# Exchange rates and the foreign exchange market

What is the link between the balance of payments and the foreign exchange market?

What is the exchange rate of a currency and what are its main sources of fluctuation?

Who are the main players in the foreign exchange market?

What is the forward exchange rate?

What is the role of expectations in the foreign exchange market?

What is the relationship between the interest rate and the exchange rate?

Is the foreign exchange market efficient?

Reminder: neglecting the capital account (${\displaystyle CK=0}$) to simplify the analysis, the balance of payments equilibrium is written as follows: ${\displaystyle CC+CF\equiv 0}$.

Both CC and CF depend on the exchange rate, ${\displaystyle E}$ = price of one currency in terms of another currency.

Within CF, it is useful to distinguish between private transactions, ${\displaystyle CF_{p}}$, and the reserve assets, RES, the latter being assumed to be independent of ${\displaystyle E}$. Then we get: ${\displaystyle CC(E,...)+CF_{p}(E,...)+RES=0}$

Two approaches to the determination of the equilibrium exchange rate related to two different historical situations :

1. Current account approach (1950-70)
2. Approach by financial account (>1970)
1) Current account approach (1950-70):

${\displaystyle CF_{p}}$ is exogenous = control of international capital flows. ${\displaystyle E}$ is determined by the current transactions -> flow balance. Historically, controls on capital movements (poorly integrated financial markets) until the early 1970s => ${\displaystyle E}$ fixed, but adjustable (Bretton Woods regime).

2) Financial Account Approach (1970+)

${\displaystyle CC}$ is exogenous = capital flows are free, and react much faster than real (fixed short-term) transactions. ${\displaystyle E}$ is determined by the capital transactions balance of stocks. Historically, integrated financial markets since the 1970s => ${\displaystyle E}$ flexible.

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# The foreign exchange market

## Rating conventions

In this lecture, writing XXX/YYYY indicates the number of units of currency XXX that is needed for one unit of currency YYY, regardless of whether XXX is the domestic or foreign currency.

Therefore, regardless of the quotation conventions, if we find 1.10 XXX/YYYY, it means that we exchange 1.10 units of XXX for 1 unit of YYYY. This is just a simple rating convention and as such is obviously not universal. The FT, for example, and many newspapers adopt the same notation, but the KO (as well as the quotation agency Reuters) adopts the reverse presentation convention (in the KO 1.10 XXX/YYYY indicates that 1.10 units of YYY are needed for 1 XXX).

Concretely, in the following, given the rating and quotation conventions adopted, 1.26 CHF/USD means that 1.26 Swiss francs are needed for 1 US dollar and that the Swiss franc is the national currency (=> if the rate were to rise to 1.33 this would indicate a depreciation of the CHF).

## Exchange rates and prices of goods

As discussed in the lecture on national accounts and balance of payments, the exchange rate is used to compare the prices of goods sold in different locations. Effects of a change in the exchange rate on the prices of goods :

A depreciation of the national currency (CHF) reduces the relative price of the exported goods (watches in the example opposite). See also Box 13.1 of the KO on overnight stays of US tourists in Paris and the EUR/USD rate.

## The foreign exchange market

Main players in the asset market: Commercial banks (main player: the 10 largest banks account for 75% of the market) and the interbank market ('wholesale' market); commercial companies (operating in several countries); non-bank financial institutions, e.g. pension funds (since the deregulation of financial markets); central banks (small volume of transactions when they are involved but high impact because of the signal effect).

Amounts: Trading volume around \$1500 billion per day. In 6 days one exceeds world trade by one year!

Characteristics: Exchange of currencies on many financial markets, with few opportunities for effective arbitrage because information circulates very quickly. The USD is still the dominant vehicle currency as most transactions are still between one currency and the USD.

## Spot exchange rate

Spot foreign currency transactions use spot exchange rates (${\displaystyle E}$ or sometimes ${\displaystyle S}$ for spot exchange rate). The validation day of a cash transaction = ${\displaystyle j+2}$ (2 days after the conclusion of the transaction).

When transactions specify a release date with ${\displaystyle d>2}$ (for example d = 30, d = 60, d = 90), the rates used are forward exchange rates. (${\displaystyle F}$ = forward exchange rate). Cf. later.

A foreign exchange swap or currency swap is a spot sale of a currency combined with a forward purchase of the same currency.

Arbitrage ensures that there are no major differences between, for example, ${\displaystyle E_{GBP/USD}^{NY}}$ and ${\displaystyle E_{GBP/USD}^{London}}$

## Notes

Quotation to the certain of the euro.

