The material in this blog post is useful to the candidates preparing for: Level I of CFA Exams.
This reading is an introduction to currency exchange rates. Understanding basics for exchange rates is important for many readings in all levels of the CFA exam.
In terms of size and daily turnover, the FX market is the largest market. It operates 24 hours a day. The market facilities international trade since the economy is becoming increasingly international. FX market is also important because it affects portfolio performance with many portfolios becoming globally diversified in nature. For investors who experience no home bias (i.e. home bias is the tendency for investors to invest domestically), portfolio performance is affected by exchange rates. For those who experience home bias, portfolio performance is still affected by FX market because most large domestic companies are expanding internationally.
The FX Market:
To understand FX market, it is necessary to become familiar with conventions. Currencies are referred to by standardized three letter codes using International Organization for Standardization (IOS). For a list of IOS codes, check the following page: ISO 4217 Currency Codes
It is important to understand that there is a difference between individual currency and exchange rate. Whereby individual currencies are singular, exchange rates refer to the price of one currency in terms of another currency. Exchange rate refers to the number of units of one currency (i.e. pricing currency) that one unit of another currency will buy (i.e. base currency)
To avoid confusion, this reading will identify exchange rate using convention (A/B) referring to number of units of currency A (pricing currency) that one unit of currency B will buy (base currency). For example, x USD/EUR means that one euro (base currency) will buy x dollars (price currency):
- Decrease in x USD/EUR means that dollar is appreciating and euro is depreciating (fewer dollars are needed to buy euro – or the euro costs less)
- Increase in x USD/EUR means that dollar is depreciating and euro is appreciating (more dollars are needed to buy euro – or the euro costs more)
Real v.s. Nominal Exchange Rates
The exchange rate that was just described refers to nominal exchange rate. The real exchange rate is a rate developed by economists to assess changes in relative purchasing power of one currency to another.
Purchasing power parity (PPP): The proposition that the same goods should cost the same amount in different countries once we have factored in the current exchange rate. In practice, differences in transportation costs and other factors mean that the relationship does not hold exactly. More importantly than exact parity in the prices of goods, purchasing power parity implies that changes in the price levels in the two countries should be reflected in changes in the exchange rate (relative version of PPP).
In practice, the conditions required to enforce PPP are not satisfied: goods are not identical globally, many goods and services are not traded internationally, capital flows are at least as important as trade flows in determining nominal exchange rates. Therefore, there are deviations in nominal exchange rates from those determined by PPP. A simple example of cross-country comparison of purchasing power is the big mac index published by the economist; to find out about it, check the following page: big mac index.
We can now determine that the price of domestic currency should be related to the exchange rate and the price of foreign currency via the relation:
This can be rewritten as
Where SD/F is quoted directly (will be explained later). In order to determine changes instead of levels:
If the real exchange rate increases, this means that the purchasing power has declined by that percentage. It is important to remember that real rates are not quoted or traded on global FX markets – they are simply indices used to measure international competitiveness of market.
To illustrate the concepts we discussed so far, let’s assume that a Japanese investor is holding long-term bonds in USD (dollars). The investor visits the states often and would like to know how these bonds affect her portfolio performance and purchasing power in terms of her domestic money (for her expenses in Japan) and in terms of dollars (for whenever she visits the united states). To examine the effects of changes in nominal rates, then:
- Everything else hold constant, an increase in nominal JPY/USD will lead to increase JPY-dominated value of her bond investments
- Everything else hold constant, a decrease in nominal JPY/USD will lead to decrease JPY-dominated value of her bond investments
Note that changes in nominal exchange rate will not affect the purchasing power for the U.S. trips. That is, because the investor uses money from its bond investments to pay for U.S. trips, the value of exchange rate will have no effect on purchasing power (i.e. paying U.S. dollars out of US-dominated bonds)
To examine the effects of changes in nominal rates on purchasing power, then:
- Everything else hold constant, an increase in nominal JPY/USD will lead to increase in real exchange rate (JPY/USD) and thereby decrease the relative purchasing power of the Japanese investor.
