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Sem 5 Prep
← Open Economy MacroExchange rate systems, cross rates and arbitrage

Formulas for this chapter

The exchange rate R

R = units of domestic currency per unit of foreign currency R rises = domestic currency depreciates R falls = domestic currency appreciates

Every question in this course. Fix the direction once and every sign in chapters 9, 16 and 18 follows.

R
For example dollars per euro, or rupees per dollar: the domestic currency is on top
Depreciation
An increase in the domestic price of the foreign currency: imports dearer, exports cheaper

Cross exchange rate

R(A per B) = dollar value of B / dollar value of A Chained form: R(Rs per EUR) = R(Rs per $) x R($ per EUR)

Given two quotes against a common currency, to find the third. Cancel the units to decide whether to divide or multiply; do not rely on memory.

A
The currency you are pricing in, the denominator
B
The currency being priced, the numerator

Arbitrage profit

Profit per unit = higher quote - lower quote Units bought = sum committed / lower quote Total profit = units bought x profit per unit

Two quotes for the same currency in two markets. Always cross-check by revaluing the whole position at the selling quote and subtracting the sum committed.

Lower quote
The market you buy in, and the divisor when converting the sum committed
Higher quote
The market you sell in

Percentage depreciation of the domestic currency

% depreciation = (R(new) - R(old)) / R(old) x 100

Comparing regimes, or sizing a currency move before applying the Marshall-Lerner arithmetic of chapter 9. Class case: 1.00 to 1.50 is 50 %, 1.00 to 1.25 is 25 %.

R(old)
The starting rate, always the denominator
R(new)
The new rate after the market moves or the authorities allow it to move
Step 2 of 23
The real wordsTheory

R, defined precisely

Assume two economies, the United States and the European Monetary Union. Domestic currency is the dollar, foreign currency the euro.

R = $/EUR = the number of dollars needed to buy one euro

If R = 1, one dollar buys one euro. Generalised: R is the number of units of domestic currency per unit of foreign currency. For India, R is rupees per dollar.

Get this the wrong way round and every sign in the next four chapters flips.

The domestic currency is on top. A bigger R means the foreign currency costs more, which means the domestic currency is worth less.

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