ECO 1 – Currency Exchange Rates_ Understanding Equilibrium Value

Exchange rates are notoriously difficult to forecast over short horizons. The purpose of this reading is not prediction but valuation: building a framework for judging whether a currency is trading near its long-run equilibrium value, so that risk exposures and hedging decisions can be taken deliberately rather than by guesswork.

Every exchange rate is a price, and like any price it is quoted with two sides. A dealer quotes a bid, the rate at which the dealer will buy the base currency, and an offer, the rate at which the dealer will sell it. The offer always exceeds the bid. The gap between them is the dealer’s compensation for providing liquidity.

What widens or narrows the spread

Three factors dominate the bid–offer spread a client is quoted:

• Liquidity of the currency pair. Major pairs trade continuously in enormous size and carry the tightest spreads. Less traded pairs, particularly emerging market crosses, carry wider spreads.
• Time of day. A pair is most liquid when the two relevant financial centres are both in their active trading hours. Dealing outside the overlap, or outside normal hours in London, North America and Asia altogether, widens the spread.
• Size of the transaction. Larger trades move the dealer’s inventory further from its desired position, so the dealer charges more for them.

The interbank spread is also a floor beneath the client spread. A dealer quoting to a client must cover the cost of laying the risk off in the interbank market, so client spreads are always at least as wide as interbank spreads and typically wider.

Cross rates from a common currency

Most currency pairs are not quoted directly against one another. Instead a cross rate is built from two quotes that share a common currency. The reliable method is to write the pairs so that the shared currency cancels algebraically, then multiply the two bids to obtain the cross bid and the two offers to obtain the cross offer.

When a quote has to be inverted first, invert each side and swap bid and offer. Given CAD/USD of 1.3199/1.3201, the USD/CAD quote is 1/1.3201 for the bid and 1/1.3199 for the offer, or 0.75752/0.75763.

Dealer quotes are not free to wander. Two constraints hold them in place. First, a dealer’s bid cannot be higher than the interbank offer, and a dealer’s offer cannot be lower than the interbank bid. Second, the cross rate a dealer quotes must be consistent with the two quotes that imply it. When either constraint is violated, a riskless profit exists and traders take it until the violation disappears.

Triangular arbitrage is the second constraint in action. Three currencies imply three exchange rates, but only two of them are independent. The third is determined. If a dealer quotes the third rate away from its implied level, a trader can move around the triangle and end up with more currency than the trader started with.

Reading the violation correctly

The direction of the trade follows from which side of the market is mispriced. If a dealer’s offer on a pair sits below the interbank bid, the dealer is selling the base currency too cheaply: buy from the dealer and sell into the interbank market. If a dealer’s bid sits above the interbank offer, the dealer is paying too much for the base currency: buy in the interbank market and sell to the dealer. In both cases the profit per unit of base currency is the gap between the two prices, as questions 3 and 4 of Example 1 show.

An outright forward contract fixes today the rate at which two currencies will be swapped on a specified later date. Any foreign exchange transaction settling later than T + 2 is a forward.

The forward rate is not a forecast. It is fixed by arbitrage. Consider an investor with one unit of domestic currency for one year. The investor can invest domestically and end with (1 + i_d), or convert at the spot rate, invest abroad at i_f, and convert back at a rate locked in today. Because both strategies are riskless and identical in every other respect, they must return the same amount. That equality defines the forward rate and is called covered interest rate parity.

The immediate consequence is the sign rule. The currency with the higher interest rate trades at a forward discount, and the currency with the lower interest rate trades at a forward premium. This is not a market view. It is arithmetic. If it were otherwise, an investor could borrow in one currency, lend in the other, hedge the exchange rate risk completely and earn a riskless profit.

Rearranged, the same relationship gives the forward premium or discount directly, quoted in price/base terms:

Forward points

In professional markets forward rates are rarely quoted outright. Dealers quote the spot bid–offer plus a number of forward points at each maturity. The points are the difference between the forward and the spot quote, already scaled to the maturity and not annualised.

Four points of technique follow from this quote sheet:

• The offer is always the larger number. Here the points are negative, so the bid is the more negative figure, −5.6 against −5.1 at one month.
• The absolute number of points grows with the term of the contract.
• To convert points into a rate, divide by 10,000 for a pair quoted to four decimal places and add to the spot quote. For JPY/USD, which is quoted to two decimal places, divide by 100 instead.
• Use the side of the market that matches the trade. Selling the base currency forward means using the bid on both the spot rate and the points.

Applying this to the table, a market participant selling EUR three months forward against the USD uses the spot bid and the three-month points bid:

1.1649 + (−15.9 ÷ 10,000) = 1.16331. The participant sells EUR three months forward at USD 1.16331 per EUR.

