Investment Implications from Global Events

The goal of today’s lecture is twofold. First, I want to introduce to you some quote conventions used in the foreign exchange or Forex markets. Second, I want to introduce and apply the simple notion of no-arbitrage to arrive at a relationship between exchange rates and domestic and foreign interest rates around the world. I will go over many examples of how arbitrage can take place in the foreign exchange markets. However, for now, you should think of no arbitrage to mean that there is no way to make money or create lottery tickets from nothing or no initial investments. Free lottery tickets means there is a chance to make money, but if you pay nothing for it, then if you buy infinite amounts of lottery tickets, there is a guarantee that you can make money from nothing.

So, why is it important to study foreign exchange rates? We have already studied a bit about the implications of certain central banking actions on foreign exchange rates under the gold standard. However, in the more modern era, most exchange rates are free floating and many government and central banking actions can have a significant impact of its currency value. Let’s go over some examples and think about its impact on country’s economy and therefore its exchange rates.

Let us look at the first bullet point. What is a fiscal cliff? A fiscal cliff is when the government decides to increase taxes while decrease spending. All else equal, the country will inevitably contract since the government is spending less and unemployment may increase since corporations may cut jobs since more resources are now allocated to pay for higher taxes rather than to make investments. Contraction means lower consumption, which means there is less demand for the domestic currency. This essentially means people are selling the domestic currencies for other things such as bonds and we will most likely see a depreciation in the domestic currencies.

QE is quantitative easing. QE is basically printing money from the central bank and using that money to buy back government debt and potentially other financial assets. In addition to buying back government securities, the Federal Reserve of the U.S. purchased a lot of mortgage-backed securities during the financial crisis. Similarly, Japan has recently been printing money to buy domestic stocks. The point of this monetary policy action is to stimulate the economy, but it also has depreciative side-effects on the domestic currency. For example, the central bank can print money, use that money to buy to bonds, this will bid up the prices of bonds and lower the yield or interest rate. This lowered interest rate makes U.S. debt less attractive and people may sell the domestic currency for other currencies and seek higher interest rate returns elsewhere.

Earthquakes in Japan, economic slowdowns in China, and turmoil in the middle east have similar depreciative effects as mentioned above. The goal is to build a full economic model so that we understand how broad macroeconomic activities and affect exchange rates and vice versa.

Institutional Details

In the international currency market, there are two main components. The first component is the worldwide forex market, which is for banks and large financial institutions that need to make large transactions. This is an OTC market, meaning there is no central clearing house. All trades are done between ad hoc. The retail market is for private investors and corporations and transactions are done through local banks.

Quote Conventions

In general, there is seniority for quoting conventions based on history, but for our purposes, it’s not that important. Not surprisingly, the british pound has been around the longest so they are often quoted first. Euro comes second, and then the USD. Additionally, because of their seniority, they are often designated as “vehicle currencies”. Therefore, you don’t need N(N-1)/2 exchange rates. You can have much less if you convert to USD first, for example, and then convert USD to other currencies. For example, there is no exchange rate quote between South Korean Won and the Brazilian Real. One way to convert KRW to BRL is to first convert KRW to USD and then convert USD to BRL.

Forex rates are typically quoted at 5 significant digits. For example, the exchange rate to convert JPY to USD could appear as 120.10 and the exchange rate to convert USD to EUR is 1.2515.

Now, let us go over some notations. In this course, I will use only 1 type of notation, but I will talk about the two typical notations that you might see on bloomberg or other trading terminals. The colon or slash notation lists the currency that you want to buy first followed by the currency you plan to use to make the purchase. The currency that you want to buy or trade for is called the “base” currency. For example, EUR:USD notation tells me that the exchange rate listed is going to tell me the price of Euros in terms of USD. The price notation, which is what I will use throughout this course, is that you typically see for goods and services. So, USD/EUR means the price of 1 Euro in terms of U.S. dollars. The base currency is Euros. There are many ways to express foreign exchange quotes in words. In the case where USD/EUR or EUR:USD = 1.25, this is equivalent to saying “1.25 USD per EUR” or “1 EUR buys 1.25 USD” or “The price of 1 EUR in USD is 1.25”. This may be confusing to you at first, but you should just think of currencies like any other commodity. Buying Euros, in this example, is the same as buying corn or oranges.