- Everything else hold constant, a decrease in nominal JPY/USD will lead to decrease in real exchange rate (JPY/USD) and thereby increase the relative purchasing power of the Japanese investor.
Finally, to examine the impacts of inflation rates (changes in price levels), then:
- Everything else hold constant, an increase in Japanese inflation rate will lead to decrease in real exchange rate (JPY/USD) and thereby increase the relative purchasing power of the Japanese investor.
- Everything else hold constant, a decrease in Japanese inflation rate will lead to decrease in real exchange rate (JPY/USD) and thereby decrease the relative purchasing power of the Japanese investor.
FX markets facilitate international trade – however, the larger portion of daily turnover in FX markets is accounted by capital transactions where investors convert between currencies for purpose of moving funds into and out of foreign assets.
FX market participants are exposed to the risk that rates will move in unfavorable directions. Hedgers, thus, use derivatives to reduce the risk that they face from potential future movements in a market variable. On the other end, speculators use them to be on the future direction of a market variable.
FX markets provide variety of products:
- Spot transactions: exchange of currencies for immediate delivery. For most currencies, this is ‘T+2’ delivery which means exchange is settled within two business days – this is the rate that most people refer to in their daily lives
- Forward transactions: only minority of transactions are spot; the majority of transactions in FX markets fall in forward market. Those are agreements to deliver foreign exchange at future date at a rate agreed upon today. Each of these contracts requires two identifications: (1) the date at which currencies are to be exchanged and (2) the exchange rate to be applied on that date.
Dealers typically quote forward rates for variety of forward settlement dates. In OTC markets, however, traders can arrange forward settlement at any future date they agree upon. In OTC markets, size can be any size agreed upon. Note that:
- The longer the term to maturity, the lower the liquidity of forward trade
- The larger the size of trade, the lower the liquidity of forward trade
Because forward contracts eventually expire, existing speculative positions or FX hedges that need to be extended must be rolled prior to settlement dates. This typically involves a spot transaction to offset (settle) the expiring forward contract and new one at more distant date – referred to as FX swap (different than currency swap). FX swaps are covered in level II in detail; for the purpose of this level, we need to know that FX swap consists of simultaneous spots and forward transactions, that swap transactions extend (roll) an existing forward position to new date, that rolling the position forward leads to cash flow on settlement day.
FX swaps are often used by market participants as funding source (i.e. swap funding). Consider the case of German-based firm that needs to borrow 1 million euros for a year. It could borrow million euros for a year in euro-dominated money. Another alternative is to borrow in US dollars, convert at exchange rate and then sell euros to convert the proceeds in a year at the forward rate.
Continuing with the illustration made in earlier section, assume that the Japanese investor is worried about the foreign investment in the States (in particular, she is worried about foreign exchange risk). If she has a one-year time horizon for her investment, then the exchange rate risk that the USD-dominated bonds faces is determined by the uncertainty over the JPY/USD spot rate one year from now. To reduce this risk, her investment manager advises her of the possibility of using forward contracts. In particular, she would need to sell USD forward.
FX markets participants can be broadly divided into two categories: sell-side (generally large FX trading banks) and buy-side (those who use banks to undertake FX transactions).
Buy side can be broken into several categories:
- Corporate accounts: corporations of all sizes engage in FX transactions (either for trade purposes, financing, or events like M&A)
- Real money accounts: investment funds managed by insurance companies and other institutional investors
- Leverage accounts: consist of hedge funds, commodity trading advisors, and trading desks (use FX trading for profit) – hedge fund managers represent most of the daily turnover
- Retail accounts: simplest example is foreign tourist exchange currency at airport kiosk. As electronic trading reduced barrier to entry into FX markets, individuals are now trading for their own accounts for speculative purposes
- Governments: public entities of all type have FX needs (i.e. maintaining military bases overseas)
- Central banks: they intervene with FX markets to influence either level or trend in exchange rates
Sell side can be broken into several categories:
- Large and growing proportion of daily turnover is accounted by largest dealing banks (Deutsche, Citigroup, UBS, HSBC)
- All other banks fall into second and third tier of FX market – many of these financial institutions are regional or local banks that lack economies of scale or global client base
What is important to notice from above is that there is an extremely wide variety of FX market participants which reflect a complex mix of trading motives and strategies that can vary with time.
