## Exchange rates

### Types

• Bilateral exchange rate: The relative price of one currency in terms of another currency. How much one currency is worth in another currency.
• Nominal exchange rate (S): A bilateral exchange rate not adjusted for inflation. The most commonly used form that is actively traded in markets. Can be written in two ways:
• Direct (price) quotation: S = (units of domestic currency) / (1 unit of foreign currency)
• Most common form, e.g: S = 9.2371 SEK / €. We can exchange 9.2371 SEK for 1 €.
• Indirect (quantity) quotation: S = (1 unit of domestic currency) / (units of foreign currency)
• Real exchange rate (s): The nominal bilateral exchange rate adjusted for relative price changes (inflation) within the two countries. Because it adjusts for inflation, it's a better predictor of changes in trade and investor flows between countries, and can move in a different direction than the nominal exchange rates.
• s = S(P*/P)
• S = Nominal (bilateral) exchange rate
• P = Domestic price level (consumer price index)
• P* = Foreign price level (consumer price index)
• Cross rate (Scc): A bilateral exchange rate calculated from two other bilateral exchange rates. Useful when lacking sufficient data to calculate a certain bilateral exchange rate. Could also be referred to as a "no arbitrage" rate because it excludes arbitrage.
• Scc = S1 / S2
• Example:
• S1 = 9.2145 SEK / €
• S2 = 14.9136 SEK / £
• Scc = (9.2145 SEK / €) / (14.9136 SEK / £) = 0.6183 £ / €
• Effective (or multilateral) exchange rate: The relative price of one currency in terms of two or more currencies. Measures one currency compared to a group or "basket" of many other currencies, typically the heavy trading partners of the country in question that are near geographically. An average exchange rate against many currencies. Useful because they capture the overall strength or weakness of a currency over time.

### Terms

• A currency appreciates: Increases in value (compared to other currencies). E.g: If we get fewer SEK per €, this means SEK appreciates against the € (or the € depreciates against the SEK)
• A currency depreciates: Decreases in value (compared to other currencies). E.g: If we get more SEK per €, this means SEK depreciates against the € (or the € appreciates against the SEK)
• Arbitrage: Exploiting price differences to make a profit. Speculation. E.g. buy in one market where price is low, and sell in another market where the price is higher. Buy at low price, sell at high price.
• Triangular arbitrage: Exploiting price differences in three markets. E.g. three exchange rates: S1 = 1 SEK / €, S2 = 1 SEK / £ and S3 = 2 € / £. If you have 1 SEK, you go to the second market, convert it into 1 £, go to the third market and convert into 2 €, then convert back into 2 SEK. You start with 1 SEK, end up with 2 SEK. As long as there exists a price difference somewhere, it can be exploited for profit.
• Spot market: The currency market that trades with immediate effect
• Forward market: The currency market that trades with future effect. A forward contract obligates the parties to trade at a specific exchange rate at a future date, such as 1 month or 1 year in the future. You can take two positions:
• "Long" position / Longing / Going long: Buying a currency at a future date at a specific exchange rate
• "Short" position: Selling a currency at a future date at a specific exchange rate
• Hedge/hedging: Reducing or eliminating a risk. Example: You can buy a forward contract to hedge a second contract that depends on a certain exchange rate to be profitable.

A theory stating that in the long-run, exchange rates should only reflect differences in price levels, so that identical goods cost the same regardless of where you buy them (the law of one price).

Law of one price: "In an efficient market all identical goods must have only one price". You should be able to buy the same goods for the same relative price regardless of in which market or in what currency you buy them.

Conditions:
• Absolute PPP condition: The relation between domestic prices (P), foreign prices (P*) and the nominal exchange rate (S), assuming that the law of one price holds.
• P = SP*
• Rewritten as: S = P/P*
• Relative PPP condition: The relation between changes in domestic and foreign price levels (ΔP and ΔP* - inflation rates expressed in percentage) and changes in the nominal exchange rate (ΔS), assuming that the law of one price holds. While Absolute PPP focuses on absolute price levels at certain points of time, Relative PPP focuses on changes in price levels. If Absolute PPP holds, then Relative PPP must hold as well. However, if Relative PPP holds, Absolute PPP doesn't necessarily hold. This makes Absolute PPP a stronger condition.
• ΔP = ΔS + ΔP*
• Rewritten as: ΔS = ΔP - ΔP*
Real world:
Holds decently in the long run but fails in the short run.

### Forward currency markets

In opposite to spot currency markets (where transactions happen immediately), in forward currency markets, people want to exchange currencies at a future date. They sign a forward contract which obligates them to transact on this future date at a specific exchange rate.

The use of forward markets is to eliminate foreign exchange risk, i.e. the risk that the nominal exchange rate will change (ΔS changes).

Covered Interest Parity Condition (CIPC)
R-R* ≈ (F-S)/S
R = Interest rate on domestic bonds
R* = Interest rate on domestic bonds
F = Forward exchange rate
S = Spot exchange rate

Can be rewritten as:
R ≈ R* + (F-S)/S
R ≈ (return on the foreign asset) + (return on the foreign currency)
• If R > R* + (F-S)/S, then the total return on domestic investment is greater, and it's only interesting to invest domestically
• If R < R* + (F-S)/S, domestic companies will invest in the foreign assets
• If R = R* + (F-S)/S, then the domestic company is indifferent between domestic or foreign assets