Currencies and what moves them

Level 1 Plain words

For every reader: the idea in plain words, no formulas.

What an exchange rate is

An exchange rate is the price of one money in terms of another. If one euro costs 1.10 dollars, a European tourist in New York gets $1.10 of shopping for each euro spent, and an American in Paris pays $1.10 for each euro's worth of dinner.

When the euro costs more dollars than before, the euro has strengthened and the dollar has weakened. That single fact touches a lot of people. An American who owns European shares gains when the euro rises, even if the shares stay flat. A US exporter sells more when the dollar is weak, because its goods look cheap abroad. A family in Mexico that receives dollars from a relative working in Texas gets more pesos when the dollar is strong.

What makes currencies move

Money flows toward places that pay well and feel safe. Five forces explain most of the large moves in exchange rates:

1. Interest rates. When a central bank raises rates, deposits and bonds in its currency pay more, and investors buy the currency to get that return.
2. Inflation. A currency that loses buying power at home tends to lose value abroad too. Over long periods, high-inflation countries see their currencies fall.
3. Trade and investment flows. A country that sells more abroad than it buys earns foreign money that it converts home, which supports its currency. A country that buys more than it sells needs foreign investors to fund the gap.
4. Fear and confidence. In a crisis investors buy the dollar, the yen and the Swiss franc, which they trust to hold value, and sell currencies of countries that look fragile.
5. Governments. Central banks buy and sell their own currency, and some tie it to another at a fixed rate. A fixed rate holds until the cost of defending it gets too high.

Why it matters to an investor

A US investor in foreign shares earns two returns: what the shares do in their own currency and what that currency does against the dollar. In a year when the euro falls 10 %, a European stock fund that gains 10 % in euros ends roughly flat in dollars. Chapter 11 shows that split for stock returns. Some funds hedge the currency away; most broad funds do not.

Level 2 How it works

For readers who want the mechanism, with the diagrams.

Beginner path stops here

Reading a quote

Currency pairs are written base/quote. EUR/USD at 1.10 means one euro (the base) costs 1.10 dollars (the quote currency). If EUR/USD rises to 1.15, the euro has gained. USD/JPY at 150 means one dollar buys 150 yen; if it rises to 160, the dollar has gained and the yen has lost.

Traders measure small moves in points, or pips, the fourth decimal place for most pairs (0.0001) and the second for yen pairs. A move from 1.1000 to 1.1050 is 50 points. To flip a quote, divide one by it: EUR/USD at 1.10 is USD/EUR at about 0.909.

Spot and forward

A spot trade settles in two business days. A forward fixes today the rate for an exchange on a later date, such as three months or a year ahead. Companies use forwards to lock in what their foreign sales will be worth at home. Investors who hedge a foreign bond fund sell the foreign currency forward.

Forward rates are set by the gap between the two countries' interest rates, through a condition called covered interest parity, which we derive in Level 3. A forward is a price fixed by arbitrage, set mainly by today's interest rates.

The drivers, one at a time

Interest-rate gaps. If US deposits pay 5 % and euro deposits pay 3 %, an investor earns 2 points more a year in dollars. Money moves toward the dollar until its price is high enough that the expected fall back offsets the extra yield. Changes in expected rate gaps move currencies more than the gaps themselves, which is why a surprise from a central bank can move a currency several percent in a day.

Inflation and purchasing power. Purchasing power parity says that the same basket of goods should cost the same everywhere once converted. It fails over months and holds loosely over decades. A light-hearted version of the same idea is The Economist's Big Mac index, published since 1986.

The balance of payments. Every international payment has two sides. Trade in goods and services plus income from abroad make up the current account; purchases of foreign assets make up the financial account. These two must offset. A country with a current-account deficit sells assets (bonds, shares, property, companies) to foreigners to pay for its imports. When foreign buyers lose interest, the currency has to fall until imports shrink or assets get cheap enough to attract them again.

Terms of trade. A country whose exports rise in price earns more foreign money for the same shipments. Australia's dollar has tended to rise with iron ore and coal prices, the Canadian dollar and the Norwegian krone with oil.

Risk sentiment. The US dollar is the main reserve currency and the currency in which much of the world's debt is written. When markets panic, borrowers everywhere need dollars to repay, and investors want the most liquid safe asset, Treasury bills. So the dollar often rises in a global crisis, even one that starts in the United States.

Central banks. A central bank can buy its own currency with reserves to hold it up, or sell it to hold it down. Selling is easier, since it can print more of its own money; buying stops when the reserves run out.

Interest rate parity

Covered interest parity links spot, forward and the two interest rates with no forecast at all. An investor with dollars can earn the dollar rate for a year, or convert to euros, earn the euro rate and lock in the conversion back with a forward. Both routes are riskless, so they must pay the same. If they do not, banks borrow in one currency and lend in the other until the gap closes.