The ECB rate is the reference exchange rate set by the European Central Bank.

The over-the-counter rate is always less favourable than the interbank market rate.

The spread between the ask price and the ask price is the profit margin for commercial banks (transaction cost) and is generally higher for the rarer currencies.

As a result of arbitrage, the direct exchange rates are equivalent to the product of the cross-exchange rates (example: CHF/USD = CHF/EUR ∙ EUR/USD).

Forward transactions are used by economic agents to hedge against the risk of unexpected exchange rate fluctuations. Example of KO players p. 361: a player sold in France for 100 euros and paid 9,000 yen to the Japanese supplier. Compare the gain per player sold in the case of i. immediate payment at the spot exchange rate YEN/EUR = 95.25, ii. future payment at a future spot exchange rate YEN/EUR = 86.95 (yen appreciation), iii. future payment covered by a yen purchase at the forward rate (YEN/EUR) = 93.46].

## Spot and forward exchange rates

Spot and forward exchange rates are closely related (especially as the term approaches).

## Forward Contracts and options

Currency forwards, futures and options are derivatives, which have grown considerably since the 1970s.

The forward purchase of a currency on the futures market is binding. Once the terms of the contract (amount, maturity) have been agreed, there is no going back even if expectations change. See example on the next page.

In the case of currency forwards (futures), the promise to deliver a given amount of a currency at an agreed term is purchased, and this promise can be resold (realizing a gain or loss in the futures market) at any time. More flexible than the forward, even if the terms of the futures contracts are standardized (= not possible to negotiate the amounts or maturity as in the case of forwards).

Example of forward contracts:

• The Chinese currency (remninbi or Chinese Yuan, CNY) is still non-convertible, i.e. it can only circulate within China and non-residents cannot hold accounts in CNY. How does a US exporting company (which fears a depreciation of the yuan) go about eliminating the exchange rate risk on the 10m of CNY (at a spot rate of 6 CNY/USD) that it will receive in 3 months, knowing that, being the non-convertible currency, it is not possible to use the futures market?
• Solution: the US company enters into a forward contract which consists in paying or receiving the difference, in dollars, compared to the agreed rate (e.g. stability at 6 CNY/USD). For example, if the yuan appreciates to ${\displaystyle 5.5}$, it will pay ${\displaystyle ({\frac {1}{5.5}}-{\frac {1}{6}})\times 10=0.15}$m of USD to the People's Bank of China, and, vice versa, it will receive 0.13m of USD from the Chinese central bank if the yuan depreciates to 6.5 CNY/USD → paris.

Typical case where the financial market develops a new instrument to circumvent a (probably transitory) difficulty → creation of a CNY vs. USD forwards market.

Alternative :

A currency option gives the right to buy or sell a specific amount of a currency at a fixed price at any time until the expiration of the specified maturity date (the other party -- seller of the option -- must sell or buy at the discretion of the owner, who in turn has no obligation to actually exercise his right).

Example: You will receive a foreign currency payment on an uncertain date in the next month. To eliminate any risk (of the foreign currency depreciating), you buy a put option that allows you to sell the currency at the fixed rate at any time during the month. In case you need to make a payment you buy a call option.

# Demand for foreign currency assets

## The financial account approach

Quotation convention: In the following we will always use the uncertainty quotation (= KO) -> we will always put the national currency in the numerator.

Central idea:

The foreign exchange market is in equilibrium when all assets denominated in all currencies offer the same expected rate of return (non-arbitrage).

${\textstyle E}$, the exchange rate, reflects the price of a (foreign) asset. Asset = transfer of purchasing power in the future. Its current price depends on the anticipation of its future price.

Rating : ${\displaystyle E^{e}}$ = anticipated exchange rate (expected, expected). e.g: ${\displaystyle E^{e}=1.25CHF/USD}$, ${\displaystyle E=1.20CHF/USD}$ -> anticipated appreciation of the USD.

Is it necessary to invest in CHF or in foreign currencies? Capital ${\displaystyle C_{0}}$ (en CHF) -> choice:

• If we place ${\displaystyle C_{0}}$ in CHF -> interest rate ${\displaystyle R}$
• If we place${\displaystyle C_{0}}$ in USD -> interest rate ${\displaystyle R^{*}}$

But this information is not enough to make a comparison between the two investments -> calculation of the expected return

## Expected rate of return

Wealth is held in various forms of assets and transfers purchasing power in the future the desirability of an asset will depend on its rate of return, but the rate of return is rarely known (e.g. the dividend associated with a share might be known, but the value of the security changes over time).