Base vs. Quote

To reiterate, the base currency is the currency that you want to buy. It is in the denominator of the convention we are going to use in this class. The “quoted” currency is the currency that is to be used to buy or exchange for the base currency. So, when we talk about a particular country, the base currency is going to be the foreign currency and the quote currency is going to be the domestic currency. Again, the numerator is going to be the domestic currency and the denominator is going to be the foreign currency. For example, if we are talking about the U.S., then its exchange rate with Japan, for example, will be quoted as USD/JPY. I am going to hammer this convention into your head because we are going to define our exchange rate model using this convention to avoid confusion in the future. We will revisit this again.

Interpreting Forex Rate Quotes Example

How do I translate the first bullet point in words? First, what is the base currency? What is the currency we are trying to buy? The base currency is USD. The quote currency is therefore EUR. One way to express this is the price of 1 USD is 0.77 EUR.

How do I translate the second bullet point in words? What is the base currency? The base currency is EUR. The quote currency is USD. One way to express this is that I can trade 1 Euro for 1.30 USD.

Forex Rates Conversion Example

Okay, now that you have somewhat of a handle on the exchange rate terminology, let’s practice some unit conversions, just to make sure you truly understand these quote conventions. Suppose The price of a liter of gasoline in France 2012 was 2.00 EUR. What is the price of a gallon of gas in dollars?

2 EUR/1L * (1L/0.26 gallon) * (1.30 USD/EUR) = 10 USD/gallon

Bid-Ask Quotes

Here are some more typical quote conventions used in most markets. The bid price is the price the dealer is willing to buy and the ask price is the price at which the dealer is willing to sell a particular currency. For obvious reasons, the bid price will be lower than the ask price. The spread is the difference between ask and bid price. The midpoint price is the simple average between the bid and ask price.

The major currencies (except the Japanese yen) are traditionally priced to four decimal places, and a pip is one unit of the fourth decimal point. For the yen, a pip is one unit of the second decimal point, because the yen is much closer in value to one hundredth of other major currencies.

For example, If the currency pair of the Euro and the U.S. Dollar (EUR/USD) is trading at an exchange rate of 1.3000 (1 EUR = 1.3 USD) and the rate changes to 1.3010, the price ratio increases by 10 pips.

The Role of Exchange Rates

Let’s start with a fundamental question of exchange rates: why do people want to exchange currencies? From a bank’s or investor perspective, exchanging currencies permits the exchange of financial asset and commodities. If I am a U.S. hedge fund and I want to buy corporate bonds of Hong Kong firms such as Tencent, I can go to the exchange rate and convert my dollars to Hong Kong dollars and use those dollars to buy Tencent corporate debt. Other than financial assets, I could also buy commodities such as oranges or gold. If I am a New Zealand grocery store company and want to sell South African oranges, I can go to the foreign exchange rate and convert my New Zealand dollars to South African Rand and use the Rand to buy oranges and ship it back to my warehouses in New Zealand. In this sense, exchange rates should be determined by by more than one asset. However, the exchange rate should be determined similarly to other asset prices. In finance, the no-arbitrage principle is the key mechanism to determine asset prices just like stocks and bonds. We can value asset when all speculation stops.

The Rate of Exchange Rates: Examples

Let’s go over some examples of how commodities and financial assets can be translated into foreign prices at the exchange rate. For a European car that costs 20,000 EUR can be sold at 25,000 USD at an exchange rate 1.25 USD/EUR (25/20). A British government bond or gilt that costs 100 GBP can be sold for 160 USD at an exchange rate of 1.6 USD/GBP (16/10).

