Creation of Exchange Rates
The first part of this course showed how to read and understand an exchange rate. The next question we need to address is how are these exchange rates determined? As we said in the last section, exchange rates represent the price of a currency in terms of another currency. Basic economics tells us that the function of any price is to balance the supply and demand for that product or service. So the simple answer is that exchange rates are determined by the supply and demand for currency. Before we explain how supply and demand specifically affect exchange rates, let’s first talk only about these two very important economic principles.
Economic Principles 101: Supply And Demand
One of the most fundamental concepts in economics is that of supply and demand. People have vastly different thoughts on prices and how they are determined. How many times have you heard people complain that tickets to a professional sporting event are "outrageously" priced and that it's unfair that "they" charge that much for them? People who make these comments believe that the seller is solely responsible for setting prices; they never even consider the demand side. On the other hand, there are people who believe that buyers are strictly responsible for determining the prices of some products. Why are American cars cheaper than the European cars? Some will tell you it's because nobody wants to buy the American cars compared to the European cars; they completely neglect to mention anything about the supply.
The fact is, the value, or price, of any good is strictly determined by the supply and the demand for it. It is both the supply of a good and the demand for it that determines price and not simply one or the other. It is like asking which blade of the scissors cuts the paper. It’s not one or the other; it’s both together that do the work. If only supply determined price, homes in New York City would be cheaper than homes in Monkey’s Eyebrow, Kentucky (yes, it’s an actual town) since there are far more homes in New York City. Similarly, if only demand determined price, then a glass of water should cost far more than the Hope Diamond since water is essential for life. We can all live without pretty rocks.
The supply of anything is simply the physical number of items that are available for sale at a specific price while the demand for that item is a perceived value that exists in the minds of consumers. Of course, this perception must be backed up by the willingness and ability to pay that price. If General Motors invents a high-performance solar powered sports car that comes with a million mile warranty, you may think the demand for it would be great. However, if it carries a ten million dollar price tag, the demand may be near zero, as far as economists are concerned.
To understand how the principles of supply and demand interact, you must understand the law of supply and the law of demand.
The law of demand says that consumers should be willing to buy (demand) more of a good as the price falls. For example, if you see something on sale, you are likely to buy more of that good than if the price had not been reduced. With the lower price, you have the incentive to buy more units than you normally would purchase.
This assumes that all other factors affecting a consumer's decision stay the same. If we didn't assume that all else stayed the same, it would be impossible to make generalizations about behavior. For instance, if price falls because the product has been declared unsafe, we may still see the number of items purchased fall and not increase, as the law of demand would otherwise predict. When economists speak about the laws of supply and demand and their effect on peoples' behavior, they assume that all else remains constant. That is, only the price changes and nothing else.
The reverse of this law is also true. If price rises, consumers will demand less of that good. As the fine (price) for speeding tickets increases, we should expect a reduction in the number of speeders. As the price of speeding tickets rises, drivers demand less speeding.
The law of supply is similar to the law of demand, but moves the opposite direction. It focuses on the producers, or suppliers, of goods. It says that more of a good will be supplied as the price rises, assuming all other factors stay the same. If the price of computer chips suddenly spikes up, you can be sure that Intel and other manufacturers will respond by making more chips. Computer chip manufacturers realize they will make more money with the higher prices so have the incentive to produce more. Conversely, if prices fall, suppliers will not bring as much to market. The laws of supply and demand hold true because of the proper self-serving incentives given to the consumers and producers.
As stated earlier, it is the supply of and the demand for any product or service that determines its value. For any given demand of a product, as the supply rises, its value will fall. Likewise, for any given supply, as the demand rises, so will its price. Notice that supply and demand tend to counterbalance each other. For example, if consumers suddenly want more of the good and drive the price up, suppliers then have the incentive to produce more, which tends to bring the price down.
