GF581 Unit 2 Baht and Yen Exchange Rate Exercise Example

Parity First, Then the View: A Unit 2 Exchange Rate Exercise on the Baht and the Yen

[Student Name]

Purdue University Global

GF581: Financial Strategies for a Global Environment

Unit 2 Exchange Rate Exercise

[Instructor Name]

[Date]

The rates and the arbitrage are illustrative; the articles and textbook cited are real.

Inputs

Spot rates: 34.00 baht per dollar and 148.00 yen per dollar. One-year deposit rates: 4.25 percent in dollars, 1.75 percent in baht and 0.75 percent in yen. Expected inflation over the next year: 2.8 percent in the United States and 0.9 percent in Thailand. Last year's spot rate: 31.50 baht per dollar. All rates are simple annual rates.

Part 1: Forward Rates From Interest Rate Parity

Formula. Grow the spot rate by the baht or yen deposit factor and shrink it by the dollar deposit factor to get the forward quoted in foreign currency per dollar (Eiteman et al., 2016).

Baht. 34.00 times 1.0175, divided by 1.0425, about 33.1847 baht per dollar.

Yen. 148.00 times 1.0075, divided by 1.0425, about 143.03 yen per dollar.

Meaning. Both currencies trade at a forward premium against the dollar, the baht by about 2.46 percent and the yen by about 3.47 percent, because their interest rates are lower. A dollar buys fewer baht a year forward than today, which exactly offsets the extra interest a dollar deposit earns.

Part 2: A Mispriced Forward and the Arbitrage

The quote. A bank quotes the one-year baht forward at 33.0547, about 0.13 baht below parity. At that rate, dollars bought forward are slightly too cheap.

The trade, per $1 million. Borrow $1 million at 4.25 percent, owing $1,042,500 in a year. Convert at spot to 34,000,000 baht and deposit at 1.75 percent, growing to 34,595,000 baht. Agree today to buy dollars a year forward at 33.0547: 34,595,000 baht buys about $1,046,600. Repay the $1,042,500 loan.

Result. A riskless profit of about $4,100 per million dollars, about 0.39 percent. Trades like this, repeated across banks, push quoted forwards back toward parity (Bekaert & Hodrick, 2018).

Part 3: Relative Purchasing Power Parity

Formula. The expected spot rate in a year equals today's spot times one plus foreign inflation, divided by one plus U.S. inflation.

Substitution. 34.00 times 1.009, divided by 1.028, about 33.37 baht per dollar.

Meaning. With Thai inflation nearly two points below U.S. inflation, relative purchasing power parity predicts the baht should strengthen by about 1.9 percent over the year. Interest rate parity's forward, 33.18, points the same way.

Part 4: What Actually Happened Last Year

Nominal change. The baht moved from 31.50 to 34.00 per dollar, a weakening of about 7.35 percent in the baht's dollar value.

Real change. Adjusting for last year's inflation, with the same rates as above, the baht's real value fell: 31.50 divided by 34.00, times 1.009 divided by 1.028, less one, is about negative 9.07 percent.

Parity said the baht should firm, but it weakened in both nominal and real terms, because parity conditions describe where rates should drift over long periods, not what capital flows, risk appetite and commodity prices do within a single year.

Part 5: Why Parity Failed This Year

Three explanations fit. First, capital flowed out of emerging Asian currencies as U.S. rates stayed high, a move driven by return differences parity does not capture over short horizons. Second, Thailand's tourism and export revenue recovered more slowly than expected, weakening demand for baht. Third, research has long found that exchange rates deviate from purchasing power parity for years at a time, with deviations shrinking by roughly half only every three to five years (Rogoff, 1996). A 9 percent real fall in one year is well within that pattern.

Part 6: The Real Rate and the Plant

The real exchange rate matters to the course company because its Rayong plant pays Thai wages and sells partly in dollars. A real fall in the baht of about 9 percent means Thai labor and local materials became about 9 percent cheaper in dollar terms relative to U.S. costs over the year, after allowing for the two countries' inflation. For the plant's export sales, that is a competitive gain. For the parent's dollar view of baht profits, it is a loss in translation. The same move helps one line of the accounts and hurts another, which is why later units separate operating, transaction and translation effects rather than treating currency risk as one number.

Checking the Arithmetic

Each result was checked by reversing it. Converting $1,042,500 back at the parity forward of 33.1847 gives 34,595,000 baht, exactly the baht deposit's value, confirming that the parity rate leaves no profit. At the quoted 33.0547 the same baht buy about $1,046,600, confirming the arbitrage gain. Growing 34.00 baht per dollar by the inflation ratio gives the purchasing power parity forecast of about 33.37, which sits close to the interest parity forward, as theory suggests it should when real interest rates are similar.

What the Exercise Shows

Interest rate parity holds closely, because arbitrage enforces it within minutes. Purchasing power parity holds only loosely and over long periods, because no simple trade forces goods prices and exchange rates into line. A treasurer should use forward rates for pricing and hedging, and should treat parity-based forecasts as a long-run anchor rather than a prediction for next year.

Conventions

Rates are simple annual rates. Forward premiums are stated as percentage changes in the foreign currency's dollar value.

References

Bekaert, G., & Hodrick, R. J. (2018). International financial management (3rd ed.). Cambridge University Press.

Eiteman, D. K., Stonehill, A. I., & Moffett, M. H. (2016). Multinational business finance (14th ed.). Pearson.

Rogoff, K. (1996). The purchasing power parity puzzle. Journal of Economic Literature, 34(2), 647-668.