So, if these implied exchange rates were to change, we can it tells us whether the quote currency is getting stronger or weaker. A currency becomes stronger if fewer dollars are needed to buy a foreign currency. A currency depreciates if more dollars are needed to buy foreign currency. Appreciation and depreciation of a currency can therefore be linked to many domestic assets and goods or commodities.

Exchange Rate Changes

Let’s review. Suppose the domestic currency we are discussing is USD. What does appreciation of the USD mean? Firstly, it means that fewer dollars are needed to buy foreign currency. Second, an appreciation means that prices of imports are lower relative to prices of exports. USD becomes stronger relative to other currencies, then the price of foreign goods should be cheaper than the goods that we ship out on average. Under fixed exchange rate regime, an appreciation of the domestic currency through repegging is called revaluation.

What does depreciation of the USD mean? You get the opposite result. If the USD becomes weaker, then more dollars are need to buy foreign currencies. In other words, foreign currency becomes more expensive. Therefore, imports are more expensive than goods to be exported. Under a fixed exchange rate regime, a depreciation of the domestic currency through regging is called devaluation.

Exchange Rate Quotes

To review again, we will be using the price notation or “direct” notation. The numerator or quote currency will be the domestic currency and the denominator or base currency will be the denominator. In this example, what is the price of 1 Euro in term of the domestic currency? The exchange rate is 1.25 USD/EUR. We will define the exchange rate E in this way where the numerator is the domestic currency and the denominator is the foreign currency. Thus, an increase in E means a depreciation. Specially, you will have to pay more for the foreign currency or the foreign currency is more expensive. A decrease in mean means an appreciation. You pay less for the foreign currency or the foreign currency is less expensive. Please only use this convention in this class otherwise it will become very confusing in the future. In our model will will define E in this manner.

The indirect convention is what I described early in this lecture. We would be using this convention in this class.

Foreign Exchange Markets

Let me briefly give you some institutional knowledge about the foreign exchange markets. The foreign exchange markets are highly active with typical daily trade volume exceeding over 1 trillion USD. As a base of comparison, the global stock markets only have an annual trade volume of 60 to 70 trillion USD.

While the players in this market may seem diverse, there are really only a few big players. There’s only about 3000 dealer institutions. Among this 3000, maybe only about 100 to 200 of them might be market makers. Market makers are institutions that match buyer and sellers for a fee. Most of the transactions are actually done by just a handful of institutional types, namely interbank trading between commercial banks and other financial institutions, central banks, and international corporations.

Centers of Foreign Exchange Trading

This chart decomposes the trade volume by country of transaction. The United Kingdom has long been the top center to convert currencies. In the 1980s when Japanese Yen was strong, there was a lot of currency conversion done in Japan. Japan is the red bar. The U.S. is the green bar and has more or less been second to the UK. Singapore is 4th, which makes sense as they the currency of trade in Asia, but that may change soon as China continues to build their military bases in the South China Sea and finishes their one belt one road initiative. Germany or the Euro comes fifth. And Switzerland is sixth, which makes sense. The Swiss franc is known to be a super safe currency.

Vehicle Currencies

We talked about vehicle currencies earlier in this lecture. Note that there is a typo in this graph. It should be 100% not 200%. Despite the UK being the most active in trading currencies, USD has the most convertibility. Almost 50% of global currencies can be converted to USD. The Deutsche Mark, not surprisingly, is the second most converted currency since Germany is the most active in trade in Europe. The dark red bar is the Euro, which appeared after the European Union was established. The Japanese Yen is the third highest converted currency, followed by the British pound.