Conversely, if consumers suddenly want less of the good and prices fall, suppliers will produce less, which tends to drive the price up. Eventually a point is reached where the amount that consumers demand is exactly equal to the amount that is supplied and price equilibrium is reached. At equilibrium, the price is no longer jumping up or down because there is no net buying or selling pressure. When the market is in equilibrium, that price is said to clear the market. In other words, every buyer willing to buy at that price is exactly matched with a seller at that same price and there are no surpluses or shortages of buyers or sellers.
When people only consider one side of the equation (supply or demand) without considering the other they are apt to make mistakes. A simple example of this occurred shortly after the September 11 attacks. Many analysts predicted that the price of airline flights would plummet since the demand for flying would obviously decrease in the presence of such high risk conditions.
While they were correct that the demand would fall they were completely wrong in their prediction. Why? Because in the presence of high risk flying conditions the airlines didn’t want to fly either. The vast majority of flights were cancelled. Despite the high risk, there were still many people who needed to travel and they outnumbered the available airline seats by a long shot. The net result was a relative increase in demand – and a drastic increase in the price of airline tickets followed. Be careful when trading currencies that you don’t take a position just because of a story that focuses on the supply or the demand side. You must consider both to be accurate.
While the economic concepts of supply and demand may sound fairly simple, we can show just how powerful their predictive values can be when trading currencies once you understand the main forces that affect supply and demand for currencies.
Factors that Affect Supply and Demand
The main factors that affect supply and demand for currency are capital flows between nations, which include interest rates, inflation, and balance of payments. In addition, psychological factors such as the government’s ability to fully back its currency will play a major role. The government can also control the supply of currency with open market operations. All of these factors will influence the supply and demand for currency and therefore the exchange rate. In many cases, these price swings can be dramatic. In the short run, technical analysis is primarily used to determine whether currencies are overbought or oversold and actions by traders will certainly affect the exchange rates as well.
To understand better, let’s assume there are just two countries, United States and Japan. Americans need yen to buy Japanese products; they have a demand for yen. While you may not actually need to acquire yen to buy a Toyota, you have to realize that somebody somewhere must be doing so since the Japanese ultimately want yen for their products. In most cases, it is the American importer of Toyotas since they must pay for the cars in yen. On the other hand, it could also be the Japanese exporters selling Toyotas in exchange for dollars and then selling the dollars in exchange for yen.
The higher the price of yen (that is, the higher the JPY/USD exchange rate) the fewer yen Americans will buy. The law of demand tells us to expect a downward sloping curve since Americans will demand fewer yen as the price of yen rises:
Figure 4-1: Demand for Yen
Figure 4-1 shows the price of yen (JPY/USD exchange rate) on the vertical axis and the quantity Americans would like to buy along the horizontal axis. As the price rises, notice that the quantity falls. The reverse also holds true; as the price of yen falls, the quantity that Americans want will increase. That’s the law of demand as applied to yen.
Where does the supply of yen come from? Japan is willing to sell yen and buy dollars for the same reason we’re willing to buy yen and sell dollars. Japan needs dollars to buy American products so Japan therefore creates a supply of yen to Americans. The more that the JPY/USD exchange rate rises the more that Japanese are willing to supply yen. We must be careful with the law of supply as applied to currencies since countries will not print more money as the price of their currency rises. Under the normal use of the law of supply this is what is expected. As the price of computer chips rises, we expect Intel to manufacture more chips.
But when dealing in currencies, you will not have the same effect since printing more money will only create heated rounds of inflations or even hyperinflations. However, it is not unreasonable to expect countries to be willing to supply more currency (not necessarily print it) when the price is high. How do they supply more currency? By purchasing goods from other countries. As the price of yen rises against the dollar, the yen has more “purchasing power” in America and the Japanese will therefore buy more U.S. products and services. In order to do so, they must sell (supply) yen and buy dollars. Therefore, it is not unreasonable to expect an upward sloping supply curve for the yen thus showing Japan’s willingness to supply more yen as the price of yen rises:
Figure 4-2: Supply of Yen
Figure 4-2 shows that as we increase the JPY/USD exchange rate (the price of yen) that the quantity supplied by Japan also increases. As the price falls, fewer yen will be supplied. This demonstrates the law of supply as applied to yen.