The expected real rate of return is the expected nominal rate of return deflated by a price index. As assets are held in different currencies, they must be expressed in the same currency in order to be comparable.

Other things being equal (which is rarely the case), investors prefer to hold assets with a higher expected real rate of return.

Two other criteria influence the choice of an asset:

• Risk (savers prefer assets with little uncertainty).
• Liquidity (savers prefer more liquid assets).

Hypothesis for the rest: comparable risk and liquidity between securities => we focus on the differences in expected real return, which are closely related to the differences in interest rates between different currencies.

## Interest rates

Interest rates on different currencies are usually different because they depend on national conditions. On the other hand, when two countries adopt the same currency, such as France and Germany in 1999, interest rates converge and then equalise. (... Is this still true today?)

## Expected return on a foreign currency investment (${\displaystyle RA^{*}}$)

Hp: the expected return is the only criterion (risk and liquidity are not taken into account).

Investment in USD → 3 transactions:

• USD purchase in ${\displaystyle t=0}$${\displaystyle {\frac {C_{0}}{E}}}$ [USD]
• USD investment → ${\displaystyle {\frac {C_{0}}{E}}1+R^{*}}$ [USD]
• sale USD in ${\displaystyle t=1}$${\displaystyle E^{e}{\frac {C_{0}}{E}}1+R^{*}}$ [CHF]

Anticipated return on USD :

${\displaystyle RA^{*}={\frac {C_{0}(1+R^{*}){\frac {E^{*}}{E}}-C_{0}}{C_{0}}}=(1+R^{*}){\frac {E^{e}}{E}}-1=R^{*}{\frac {E^{e}}{E}}+{\hat {E}}^{e}}$

where ${\displaystyle {\hat {E}}^{e}\equiv {\frac {E^{e}}{E}}-1={\frac {E^{e}-E}{E}}}$

is the anticipated depreciation rate of the CHF.

=> ${\displaystyle RA^{*}=R^{*}({\hat {E}}^{e}+1)+{\hat {E}}^{e}=R^{*}+{\hat {E}}^{e}+R^{*}\times {\hat {E}}^{e}}$

## Approximation

If ${\displaystyle R^{*}}$ and ${\displaystyle {\hat {E}}^{e}}$ are low enough, their product can be neglected (e.g: ${\displaystyle R^{*}=0.5}$% and ${\displaystyle {\hat {E}}^{e}=0.2}$% => ${\displaystyle R^{*}\times {\hat {E}}^{e}=0.001}$%) → rule of thumb.

The expected return on the USD then becomes, approximately :

${\displaystyle RA^{*}=R^{*}+{\hat {E}}^{e}\equiv R^{*}+{\frac {E^{e}-E}{E}}}$

Intuition : ${\displaystyle RA^{*}\cong interest+gain\ (loss)\ of\ change}$. If a depreciation (appreciation) of the national currency is anticipated in the future, this means that when the USD is converted into CHF (at the end of the investment period), a foreign exchange gain (loss) is expected.

On what depends ${\displaystyle RA^{*}}$? Three determinants...

## Variation of E

How is it evolving ${\displaystyle RA^{*}}$ when ${\displaystyle E}$ varies ?

→ Example (table 14.4 of KO) with ${\displaystyle R^{*}=6}$%, ${\displaystyle E=1.0}$ and ${\displaystyle E^{e}=0.95}$ : the more ${\displaystyle E}$ is low ceteris paribus, the more the ${\displaystyle RA^{*}}$ is high. Intuition: the cheaper the currency, the higher the expected return on that currency, all other things being equal.

${\displaystyle R^{*}+{\hat {E}}^{e}=0.06+{\frac {0.95-1.0}{1.0}}=0.06-0.05=0.01}$

If ${\displaystyle E^{e}}$ remains unchanged, as ${\displaystyle E}$ depreciate (appreciation of EUR), the rate of anticipated depreciation increases as well as the ${\displaystyle RA^{*}}$:

An appreciation today of the national currency at an anticipated exchange rate (${\displaystyle E^{e}}$) which remains constant implies an expectation of a larger future foreign exchange gain (or a smaller foreign exchange loss) as the expected depreciation margin increases (or the margin of appreciation decreases).

