Purchasing Power Parity FX 1

The Behavior of FX Rates • Fundamentals that affect FX Rates: - Inflation rates differentials 𝐼 𝐼 - Interest rate differentials 𝑖 𝑖 - Income growth rates 𝑦 𝑦 - Trade flows - Other: trade barriers, expectations, taxes, etc. Formal Theories PPP IFE Monetary Approach Balance of Trade • Goal 1: Explain 𝑆 with a theory, say T1. Then, S = f(.) Different theories can produce different f(.)’s. Evaluation: How well a theory match the observed behavior of St. • Goal 2: Eventually, produce a formula to forecast 𝑆 = f(Xt)  E[St+T]. 1 • We want a theory that matches observed 𝑆 . But, not realistic to expect a perfect match. Q: On average, is 𝑆 ≈ S ? Or, alternatively, is E[𝑆 ] = E[S ]? • Like many macroeconomic series, exchange rates have a trend –in statistics the trends in macroeconomic series are called stochastic trends. It is better to try to match changes, not levels. • Now, the trend is gone. Our goal is to explain𝑒 , , the percentage change in 𝑆 . (Notation: Many times 𝑠 = 𝑒 , ). • The data will show us if the model we are using, say T1, matches, on average, the observed behavior of 𝑒 , . Q for the data: Is E[𝑒 , ] = E[𝑒 , ]? 2 • We will use statistics to formally tests theories. • Data: Distribution of MXN/USD monthly % changes, 𝑒 , (1993:Feb – 2022: Dec) Distribution shows appreciation of USD Descriptive Stats: E[𝑒 , ] = Average monthly % change = 0.52% (6.3%, annualized) SD[𝑒 , = 3.51% (12.2% annualized). • A good theory should predict, on average, an annualized change of 6.3% for 𝑒 , . A better theory should also predict a 12% annualized volatility. • Descriptive stats for 𝑒 , for monthly JPY/USD and the MXN/USD. JPY/USD Mean USD/MXN -0.0014 0.0052 Standard Error 0.0011 0.0019 Median 0.0002 0.0004 Standard Deviation 0.0262 0.0351 Sample Variance 0.0007 0.0021 Kurtosis 4.0886 33.3631 Skewness -0.4276 3.9122 Minimum -0.1052 -0.0887 Maximum 0.0807 0.3500 577 350 Count • Developed currencies tend to be less volatile, with smaller means/medians. They are not normal distributed, but closer to “normal.” 3 Purchasing Power Parity (PPP) Purchasing Power Parity (PPP) PPP is based on the law of one price (LOOP): Goods, once denominated in the same currency, should have the same price. If they are not, then some form of arbitrage is possible. Example: LOOP for Oil. Poil-USA = USD 60 Poil-SWIT = CHF 120  StLOOP = USD 60 / CHF 120 = 0.50 USD/CHF. If 𝑺𝒕 = 0.75 USD/CHF  Oil in Switzerland is more expensive (in USD) than in the US: Poil-SWIT (USD) = CHF 120 * 0.75 USD/CHF = USD 90 > Poil-USA Example (continuation): 𝑺𝒕 = 0.75 USD/CHF > 𝐒𝐭𝐋𝐎𝐎𝐏 (LOOP is not holding) Trading strategy: (1) Buy oil in the US at Poil-USA = USD 60. (2) Export oil to Switzerland (3) Sell US oil in Switzerland at Poil-SWIT = CHF 120. (4) Sell CHF/buy USD at then 𝑆 . Strategy, exporting US of oil to Switzerland, will affect prices: 1) Poil-USA↑  𝐒𝐭𝐋𝐎𝐎𝐏 ↑ (= Poil-USA↑/Poil-SWIT↓) 2) Poil-SWIT↓ 𝑆 ⟺ 𝐒𝐭𝐋𝐎𝐎𝐏 (convergence). ¶ 3) 𝑆 ↓ 4 Example (continuation): LOOP Notes : ⋄ LOOP gives an equilibrium exchange rate. Equilibrium is achieved when there is no trade in oil. (because of pricing mistakes): LOOP holds for oil! ⋄ LOOP is telling what 𝑆 should be (in equilibrium). Not what 𝑆 is in the market today. ⋄ Using the LOOP we have generated a model for 𝑆 . When applied to many goods, we have the PPP model. Problem with LOOP: There are many traded goods in the economy. Solution: Use baskets of goods. PPP: The price of a basket of goods should be the same across countries, once denominated in the same currency. That is, USD 1 should buy the same amounts of goods in the U.S. or in Colombia. 5 • A popular basket: The CPI basket. • In the U.S., the basket typically reported is the CPI-U. It represents the spending patterns of all urban consumers and urban wage earners and clerical workers. (87% of U.S. population). • U.S. basket weights: US: CPI-U Weights 12% Food 14% Food Energy Household Furnishings Apparel 7% New vehicles 10% 7% Used cars and trucks Recreation 3% 4% Housing Health care 3% Housing 2% 32% 6% • Weights are different in different countries. • China’s basket weights: • Relative to the U.S. weights, heavier weight given to Food & Clothing (Apparel, in the U.S.) and lower to Housing and Household Services (Energy, in the U.S.). 