Uncovered interest parity is the same idea without the forward: it says the currency with the higher rate should be expected to fall by the rate gap. That one is a forecast, and it fails often in the data. High-yield currencies have tended to hold their value or even rise for long periods, which is what makes the carry trade pay.

The carry trade

A carry trade borrows in a low-rate currency and invests in a high-rate one. For long stretches in the 2000s investors borrowed yen at near-zero rates and held Australian dollars or New Zealand dollars paying several percent. The trade earns the rate gap slowly and loses suddenly, because the high-rate currencies tend to fall hardest in a panic, just when everyone exits at once. Markus Brunnermeier, Stefan Nagel and Lasse Pedersen described this crash pattern in "Carry Trades and Currency Crashes" (NBER Macroeconomics Annual, 2008).

Fixed, floating and in between

Most large economies let their currencies float. Others peg to the dollar or the euro, use a crawling band, or have joined a currency union. A peg removes day-to-day risk for traders and borrowers, which encourages them to borrow in the anchor currency without hedging. When the peg breaks, those unhedged debts become the crisis. Level 4 shows this three times.

The Federal Reserve's broad trade-weighted dollar index, FRED series DTWEXBGS, measures the dollar against the currencies of the main US trading partners.

Level 3 The math

For Series 65 and CFA readers: formulas and worked examples.

Series 65 path stops here

Covered interest parity

Quote the exchange rate $S$ as dollars per unit of foreign currency. Let $i_d$ be the one-year dollar rate and $i_f$ the one-year foreign rate. One dollar invested at home grows to $1 + i_d$. The same dollar converted to $1/S$ units of foreign currency, invested abroad and converted back at the forward $F$ grows to $(1 + i_f) F / S$. With no arbitrage the two match:

In words, the forward rate equals the spot rate times one plus the home interest rate, divided by one plus the foreign interest rate.

Since 2008, covered parity has shown persistent small gaps, called the cross-currency basis, because banks face balance-sheet costs that keep them from running the arbitrage at unlimited size. Wenxin Du, Alexander Tepper and Adrien Verdelhan documented these gaps in "Deviations from Covered Interest Rate Parity" (Journal of Finance, 2018). The gaps are tens of basis points, small next to the rate differentials themselves.

Hedging currency in a portfolio

Covered parity also says what currency hedging costs or pays. A US investor who owns euro assets and sells euros forward for a year locks in the forward rate instead of the future spot. With the forward above spot, as in the example, the hedge adds about the rate gap to the return: the investor sells euros forward at a premium of 1.9 % over spot. A hedged euro bond therefore earns roughly its own yield plus the gap between dollar and euro rates, which brings it close to a US bond's yield. When foreign rates are above US rates, the arithmetic flips and hedging costs the investor that gap every year.

Whether to hedge depends on the asset. Currency swings can be larger than the price swings of a high-grade foreign bond, so most investors who hold foreign bonds for stability hedge them. For foreign shares, which swing more on their own, currency adds less to the total risk, and many investors leave it unhedged as a form of diversification against a falling dollar.

Uncovered interest parity and the forward puzzle

If investors cared only about expected returns, the expected future spot rate would equal the forward:

In words, the currency with the higher interest rate should be expected to fall by about the interest-rate gap over the year.

Eugene Fama tested this in "Forward and Spot Exchange Rates" (Journal of Monetary Economics, 1984) and found the opposite sign on average: currencies with higher rates tended to rise a little, not fall. That forward premium puzzle is the statistical basis of the carry trade. The reward has a cost: rare, sharp losses that a simple average hides.

Carry, in numbers

Purchasing power parity and the real exchange rate

Absolute PPP says $S = P / P^{*}$, the home price level over the foreign one. The weaker form, relative PPP, says the exchange rate moves to offset inflation gaps:

In words, over $n$ years the dollar price of a foreign currency should rise by the ratio of home to foreign inflation, compounded.

The real exchange rate measures that directly. Define $q = S P^{*} / P$, the foreign price level converted to dollars, relative to the US price level:

In words, the real exchange rate is the cost of the foreign basket in dollars, divided by the cost of the home basket.

Kenneth Rogoff's survey "The Purchasing Power Parity Puzzle" (Journal of Economic Literature, 1996) put the half-life of deviations from PPP at three to five years in the studies he reviewed. PPP is a slow anchor, useful for asking whether a currency looks dear after a long run and of little use for next month.

Overshooting

Rudiger Dornbusch showed in "Expectations and Exchange Rate Dynamics" (Journal of Political Economy, 1976) why currencies jump further than the news seems to justify. If uncovered parity holds, a currency whose interest rate rises above the foreign rate must be expected to fall by the gap each year. The only way it can be expected to fall from here and still end at its long-run value is to jump up first.