Once you understand the laws of supply and demand as applied to yen, the exchange rate is simply the price that exactly balances these two sides. Figure 4-3 shows a hypothetical clearing price at the quote of JPY/USD = .8535:
Figure 4-3: Supply and Demand for Yen
In this example, if the exchange rate (price) were higher than .8535 then the Japanese would be willing to supply more yen than Americans are willing to buy. If the exchange rate were lower than .8535 then Americans would want to buy more yen than the Japanese are willing to supply. At an exchange rate of .8535 Americans can buy all of the yen that the Japanese are willing to supply. The market is cleared and we say the price (exchange rate) is in equilibrium. When prices are in equilibrium that just means there are no forces at this time that are making the exchange rate move from this price.
However, prices do change. The reason is that some force presents itself that affects the price of yen. One of the most obvious is an increased desire for Japanese goods. Specifically, if Americans suddenly demanded more Japanese goods, they must pay for those goods by purchasing yen. The higher demand for Japanese products creates the need for buying Japanese Yen and, in turn, creates a supply of U.S. Dollars on the market. The buying pressure on the yen will raise the price of yen in terms of dollars. We would say the yen is rising against the dollar or, equally valid, the dollar is falling against the yen.
From the first section, the strength of the yen and weakness of the dollar in this example should be clear since those consumers trading in their dollars for yen are effectively selling the currency pair USD/JPY and will therefore sell dollars to buy yen. Specifically, if the America importers pay for the cars in yen they must sell dollars to buy yen. If the Japanese exporters sell cars in exchange for dollars they will then sell those dollars to buy yen. No matter how you look at it, the increased demand for Japanese products will increase the value of the yen against the dollar.
We could also look at it from the inverse set of quotes and say that they are buying the currency pair JPY/USD and will buy yen to sell dollars. Either way you look at it, these actions will weaken the dollar against the yen. An increased demand for yen (with supply being constant) will increase the JPY/USD exchange rate. This occurs because Americans are willing to pay more dollars per yen at every quantity level, which creates a rightward shift in the demand curve. For example, you may see the JPY/USD quote rise from the previous level of .8535 to a new level of .9035, which is depicted in Figure 4-4:
Figure 4-4: Increased demand for yen results in higher exchange rate
Notice that when we talk about an increased demand that the demand curve shifts upward to the right. The opposite is true for a decrease in demand; the curve will shift downward to the left.
We could also look at this example from the perspective of the dollar by taking the reciprocals of the above quotes. In this example, if the JPY/USD quote moves from .8535 to .9035 then the USD/JPY quote must move from 1/.008535 = 117.16 to 1/.009035 = 110.68. With the dollar as the base currency, notice that the quote has fallen from 117.16 to 110.68, which the dollar has weakened against the quote currency (JPY) or that the yen has strengthened against the dollar. If Americans sell dollars to buy yen then the supply of dollars is increasing, which means its value will fall against the yen (assuming a constant demand). Whether you’re reading the JPY/USD quote of the USD/JPY quote, the conclusions are exactly the same.
To better understand the supply and demand for currency, it helps to consider a quote from Adam Smith who is considered to be the father of economic thinking: “It is not for its own sake that men desire money, but for the sake of what they can purchase with it.” Adam Smith is saying that if you couldn’t buy anything with your money, it would be nothing but worthless pieces of paper. If you keep that in mind, it will help you to understand why countries supply and demand currency; they do so because they supply and demand goods and services. So why might the Japanese Yen rise against the dollar? It will rise if Americans demand more (import more) Japanese goods.
Once again, when considering supply and demand, you must remember that they are two sides of the same coin. Supply cannot exist without demand and demand cannot exist without supply. The supply of dollars equals the demand for yen and vice versa. So just because you read an article that says Americans are importing more Japanese goods does not necessarily mean that the yen will rise against the dollar.