A newly struck forward is worth nothing to either side and involves no payment at inception. Value accrues from then on, driven by movements in the spot rate and by shifts in either currency’s interest rate. The mark-to-market value is the profit or loss that would be realised by closing the position at current market prices.

Closing out means entering an equal and opposite forward to the same settlement date, using the spot rate and forward points available now. This produces a known cash flow on the settlement date, which is then discounted back to today.

Which side of the market applies

The offsetting trade is defined relative to the original position. A long GBP 10 million position is closed with a short GBP 10 million position. Because a long position in one currency is a short position in the other, always state which currency the position is expressed in. The net gain or loss will then appear in the other currency.

Four candidate predictors of the future spot rate follow from the parity framework, and each carries a different assumption. Knowing which assumption you are making is more important than the arithmetic.

Two implications deserve emphasis. Using the forward rate as a forecast assumes risk neutrality, not a random walk. If uncovered interest rate parity holds, movements in the spot rate approximate a random walk but are not one, because current interest spreads determine expected movements. Conversely, forecasting that the spot rate will simply equal today’s spot rate assumes a random walk; risk neutrality does not deliver that result unless the interest rate differential happens to be zero.

Assessing long-run fair value

Purchasing power parity provides the most common anchor for long-run fair value. Its record is instructive. Over short horizons the relationship between exchange rate changes and inflation differentials is weak to non-existent. Where inflation differentials are large and sustained, the relationship asserts itself even over relatively short periods, because the inflation signal overwhelms the noise. Over long horizons the relative version performs respectably across a broad range of currencies.

The practical conclusion is that purchasing power parity is a poor timing tool and a reasonable valuation anchor. A currency 10% above its purchasing power parity value is not a sell signal for next quarter. It is information about the direction of the eventual correction and about how much room the currency has to move.

The carry trade is a bet that uncovered interest rate parity does not hold. The investor borrows in a low-yielding funding currency, converts at the spot rate, and invests in a high-yielding currency. Uncovered interest rate parity says the high-yielding currency should depreciate by exactly the yield spread, wiping out the gain. The carry trader is betting it will not.

The risk profile

Carry trades tend to earn small, steady gains for extended periods and then lose heavily in short bursts when positions unwind. Three features follow:

• Negative skew and fat tails. The return distribution is not normal. It has fat tails and is skewed toward a higher probability of large losses. This is the crash risk of the strategy.
• Leverage drives volatility. The volatility of returns on the investor’s equity base is explained primarily by leverage, not by the yield spread itself.
• Crowding amplifies the unwind. Because many investors hold similar positions, an initial adverse move triggers simultaneous liquidation, which drives the move further.

Note what made this trade profitable. The yield pickup was 1.60%, but the JPY/AUD cross rate fell from 71.78 to 71.65, meaning the AUD depreciated slightly against the yen. Uncovered interest rate parity would have required a depreciation of roughly 1.60% to eliminate the gain. The actual depreciation was far smaller, and the difference is the profit.

The parity conditions anchor the long horizon and say almost nothing useful about value today. Trade and capital flows close part of that gap.

A country’s balance of payments comprises its current account and its capital and financial account. The current account reflects flows in the real economy, the production and exchange of goods and services. The capital account reflects financial flows. A current account deficit must be matched by a capital account surplus: a country importing more than it exports has to attract funds from abroad to pay for the difference.

Why capital flows usually dominate in the short run

Over the long term, persistent current account deficits tend to weaken a currency and persistent surpluses tend to strengthen it. Over the short to intermediate term, investment and financing decisions usually dominate, for four reasons:

1. Prices of real goods and services adjust far more slowly than exchange rates and other asset prices.
2. Producing real goods takes time and demand decisions carry substantial inertia, whereas liquid financial markets allow financial flows to be redirected almost instantly.
3. Current spending decisions involve only current production, while investment decisions also involve the reallocation of existing portfolios, a far larger pool.
4. A shift in what investors expect the rate to do can by itself set off enormous short-term flows, so the observed rate tracks the prevailing view of liquid asset owners closely.

Three channels from the current account to the exchange rate

The flow supply and demand channel. Buying and selling internationally traded goods requires exchanging currency. A surplus country sees demand for its currency rise and its currency appreciate; a deficit country sees the reverse. These moves should eventually be self-correcting, because currency strength erodes the surplus country’s competitiveness and currency weakness improves the deficit country’s.

How far the exchange rate must move to restore balance depends on the initial gap between imports and exports, on how import and export prices respond to the exchange rate, and on how demand responds to those prices. Both responses are weaker than intuition suggests. Empirical studies commonly find that a 1% decline in a currency’s value raises import prices by only about 0.5%, and in some cases less, because foreign producers cut margins to protect market share. Limited pass-through means the required exchange rate adjustment is larger than it would otherwise be. Demand responses are also sluggish, so lags of several years can separate the exchange rate move, the eventual traded goods price change, and the correction of the imbalance.