The balance of payments as an identity

In words, the current account, the capital account and the financial account sum to zero once each flow is counted with its sign, with statistical errors folded in.

Nothing in the identity says which side moves first. A country can run a current-account deficit because foreigners want its assets (the United States for much of the past forty years) or because it is spending beyond its means and must borrow to keep going (Thailand before 1997). A deficit of the first kind can last for decades. One of the second kind ends when lenders stop.

Level 4 History, analysed

For readers who want past episodes run through the Level 3 math.

The Plaza Accord, 1985

Through the early 1980s the dollar had risen as Volcker's Federal Reserve held real interest rates far above those abroad. That climb is the rate-gap driver at work. Once US rates fell and the five governments said they would sell dollars together, the expectation of a falling dollar fed on itself. Against the yen, the dollar went from about 240 to about 150 within roughly two years, a fall of −37.5 %. In February 1987 the same governments met at the Louvre to stop the fall. Japanese exporters, squeezed by the strong yen, pushed hard into cost cuts and overseas plants, and the Bank of Japan's low rates in response fed the asset boom that Chapter 11 covers.

Sterling leaves the ERM, 1992

The peg asked Britain to keep rates high enough to match the Bundesbank, which was holding rates up to contain inflation after German reunification, while Britain was in recession. Traders could see that the UK would prefer to devalue rather than suffer much higher rates for long.

The math of a peg defence shows why a rate rise of a few points could not work. A holder of sterling who expects a 10 % devaluation within a month loses that 10 % unless the interest rate pays it back. The yearly rate needed is:

In words, the yearly interest rate that compensates for an expected devaluation $d$ within $m$ months is one over one minus $d$, raised to twelve over $m$, minus one.

For a 10 % fall expected within a month that comes to 254 % a year. For a 5 % fall expected within a week, it comes to 1,073 %. A base rate of 15 % does not come close. The defender's only other tool, selling reserves, runs out, and speculators know how much is left. George Soros's Quantum Fund was widely reported to have made about a billion dollars betting on the devaluation.

Thailand floats the baht, 1997

Thai banks and companies had borrowed in dollars at lower rates than baht loans charged, trusting the peg. The current account ran a large deficit funded by short-term foreign loans. When the baht fell past 50 to the dollar by January 1998, the baht cost of a dollar loan rose +100 %. A company whose revenue was in baht now owed twice as much in its own money. That is the balance-sheet channel: the currency fall, which might help exporters in normal times, bankrupted borrowers instead. Indonesia, South Korea and Malaysia followed, and Chapter 11 shows what it did to emerging-market shares.

The carry trade unwinds, 2008

From mid-2008 to late October 2008, as the crisis spread, investors closed yen-funded carry trades in a hurry. The Australian dollar lost close to half its value against the yen in a few months. Run the Level 3 carry arithmetic on that: a 4-point carry pays for a 10 % fall in about two and a half years, so a fall of that size wiped out more than a decade of carry. A trader using leverage lost far more than their own capital. The same pattern returned in a smaller form in early August 2024, after the Bank of Japan raised rates.

The Swiss franc floor ends, 2015

From 1.20 to 0.90, the euro lost −25.0 % against the franc and the franc gained +33.3 % against the euro. Retail currency brokers let customers trade at leverage of 50 to 1 or more. At 50 to 1, a 2 % move against the trader equals 1.0 times the trader's own money, and a 25 % move equals 12.5 times. Customers who had bet on the floor holding ended with negative balances their brokers could not collect. Several brokers failed or needed rescue. The lesson for anyone holding a pegged currency: the peg reduces day-to-day volatility and concentrates the risk in one day.

The dollar in 2022

America's central bank raised its target from 0–0.25 % on 16 March 2022 to 4.25–4.50 % by 14 December 2022. In Frankfurt, the European Central Bank began raising rates only in July 2022, and the Bank of Japan kept its policy rate below zero. Level 2's rate-gap driver moved the dollar as it predicts. In July 2022 the euro fell below parity with the dollar for the first time since 2002. The yen weakened past 150 per dollar in October, and Japan's Ministry of Finance intervened to buy yen in September and October, its first such purchases since 1998. The broad dollar index reached its highest level in about two decades late in the year (FRED DTWEXBGS).

Overshooting gives a size for the move. A gap that markets expect to be about three points wider for two years calls for a dollar jump of about 6.1 % on top of the move already priced, and the safe-haven driver added more as stocks and bonds fell together. When US inflation began to cool and markets priced in rate cuts, the dollar gave back part of the rise from late 2022.