Even though Americans may be demanding more yen you must also consider the supply side as well. If Japanese are supplying far more yen (demanding more dollars) than we’re willing to supply then you may see a decrease in the JPY/USD exchange rate. Whenever you see an analysis stating an effect due to one specific cause (i.e., the yen will rise against the dollar if Americans demand more Japanese products) it assumes that all other factors (including supply) remain constant.
When trying to determine the effect of an action on an exchange rate you must be very careful in your analyses. For example, there are two factors that can affect the JPY/USD exchange rate. First, the price of Toyotas may rise in yen terms. That is, the price of Toyotas may be rising in Japan. If the exchange rate stays the same then Toyotas will cost more dollars. On the other hand, the price of Toyotas could stay the same in Japan but the JPY/USD exchange rate rises for other reasons. That too will cause an increase in the price of Toyotas for Americans.
Another reason you must be careful with currency analyses (or any other type of economic analysis for that matter) is that there can be unintended consequences, which occur when a decision yields an unexpected outcome. The reason they occur is that some actions set off a chain reaction of events that are difficult to track and end up yielding the opposite effect. For example, in 1989, the Exxon tanker Valdez created one of the worst oil spills in U.S. history. As a consequence, many coastal states pursued legislation that placed unlimited liability on tanker operators. The idea, of course, was that a large penalty would create a powerful disincentive for being negligent thus creating a safer environment, free from future oil spills.
But true self-serving interests of corporations created an unintended consequence. Rather than live with the potential penalties, the oil-importing corporations simply hired foreign ships to deliver the oil to the U.S. and escaped the laws holding their fleets to the newly established laws. Rather than seeing reliable U.S. ships on the horizon, the coastal states saw shady independent operators with less than satisfactory ships and questionable insurance. Rather than decrease the chances of an oil spill, their legislation actually increased it – an unintended consequence.
Similar unintended consequences can occur when analyzing exchange rates. For example, the U.S. government may place tariffs on all Japanese cars thus increasing their price and Americans will buy fewer Japanese cars. This is often the desired effect of a tariff. However, by raising the price of Japanese cars, the demand curve shifts left as Americans shift their preferences over to the cheaper American cars.
The price of the yen will fall against the dollar (and the dollar will rise against the yen). The result of the strong dollar against the yen means that the Japanese will now import fewer American cars. By increasing the price of the Japanese cars through tariffs, the government can cause a decrease in American car exports – an unintended consequence. So while the announcement of a tariff on Japanese cars may lead you to believe that the JPY/USD exchange rate will fall, it could actually rise depending on the net effect of all car imports and exports.
The J-Curve
The above effect is similar to a consequence called the J-curve effect. The J-curve is an effect that appears when an exchange rate changes suddenly, often through government devaluation. However, the effect can be due to sudden market changes as well. To understand the J-curve, you must understand the concept of net exports, which is simply the amount of exports from a country less the amount of imports. Net exports are a component of the national income accounting equation that seeks to tally up the value of all final goods and services produced by a country; that is Gross Domestic Product (GDP). Net exports are important to track since a country’s imports must be paid for by its exports. However, changes in exchange rates can produce contradictory results from what you might expect in the levels of net exports.
If we use VolumeX and VolumeI to represent the volumes of exports and imports respectively, then the dollar value of net exports is simply the dollar value of VolumeX minus the dollar value of VolumeI. However, in order to find the dollar value for the imports we must convert the currency. Assuming the exchange rate (E) is given in American terms (USD/JPY), the total price of exports from the United States is Price * VolumeX. The dollar value of the imports is (Foreign Price/E) * VolumeI. The difference between these two prices is the value for net exports.