The portfolio balance channel. Running a deficit transfers financial wealth abroad, from the deficit country to its trading partners. Investors in surplus countries accumulate claims on the deficit country. If those investors become unwilling to hold an ever-larger share of their portfolios in the deficit country’s assets, they rebalance, and the deficit country’s currency falls.

The debt sustainability channel. A country running persistent deficits accumulates external debt. Once the market judges the resulting debt burden unsustainable, a sharp currency depreciation may be required to restore the balance, rather than the gradual adjustment the other channels imply.

Capital flows: push and pull

Capital flows into a country for reasons that originate at home, called pull factors, and reasons that originate abroad, called push factors. Pull factors include sound fiscal and monetary policy, credible institutions, an open capital account and a functioning financial system. Push factors include low yields in developed markets, which drive investors toward higher-yielding assets, and long-run shifts in strategic asset allocation. As an example of the latter, the emerging market share of world GDP at current prices was over 40% as of 2019, up from 17% in the 1960s, and index weights have followed, drawing allocations with them.

Capital inflows are beneficial but dangerous in surges. Surges preceded three major crises in the 1990s: the European Exchange Rate Mechanism crisis of 1992 to 1993, the Mexican peso crisis of late 1994, and the Asian currency and financial crisis of 1997 to 1998. Each was preceded by a build-up of large, highly leveraged speculative positions, and in each case the sudden unwinding of those positions triggered the attack on the currency.

The Mundell–Fleming model

The Mundell–Fleming model traces how monetary and fiscal policy affect interest rates and activity, which in turn drive capital and trade flows and finally the exchange rate. It focuses only on aggregate demand and assumes enough slack in the economy that output can rise without prices rising.

Under flexible exchange rates, expansionary monetary policy lowers domestic interest rates, which induces capital to move toward better-paying markets and pushes the currency down. The stronger that sensitivity of flows to yield gaps, the sharper the fall.

Expansionary fiscal policy raises interest rates, because larger deficits must be financed. With mobile capital, higher rates attract capital and the currency appreciates, potentially substantially. But if capital is immobile and insensitive to rate differentials, the same policy raises aggregate demand, increases imports, worsens the trade balance and pushes the currency down, with no offsetting inflow to support it. The degree of capital mobility therefore reverses the sign of the fiscal effect.

The policy mix

Because the two policies work through different channels, the combination matters more than either alone.

Restrictive monetary policy combined with expansionary fiscal policy raises real rates and is strongly bullish for the currency. The opposite combination is bearish. Mixes that push real rates in opposite directions are indeterminate.

With capital immobile, the effects run through the trade balance instead. Both policies expansionary boosts imports and is bearish; both restrictive cuts imports and is bullish.

Note that the two tables are almost mirror images. The high-mobility case is more relevant for the G–10 countries, where capital moves freely. The low-mobility case is more relevant for emerging markets that restrict capital movement. A classic illustration of the high-mobility case is Germany from 1990 to 1992: a highly expansionary fiscal policy to fund unification combined with an extraordinarily restrictive Bundesbank monetary policy to contain the resulting inflationary pressure drove German rates sharply higher and the currency appreciated.

Monetary models of exchange rate determination

Mundell–Fleming routes monetary policy to the currency through interest rates and output, leaving the price level out of the story entirely. The monetary models invert that: output is held fixed and the transmission runs through prices and inflation instead.

Under the pure monetary approach, money supply and prices move one for one: raise the domestic money stock by some percentage and the domestic price level rises by the same percentage. If purchasing power parity holds, that increase in domestic prices relative to foreign prices produces a proportional fall in the currency’s value. Its weak point is the reliance on purchasing power parity over every horizon, short as well as long, which is not how the relationship behaves.

The Dornbusch overshooting model repairs this by assuming prices are sticky in the short run and fully flexible in the long run. In the long run, an increase in the money supply raises prices proportionally and the currency depreciates, as the pure monetary model says. In the short run, with prices inflexible, the increase in nominal money supply lowers the domestic interest rate. With highly mobile capital this triggers a capital outflow that drives the currency below its new long-run equilibrium. As domestic nominal rates subsequently rise, the currency appreciates back toward the path the conventional monetary approach predicts.

The portfolio balance approach

The Mundell–Fleming model is essentially short run and makes no allowance for the long-term effects of the budget imbalances that sustained fiscal expansion produces. The portfolio balance approach fills that gap. Global investors hold a diversified portfolio of domestic and foreign assets and adjust the mix in response to expected return and risk.

A growing budget deficit steadily increases the supply of domestic bonds. Investors will hold them only if compensated with a higher expected return, which can come from higher interest rates or a higher risk premium, from an immediate currency depreciation deep enough that investors then expect subsequent appreciation, or from a combination. The result is that expansionary fiscal policy, bullish for the currency in the short run through the interest rate channel, becomes bearish in the long run as the debt stock accumulates.