6 • The different weights is a problem when comparing CPI baskets: The composition of the index may vary widely across countries. • For example, in Europe, the weight of the food category changes substantially as the income level increases. Absolute version of PPP: The FX rate between two currencies is the ratio of the two countries' general price levels: 𝐒𝐭𝐏𝐏𝐏 = Domestic Price level / Foreign Price level = Pd / Pf Example: LOOP for CPIs. CPI-basketUSA = PUSA = USD 5,577 CPI-basketSWIT = PSWIT = CHF 6,708  𝐒𝐭𝐏𝐏𝐏 = USD 5,577/CHF 6,708 = 0. 8314 USD/CHF. If St  0. 8314 USD/CHF, there will be trade of the goods in the baskets. Suppose 𝑺𝒕 = 1.09 USD/CHF > 𝐒𝐭𝐏𝐏𝐏 . Then, PSWIT (in USD) = CHF 6,708 * 1.09 USD/CHF = USD 7,311.72 > PUSA = USD 5,577 7 Example (continuation): (disequilibrium: 𝑺𝒕 = 1.09 USD/CHF > 𝐒𝐭𝐏𝐏𝐏 ) PSWIT (in USD) = CHF 6,708 * 1.09 USD/CHF = USD 7,311.72 > PUSA = USD 5,577 Potential profit: USD 7,311.72 – USD 5,577 = USD 1,734.72 Traders will do the following pseudo-arbitrage strategy: 1) Borrow USD 2) Buy the CPI-basket in the U.S. 3) Sell the CPI-basket, purchased in the U.S., in Switzerland. 4) Sell the CHF/Buy USD 5) Repay the USD loan, keep the profits. Note: “Equilibrium forces” at work: 2) PUSA ↑ ( 𝐒𝐭𝐏𝐏𝐏 ↑ = PUSA ↑ / PSWIT ↓) 3) PSWIT ↓ 4) 𝑺𝒕 ↓ 𝑺𝒕 ⟺ 𝐒𝐭𝐏𝐏𝐏 (converge) ¶ • Real v. Nominal Exchange Rates The absolute version of the PPP theory is expressed in terms of 𝑆 , the nominal exchange rate. We can write the absolute version of the PPP relationship in terms of the real exchange rate, Rt. That is, Rt = 𝑺𝒕 Pf / Pd = 1 Rt allows us to compare prices, translated to DC: If Rt > 1, foreign prices (translated to DC) are more expensive If Rt = 1, prices are equal in both countries –i.e., PPP holds! If Rt < 1, foreign prices are cheaper Economists associate Rt > 1 with a more efficient domestic economy. 8 Example: We have Big Mac (“the basket”) prices in Switzerland & the US: Pf = CHF 6.70 Pd = USD 5.36 𝑺𝒕 = 1. 0836 USD/CHF  Pf (in USD) = USD 7.26 > Pd Rt = 𝑺𝒕 PSWIT/PUS = 1. 0836 USD/CHF * CHF 6.70/USD 5.36 = 1.3545 Taking the Big Mac as our basket, the U.S. is more competitive than Switzerland. Swiss prices are 35.45% higher than U.S. prices, after taking into account the nominal exchange rate. To bring the economy to equilibrium –no trade in Big Macs-, we expect the USD to appreciate against the CHF. According to PPP, the USD is undervalued against the CHF.  Trading Signal: Buy USD/Sell CHF. ¶ • The Big Mac (“Burgernomics,” popularized by The Economist) has become a popular basket for PPP calculations. Why? 1) Standardized, common basket: beef, cheese, onion, lettuce, bread, pickles and special sauce. (CPI baskets, not standardized). Sold in 120+ countries. Big Mac (Sydney) Big Mac (Tokyo) 2) Very easy to find out the price. 3) It turns out, it is correlated with more complicated common baskets. • In theory, traders can exploit the price differentials in BMs. The Economist's Big Mac Index 9 • In the previous example, Swiss traders can import US BMs. From UH (US) to Rapperswill (CH) • Not realistic. But, the components of a BM are internationally traded. LOOP suggests that prices of components should be similar in all markets. The Economist reports the real exchange rate: Rt = 𝑆 PBigMac,f/PBigMac,d. For example, in Dec 2022, for the British pound (GBP): Rt = [1.2318 USD/GBP * GBP 3.79] / USD 5.36 = 0.87099  (12.90% overvaluation) Example: (The Economist’s) Big Mac Index in Dec 2022. 𝐒𝐭𝐏𝐏𝐏 = PBigMac,d / PBigMac,f (The Economist reports Rt – 1 = 𝑺𝒕 PBigMac,f/PBigMac,d=USD – 1). Rt > 1 Rt < 1 10 Example: (The Economist’s) Big Mac Index (January 2011) Rt = StPBigMac,f/PBigMac,d (US=domestic)  Rt=1 under Absolute PPP Example: Big Mac Index - (Rt - 1). Changes over time in 2000 - 2022. Real FX: AUD, BRL, CAD, CHF, JPY, DKK & GBP 1.4 1.2 1 0.8 0.6 0.4 0.2 0 ‐0.2 ‐0.4 AUD BRL CAD CHF DKK 4/1/2022 5/1/2021 6/1/2020 7/1/2019 8/1/2018 9/1/2017 10/1/2016 11/1/2015 1/1/2014 JPY 12/1/2014 2/1/2013 3/1/2012 4/1/2011 5/1/2010 6/1/2009 7/1/2008 8/1/2007 9/1/2006 10/1/2005 11/1/2004 1/1/2003 12/1/2003 2/1/2002 3/1/2001 4/1/2000 ‐0.6 GBP Rt does move over time. Rt departures from 1, can be very persistent. 11