Negative relationship between ${\displaystyle E}$ and ${\displaystyle RA^{*}}$. All other things being equal, an appreciation of the national currency (here CHF) increases the AR of a foreign currency investment (here USD).

## Influence of ${\displaystyle E}$ on ${\displaystyle RA^{*}}$

So, in general, if we see today a...

• Appreciation of national currency (${\displaystyle E}$↘) ${\displaystyle RA^{*}}$↗ (exchange gain)
• Depreciation of national currency (${\displaystyle E}$↗) ${\displaystyle RA^{*}}$↘ (loss on exchange)

The curve describes the evolution of ${\displaystyle RA^{*}}$ as a function of ${\displaystyle E}$

## Influence of ${\displaystyle E^{e}}$ (and ${\displaystyle R^{*}}$) on ${\displaystyle RA^{*}}$

If we're expecting a...

• (${\displaystyle E^{e}}$↘) => ${\displaystyle RA^{*}}$↘ (exchange rate loss)
• Depreciation of national currency (${\displaystyle E^{e}}$) => ${\displaystyle RA^{*}}$ (exchange rate gain)
-> in this case: displacement of the whole curve (idem if ${\displaystyle \Delta R^{*}}$)
Erreur lors de la création de la vignette : Fichier manquant

# Balance in the foreign exchange market: ${\displaystyle PTI_{NC}}$

## Equilibrium condition: ${\displaystyle PTI_{NC}}$

Assumptions: The agents share the same expectations (${\displaystyle E^{e}}$) and face the same interest rates ${\displaystyle R=R_{0}}$ and ${\displaystyle R^{*}=R_{0}^{*}}$ exogenous. In the event of an imbalance in the foreign exchange market, it is the spot exchange rate, E, that adjusts.

Intuition: ${\displaystyle E}$ will vary until there is no longer any incentive to change the portfolio allocation between the two currencies = when the expected returns on the two currencies become equal.

Rating: ED: excess demand; ES: excess supply.

• If ${\displaystyle R_{0} => ${\displaystyle E}$↗ => ${\displaystyle {\hat {E}}^{e}}$↘ => ${\displaystyle RA^{*}}$↘ = narrows the gap ${\displaystyle RA^{*}-R_{0}}$
• If ${\displaystyle R_{0}>RA^{*}=R_{0}^{*}+{\hat {E}}^{e}:ES_{currency}}$ => ${\displaystyle E}$↘ => ${\displaystyle {\hat {E}}^{e}}$↗ => ${\displaystyle RA^{*}}$↗ = narrows the gap ${\displaystyle R_{0}-RA^{*}}$

Equilibrium for the investor corresponds to a situation of "non-arbitrage" when:

${\displaystyle R=RA^{*}=R*+{\hat {E}}^{e}=R^{*}+{\frac {E^{e}-E}{E}}}$ [1]

= unhedged interest rate parity relationship (${\displaystyle PTI_{N}C}$), which corresponds to the equilibrium of the foreign exchange market (${\displaystyle E}$ adjusts). This relationship gives us a model for determining the spot exchange rate. If we know the interest rate differential and the expected exchange rate we know the spot exchange rate.

## Graphical representation of the balance

If ${\displaystyle R=R_{0}}$, the only value of ${\displaystyle E}$ that satisfies the condition ${\displaystyle R_{0}=RA^{*}}$ is the one that lies vertical to ${\displaystyle R_{0}}$ on the curve ${\displaystyle RA^{*}(E)}$. Any other value of ${\displaystyle E}$ below or above this curve will lead to an immediate fit of ${\displaystyle E}$ and a return to the curve ${\displaystyle RA^{*}(E)}$ => equilibrium condition :

${\displaystyle R=R^{*}+{\frac {E^{e}-E}{E}}=RA^{*}(E_{-},R_{+}^{*},E_{+}^{e})}$

The curve ${\displaystyle RA^{*}(E,...)}$, describes the couples (${\displaystyle R}$, ${\displaystyle E}$) that satisfy the condition of no shading (= ${\displaystyle PTI_{nc}}$).