Key Notions in Foreign Exchange Markets

A few more terminologies and then we will be ready to talk about one way in which foreign exchange rates can be derived. In order to build our first financial model, we will rely on the assumption that forward or futures contracts can be created easily. So, everyone here should know what spot prices are. The spot price of a barrel of oil is the instantaneous price that one can pay to get a barrel of oil. The spot price of an Tencent stock is the current price at which one can buy on the market at this instant. Similarly, the spot exchange rate is the current exchange rate in which I can buy a particular currency. Given this spot rate, I am assuming that I can contract with someone easily to lock in specific price that I wish to pay in the future. For example, suppose the Euro is trading at 1.24 USD and I want to buy 1 Euro in 1 month at 1.24 USD. I am assuming that I can find someone willing to accept 1.24 USD in return for 1 Euro in 1 month. I am assuming that 1.24 USD/EUR is the market agreed upon 1 month forward exchange rate, but it could easily be something else, such as 1.25 or 2. Note that neither me nor the counterparty needs to hold USD or EUR to initiate this contract. So long as we both have EUR and USD in 1 month to make the exchange, everything is good. Forward contracts are essentially side bets on the underlying asset, which is EUR in this case. We will talk more about the forward exchange market more in a later slide.

Our first assumption is that there should only be 1 unique spot price for each currency. If there are more than 1 spot price, then arbitrage is possible. Consider the example listed here. If the exchange rate for USD for GBP is 1.6 in New York but 1.59 USD in London, there’s two ways to do arbitrage:

1. Buy 1 GBP in London for 1.59 USD and sell 1 GBP in New York for 1.60 USD.
2. Buy 1 USD in New York for 0.625 GBP and sell 1 USD in London for 0.62893 GBP.

Remember, our goal is to eventually link foreign exchange rates to the macroeconomy of each country. In order to link exchange rates to economy of each country, we will start by linking countries through banks, specifically through interest rates. We want to conclude that bank deposits of all currencies should offer the same return at all time horizons. If I deposit 1 USD in in a U.S. bank for 1 month, it should give me the same returns as depositing 1 EUR in a European bank for 1 month. If there is no arbitrage, then differences in interest rates must be offset set by appreciation or depreciation of the domestic currency. This must hold for all deposit horizons: 1-month, 2-month, 3-month, 1-year, 5-year, 10-year, etc.

No Arbitrage and Interest Parity Conditions

Another way of saying no arbitrage is that there cannot be a free lunch in market equilibrium. You can make something from nothing. There are basically three things that needs to satisfied in order to have arbitrage:

1. There can be no risk. Specifically, there can’t be future risk or spot risk.
2. There can’t be any net investment. You can’t put up any of your own capital.
3. You must make a profit.

We will go over several examples to make sure you fully understand what arbitrage means.

In this course, there will be using three interest parity conditions. Each new parity that I introduce will have stronger assumptions. Today’s goal is to introduce just the covered interest parity, which must hold in the absence of arbitrage. I will talk about the rest later.

The Forward Exchange Market

The forward exchange market is similar to the spot exchange market. While the spot exchange rate is the rate for immediate exchange of currencies, the forward exchange rate is the rate that you can trade currencies sometime in the future that you lock in today. For example, 30-, 60-, 90-day forward contracts have quoted exchange rates that you can lock in today. It can fluctuate just like spot prices because beliefs about future prices can be updated with new information.

Consider the example of trading USD for JPY. To open the contract, all you need to do is find a counterparty to accept that will accept USD and pay you JPY on a specific date in the future. To close the contract, you simply pay F USD to your contract partner on the future date. F is quoted the same way as E. That is the domestic currency is the numerator and the foreign currency is in the denominator.

Covered Interest Parity: Variables

Let me show you the equation of the covered interest party or CIP first. For now, we will just work in 1 period rates and not continuously compounded rates. Suppose the domestic country is the U.S. and the foreign country is Japan. The left hand side are gains for depositing USD in a U.S. bank. The right hand side is the full return of depositing JPY at a Japanese bank. The term next to the JPY return is the return on foreign currency. To remind you again, E is the spot exchange rate, denoted in USD/JPY. The forward exchange rate F is also denoted in USD/JPY.

Covered Interest Parity: Other Forms

The (F-E)/E term is called the forward premium of JPY against the USD. Note that this term can be either positive or negative. To remind you again, if the USD appreciates if E decreases. If USD is expected to appreciate F decreases. Thus, a negative forward premium in which F<E suggests that the USD will appreciate against the JPY. A positive forward premium in which F>E implies that USD will depreciate against the JPY. Under no arbitrage, we want to conclude two things:

1. If domestic interest rates are higher than foreign interest rates, then the domestic currency must depreciate. Otherwise, there will be arbitrage.
2. If domestic interest rates are lower than foreign interest rates, then the domestic currency must appreciate. Otherwise, there will be arbitrage.