Market Size and Composition
Statistics are not immediately available for an OTC market; the BIS Triennial Survey provides a comprehensive source of information on the size and structure of the FX market worldwide cooperative effort coordinated by the Bank for International Settlements (BIS) every three years. The last survey, in December 2010, carried out by 53 central banks and monetary authorities
Global FX turnover as of April 2010
- Average daily turnover is $4 trillion
- Significant increase in FX activity compared to 2007 (20% at current exchange rates)
- London is the most active trading centre (37% of total turnover), followed by New York (18%), Tokyo (6%), and Singapore (5%).
The graph below shows FX turnover by instruments. The largest portion of transaction as explained earlier is by swaps
The graph below shows FX flows by counterparty. It is important to note that the use of FX transactions by financial clients have exceeded interbank for the first time in the history.
The graph below shows the top five currency pairs in terms of their percentage share of average daily global FX turnover:
Currency Exchange Rates
Direct and Indirect Quotes
As mentioned, exchange rates represent the price of one currency in terms of the other and it can be expressed as:
- Currency A buys how many units of B
- Currency B buys how many units of B
It is obvious that the two prices are the inverse of each other.
A direct quote takes the domestic currency as the price currency and foreign currency as the base currency. For example, for a Paris-based investor, EUR/GBP would be a direct quote because EUR (the domestic currency) is the price currency and GBP (the foreign currency) is the base currency. An exchange rate of 1.2225 EUR/GBP means than 1 GBP costs 1.2225 Euros.
An indirect quote takes the domestic currency as the base currency and foreign currency as the price currency. For example, for a Paris-based investor, GBP/EUR would be an indirect quote because EUR (the domestic currency) is the base currency and GBP (the foreign currency) is the price currency. An exchange rate of 0.8180 GBP/EUR means than 1 EUR costs 0.8180 GBP.
Again, it is obvious that the two rates are the inverse (reciprocal) of each other.
- Note: The reading in the CFA curriculum describes conventions used in the market for major currencies, such as the quote convention, the name of it, how it is quoted and others. Refer to the original reading for more information
An important concept here is that quotes are two-sided prices. When client asks for quotes:
- Dealer will provide the bid – the price at which the bank is willing to buy the currency
- Dealer will provide the ask (or offer) – the price at which the bank is willing to sell the currency
Note that ask price is always higher than bid price – makes sense?
This is similar to what happens in most markets; however, there are two currencies involved here so which one is being bought and which one is being sold?
Let’s go back to basics now. The two-sided price is quoted by dealer in terms of BASE currency. That is, it shows the number of units of price currency that the client will receive from dealer for one unit of base currency (if at bid) or the number of units of price currency that the client will give to the dealer for one unit of base currency (if at ask/offer)
Banks and other dealers generally do not charge commissions on foreign currency transactions. Instead, they make their profit from the bid-ask spread. Unless it is provided that you are a market-maker, you are a market-taker. That is, you buy at the “ask” and sell at the “bid.”
To convert bid-ask from one convention to another you need to do the following:
- Inverse the bid and it will be ask price in the new quotation
- Inverse the ask and it will be bid price in the new quotation
Report the bid (#2) before the ask (#1)
For example, if X/Y has a bid-ask quote of 4 ~ 5 then the Y/X bid-ask quote of 0.20 ~ 0.25
Note that for the most part of level I, the reading is focused on single number (quote) without paying much attention to bid-ask quotes.