## Comparative static: increase in R

An increase in the domestic interest rate makes domestic assets more attractive, leading to excess demand for the domestic currency (= ${\displaystyle ES_{currencies}}$) => appreciation of the domestic currency (${\displaystyle E}$↘)

## Comparative static: increase of ${\displaystyle E^{e}}$

Anticipation that the national currency will depreciate leads agents to reallocate their wealth on foreign currency investments => ${\displaystyle ED_{currencies}}$ => the national currency depreciates (${\displaystyle E}$↗)

## Comparative static: increase of ${\displaystyle R^{*}}$

Foreign assets become more attractive => agents will increase their demand for foreign assets => ${\displaystyle ED_{currencies}}$ => Domestic currency depreciates (${\displaystyle E}$↗)

Erreur lors de la création de la vignette : Fichier manquant

## Summary of the ${\displaystyle PTI_{NC}}$

Determines the value of E that satisfies the non-arbitration condition. All points along the curve are equilibrium points.

But: on what depends ${\displaystyle R}$, ${\displaystyle R^{*}}$, ${\displaystyle E^{e}}$? chap.12-15.

## Continuation...

The model based on the unhedged interest rate parity represents a first step in determining the exchange rate. We now have to complete it by developing a theory of interest rate formation and expectations.

rNB: ${\displaystyle i_{\}=R}$ and ${\displaystyle i_{\mathrm {\euro} }=R^{*}}$ in our rating (Source: Feenstra-Taylor).

# Empirical verifications

## Checking the ${\displaystyle PTI_{NC}}$: perfect expectations

The condition of ${\displaystyle PTI_{NC}}$ is particularly interesting for forecasting purposes. Under the assumption of perfect expectations (${\displaystyle {\hat {E}}^{e}={\hat {E}}}$), the differential ${\displaystyle R-R^{*}}$ could be used as a prediction of ${\displaystyle {\hat {E}}}$.

Basic idea: if the assumptions underlying the ${\displaystyle PTI_{NC}}$ (in particular risk neutrality) are correct and the agents are rational (ie. use all available information and do not make systematic errors), the effective depreciation rate of the national currency, <should be equal to the expected rate of depreciation ${\displaystyle {\hat {E}}^{e}={\frac {E_{t+1}^{e}-E_{t}}{E_{t}}}}$, (equal to ${\displaystyle R-R^{*}}$ according to the ${\displaystyle PTI_{NC}}$) plus "white noise": ${\displaystyle {\hat {E}}=R-R^{*}+u}$, where ${\displaystyle u}$ is a prediction error of null mathematical expectation.

However, in reality the ${\displaystyle PTI_{NC}}$ is very poorly verified, both in terms of the magnitude of the variations and in terms of their direction.

## Foreign exchange market efficiency

How to interpret this? => foreign exchange market not efficient? If there is a systematic bias in forecasts -> test of market "efficiency", an efficient market is defined as a market where participants are risk neutral and form their expectations in a rational manner [they take into account all the information available to them rather than basing their predictions solely on the past (adaptive expectations)].

If markets are efficient, at any point in time the prices of currencies, or equities, are correctly valued (no over- or underestimation) and price movements will follow a random path.

Econometric tests have shown that markets are not efficient in this sense.

Three possible explanations :

1. role of the risk premium (${\displaystyle \rho }$): ${\displaystyle R+\rho =R^{*}+{\hat {E}}^{e}}$
2. Role of unpredictable events ( news )
3. rationality of investors limited?

Risk premium: in this case the forecast bias would come from omitted variables that are to be modeled.

It is likely that the role of "news" (unanticipated events) is a major cause of changes in exchange rate values.

Participants could make systematic errors despite their rationality and learn about market behaviour through a learning process (adaptive expectations) based on the past → unrealistic expectations of future prices (at the origin of the real estate bubble and the last financial crisis).

# Summary

The financial account approach focuses on the BOP FC as a determinant of the exchange rate (particularly relevant from the 1970s onwards with the gradual liberalisation of the capital market and the growing importance of transaction volumes in the asset market).

There are two exchange rate quotations: the uncertain quotation (= domestic currency units per foreign currency unit) and the certain quotation (foreign currency units per domestic currency unit).

Investment decisions depend (among other things) on the rate of return on assets

The expected rate of return on a foreign currency investment depends on the foreign interest rate and expectations of foreign exchange gains (or losses).

The asset market is in equilibrium when the uncovered interest rate parity condition is verified (${\displaystyle PTI_{NC}}$)

The spot exchange rate adjusts to ensure equilibrium in the asset market => the ${\displaystyle PTI_{NC}}$ can be used to make predictions about the evolution of the exchange rate

A rise in the foreign interest rate, an expected depreciation of the domestic currency or a fall in the domestic interest rate causes an increase in the exchange rate (= depreciation of the domestic currency).