We can express CIP in a much simpler way. If you multiply things out and assuming R^* and (F-E)/E are small, then we can rewrite CIP as R - R^* = (F-E)/E. This should make things much more intuitive. R-R^* is the interest rate differential and (F-E)/E is the forward premium. We will work with this form later in the course. However, for now, we will use the other form to prove to you that this parity must hold.

Covered Interest parity: Arbitrage

To remind you again, arbitrage can only occur if profit is made without risk or investment. This it the definition of arbitrage. I will prove to you that the absence of arbitrage implies parity between (1+R) and (1+R^*)(1+(F-E)/E). We can rewrite the right hand side term by dividing E through and subtracting 1. Consider the case in which domestic interest rate returns are greater than foreign interest rates adjusted for the forward premium. I will show a scenario in which arbitrage is possible.

Consider the following setup. Suppose an American investor who lends 1 JPY for 30 days can exchange the JPY repayment that is due in 30 days at F and can enter a contract over F USD with any investor today. I will argue that if (1+R) is greater than (1+R^*) (F/E), then arbitrage exists. What this is basically saying is that I should borrow at the foreign interest rate and lend at the domestic rate in order to make risk free profit.

Covered Interest Parity: Proof

The plan is to borrow 1 JPY in Japan for 30 days and in 30 days, pay back JPY at (1+R^*). But, in the meantime, exchange the 1 JPY for E USD and invest it for returns of E(1+R).

1. The first thing is to remove future risk. It is possible that the USD appreciates or depreciates. If USD appreciates too much, I could lose money investing in JPY. If the USD depreciates, that could also change my profits. The point to is achieve certainty and remove all sources of risk. To remove that risk, I enter into a forward contract to receive (1+R^*) in exchange for (1+R^*)F in 30 days.
2. Next, we will exchange the borrowed 1 JPY for E USD on the spot market. This removes spot price risk or prices changes JPY.
3. Next, to make sure we don’t actually hold onto any assets or currency, we will lend out E USD on the US market for E(1+R) in 30 days. Not holding onto anything means we are not making an investment in anything, namely holding onto USD.
4. At the end of the 30 days we will receive E(1+R) from our loan and pay F(1+R^*) from our forward contract to get (1+R)^* to be paid back from our initial loan. Therefore, arbitrage profit is made if the parity is broken.

Covered Interest Parity: Review

Therefore, in our example, if this parity is ever broken, arbitrageurs will borrow JPY and invest in USD for the higher return. This speculation will bid for and appreciate the USD (reducing E until equality is restored).

Covered Interest Parity: Example 1 (Long Domestic)

1. Borrow 1 Euro for 1 year. In 1 year, pack back (1+R^*) Euros.
2. Enter into forward contract: agree to pay F(1+R^*) USD in 1 year and have your contract partner pay (1+R^*) EUR in 1 year
3. Exchange the borrowing 1 EUR for E USD on the spot market
4. Lend out E USD on the US market for E(1+R) in 1 year.
5. Receive E(1+R), pay F(1+R^*)

(1+R) = 1.08 > (1+R^*)(F/E) = (1+0.12)(1.53/1.6) = 1.071

Covered Interest Parity: Example 2 (Short Domestic)

1. Borrow E USD on the U.S. market and pay E(1+R) in 1 year
2. Exchange the borrowed E USD for 1 EUR in the spot market
3. Deposit 1 EUR at a European bank for (1+R^*) EUR in 1 year
4. Enter a forward contract over (1+R^*): have someone agree to pay you USD F(1+R^*) in 1 year in exchange for (1+R^*) in 1 year
5. Pay E(1+R), receive F(1+R^*)

(1+R) = (1+0.08) < (1+R^*)(F/E) = (1+0.12)(1.53/1.55) = 1.105