Governments resist excessive inflows and currency bubbles using two tools: direct intervention in the foreign exchange market, and capital controls.

Forms of capital control

The forms controls take vary widely. Malaysia and other countries caught in the Asian financial crisis barred their banks from quoting transactions that involved selling the domestic currency. Brazil has taxed currency transactions to slow them down. Thailand in 2006 met an inflow-driven appreciation of the baht by demanding that 30% of any investment be parked for a year in a deposit paying nothing. Vietnam has capped how much of a local financial institution foreigners may own. Ukraine lost its place in the MSCI Frontier Markets equity index in 2015 once its central bank blocked foreign holders from taking home the proceeds of share sales. Venezuela by 2016 ran four separate exchange rates at once, the bolivar-to-dollar rate depending on what the dollars would be spent on, which pushed a great deal of demand into the black market before the regime was eased in 2018 and 2019.

Opinion on capital controls has shifted. They were once regarded as distorting global trade and finance, easy to circumvent, and liable to deflect flows onto other countries. The IMF has since said that the benefits may exceed the costs, and after repeated episodes of damaging capital flow surges, some argue controls may be needed to prevent exchange rate overshooting, asset bubbles and deteriorating financial conditions.

Does intervention work

The answer differs sharply between developed and emerging markets, and the reason is arithmetic rather than ideological.

In developed markets, the volume of intervention is small relative to daily turnover in G–10 currencies. For most developed countries the ratio of official FX reserves to average daily turnover in that currency is negligible, so central banks simply do not hold enough reserves to shift supply and demand meaningfully. Most studies conclude the effect is limited. There is an asymmetry worth noting: a central bank trying to weaken its own currency could in principle create and sell an unlimited amount of it, accumulating reserves in exchange. But persistent intervention of this kind undermines the effectiveness of domestic monetary policy.

In emerging markets the evidence is more mixed but more favourable. Intervention appears to lower exchange rate volatility, though no statistically significant relationship has emerged between intervention and the level of the exchange rate. Emerging market central banks hold reserves that are sizeable relative to daily turnover in their own currencies, which gives them considerably more firepower than their developed market counterparts, and reserve holdings have expanded rapidly, so effectiveness may now be greater than in the past.

Warning signs of a currency crisis

Currency crises arrive suddenly. Over the six months from August 2008 to February 2009, 23 currencies lost at least 25% against the US dollar. Among developed markets, the Australian dollar, Swedish krona and UK pound each gave up 35% or more. Among emerging markets, the Brazilian real, Russian rouble and South Korean won each lost more than half their value.

The speed comes from forced repositioning. A carry trader long the Brazilian real and short the US dollar must sell reals and buy dollars once the real starts falling. A Brazilian borrower who financed in dollars must do the same to cover future repayment. Both actions intensify the selling. It is this mass liquidation of vulnerable positions, reinforced by speculative offshore selling, that produces the excessive moves seen in crises.

Two schools of thought disagree on causes. One holds that crises are precipitated by deteriorating fundamentals, which deteriorate steadily and therefore predictably. The other holds that crises can strike economies with sound fundamentals, through sudden self-fulfilling shifts in sentiment or contagion from crises elsewhere, for example when a country devalues to keep its exports competitive with a neighbour that has already devalued.

An ideal early warning system would predict actual crises without issuing false alarms, would rely on indicators available on a timely basis rather than with long lags, and would be broad based, because crisis-prone countries typically exhibit several problems at once. Studies have identified the following conditions in the run-up to crises:

1. Restrictions on cross-border capital movement have recently been lifted.
2. Foreign money has arrived in size relative to the economy, and the most dangerous form of it is short-dated borrowing denominated in a foreign currency.
3. Trouble in the banking system runs alongside the currency trouble, frequently arriving first.
4. The exchange rate is pegged or managed rather than floating, which leaves a level for speculators to attack.
5. Official reserves are draining away quickly as the crisis nears.
6. The currency sits well above its own long-run average.
7. Export earnings have been weakening against the import bill, so the terms of trade are turning down.
8. Broad money is growing fast and M2 is rising relative to bank reserves.
9. Inflation is running materially above its level in calm periods.

These factors are interrelated and feed off one another. Liberalised markets and foreign borrowing by domestic banks produce large inflows. If the borrowing is in foreign currency and the domestic currency starts to depreciate, banks struggle to service short-maturity debt. Foreign investors withdraw and speculators short the currency, driving it lower. A government defending the currency can raise interest rates, which worsens the banking sector’s condition and slows the economy, or intervene directly, which spends down reserves. If the government appears unwilling or unable to defend the currency, outflows and speculative attacks intensify. Meanwhile an overvalued currency makes exports uncompetitive, so the country earns less foreign currency precisely when it needs reserves most.