015-voters-polls.
 The Economist (2). “Macri-economics,” (October 31, 2015). Accessed July 14, 2016. www.economist.com/news/americas/21677250-profile-possible-president-macri-economics.
 Turner, Taos. “Argentina’s peso sinks after currency controls lifted; peso loses quarter of its value against the U.S. dollar a day after new government moves to kick-start economy.” The Wall Street Journal Online, (December 17, 2015). Accessed June 25, 2016. http://www.wsj.com/articles/argentinas-peso-depreciates-sharply-after-currency-controls-lifted-1450365003.