Appreciation and Depreciation
Regardless of the convention used, changes in rates can be expressed as percentages of appreciation or depreciation of one currency against the other. What matters here is to know which currency is being used as price currency and which is being used as base currency.
If the current 1.28 USD/EUR changes to 1.33 USD/EUR then we can express the percentage change as: 1.33/1.28 – 1 = 3.9%. In this case, we say that the euro has appreciated by 4% against US dollar.
- Note: appreciation/depreciation is always calculated with reference to the base currency. Don’t get it confused.
If we want to find by how much the US depreciated against the Euro, we need to convert USD/EUR to EUR/USD and therefore: (1/1.33)/(1/1.28) – 1 = -3.76% which means the US dollar has depreciated by 3.76% against the Euro.
- Note: there will always be difference between by how much X appreciated against Y and by how much Y depreciated against X. This is simply a matter of arithmetic.
Given two exchanges that involve three currencies, it is possible to find the cross-rate. That is, given A/B and B/C we can always find what A/C will be – This is simple math:
If you were given B/A and B/C and you were asked to find what A/C is, then applying simple mathematics:
If the cross-rate is not consistent with the actual market rate, then the market will arbitrage mispricing. This arbitrage is referred to by triangular arbitrage which would continue until mispricing is eliminated.
For example, assume you are given 3 quotes: A/B, B/C and A/C. The first step here would be to calculate what would A/C cross-rate be using A/B * B/C; then, we should compare the cross-rate with the quoted rate. If and only if there is discrepancy between the quoted rate and the cross-over rate, then arbitrage is possible and we apply the chain rule method to find it:
- Convert 1 unit of A to B and then B to C and then C to A – if the result is greater than 1, then there is profit from implementing this strategy. If the result is lower than 1, then:
- Convert 1 unit of A to C and then C to B and then B to A – there will be profit for sure.
In FX markets, forward rates are typically quotes in terms of points (referred to as pips). These points are simply the difference between forward exchange rate quote and spot exchange rate quote and they are scaled so that they can be related to the last decimal in the spot quote:
- When forward rate is higher than spot rate, the BASE currency is trading at forward premium
- When forward rate is lower than spot rate, the BASE currency is trading at discount
Typically, quotes for forward rates are shown as number of forward points at each maturity. They are also called swap points because FX swap consists of spot and forward transactions. For example, if you are given the following table:
|Maturity||Spot Rate/Forward Points|
To find the three-month forward rate, we then find:
Occasionally, one will see the forward rate represented as percentage of spot rate rather than number of points. In order to convert spot quote into forward quote when points are shown as percentage, we multiply spot rate by one plus percentage of premium or discount. For the previous example, the three-month forward discount is -0.045% and therefore:
Interest Rate Parity
The proposition that exchange rates must change so that the return on investments with identical risk will be the same in any currency. It holds when any forward premium or discount just offsets differences in interest rates so that investor will earn the same return investing in either currency.
No matter what the quotation is, the currency with the higher (lower) nominal interest rate will be selling at a forward discount (premium) relative to the other when interest rate parity holds. When currencies are freely traded and forward contracts are available in the marketplace, interest rate parity must hold. If it does not hold, arbitrage trading will take place until interest rate parity holds with respect to the forward exchange rate. Such arbitrage is referred to as covered interest arbitrage: borrowing one currency, exchanging it for the other, investing it, and entering into a forward contract to convert the proceeds at the end of the loan period back into the borrowed currency.
Therefore, expressing forward in terms of forward pips or points:
If we assume that investment horizon is fraction (τ) of the period for which interest rates are quoted.
From previous formulae:
- The increase in number of points is approximately proportional to the increase in term of the contract (maturity)
- The increase in number of points is proportional to the increase in interest rate differential (i.e. interest rate spread)
- Note: the reading in the CFA curriculum has two more sections that I don’t cover here: currency regimes and trade balances (Marshall–Lerner condition and absorption method) – Refer to the original reading for those sections