Normally, net exports are counted by including all products but we’re going to simplify the example by considering only one product exported and one product imported. The true net export figure you read about is found by exactly the same steps but will just produce much bigger numbers. Assume that the exchange rate between the U.S. and Japan is USD/JPY = 100 and that the U.S. exports one million units at $100 each while also importing one million units at 7,200 yen each. In dollar terms, the value of net exports is:
Net Exports = (Price * VolumeX) – [(Foreign Price/E) * VolumeI]
= ($100 * 1,000,000 units) – (7,200/100) * 1,000,000 units
= $100 million – $72 million
= $28 million dollars of net exports
In other words, the U.S. exported $28 million worth more than it imported. Now let’s assume that the prices in each country stay the same but that the dollar is suddenly weaker and trading for USD/JPY = 90. With a weaker dollar, we should now expect the level of exports to increase (to more than one million units) and the level of imports to decrease (to less than one million units).
Consequently, net exports should rise to a number greater than $28 million. The reason we should expect a risk in net exports is that the weaker dollar makes imports more expensive so Americans will buy fewer units while, at the same time, making exports cheaper so that the Japanese buy more units. If the U.S. exports more and buys less then the value of net exports should increase. We may, for example, see the level of exports rise to 1,150,000 while the level of imports falls to 995,000 thus driving up the level of net exports as follows:
Net Exports = (Price * VolumeX) – [(Foreign Price/E) * VolumeI]
= ($100 * 1,150,000 units) – (7,200/90) * 995,000 units
= $115 million – $79.6 million
= $35.4 million dollars of net exports
It is reasonable then to expect that net exports should rise if the home currency falls against one of the trading partners. However, in the short run, it is possible for the level of exports or imports to not adjust quickly. This is due to the fact that people haven’t had time to adjust tastes and preferences based on the change in relative prices. If the volumes do not change but only the relative prices (due to the change in the exchange rate falling from USD/JPY = 100 to USD/JPY = 90) then we may actually see a fall in the level of net exports, which is counterintuitive to what we would naturally expect:
Net Exports = (Price * VolumeX) – [(Foreign Price/E) * VolumeI]
= ($100 * 1,000,000 units) – (7,200/90) * 1,000,000 units
= $100 million – $80 million
= $20 million dollars of net exports
In the first scenario, we found that net exports equaled $28 million. If the exchange rate falls and volumes do not quickly adjust, we have shown that exports will fall to $20 million rather than rise to $35.4 million as the long-run theory would suggest. If you look at a graph of net exports at the point where a currency has weakened, you may actually see a quick fall in the chart, which rises over time thus forming a letter “J,” which is why it is called the J-curve effect. Figure 4-5 shows how the formation of the “J” comes about:
Figure 4-5:
Incidentally, we can see the opposite effect if the currency, instead, appreciates quickly. In these cases, you will see a sudden rise in net exports followed by a fall. The J-curve effect is important for currency traders to understand because much of the data used to forecast exchange rates relies on changes in net exports and you must realize that opposite effects can and do occur in the short run.
The Force of Inflation
There are other forces that create changes in the supply and demand for currency other than peoples’ tastes for foreign products. One of the most notable is inflation. Inflation is a general rise in the price level that is caused by “too much money chasing too few goods.” If inflation increases in the United States, the price level for American goods will rise and that will decrease the Japanese demand for dollars, which is the same thing as saying the Japanese will supply fewer yen. This creates a leftward shift in the supply curve and the JPY/USD exchange rate will rise as shown in Figure 4-6:
Figure 4-6:
If the net inflation rate rises in the U.S. as compared to Japan then the U.S. Dollar will weaken against the Japanese Yen. By “net” inflation rate, we mean that amount by which the inflation rates differ. If inflation is 5% in the U.S. and 3% in Japan then the net U.S. inflation rate is 5% - 3% = 2%. Just because inflation is present in the U.S. does not mean that the dollar will fall against the yen. It’s only when the U.S. inflation rate is higher than that of Japan will you see a weakening of the dollar against the yen.
In these examples, we assumed the yen rose from .8535 to .9035. By how much did the yen appreciate? We can find that by a simple formula, by taking the new yen quote and subtracting off the beginning yen quote then dividing that answer by the beginning yen quote
This formula just calculates the percentage change as we move from the beginning yen quote to the new one. It is basically the same formula that we used to find the bid-ask spread percentage in the first section.
In this example, the yen has appreciated against the dollar by (.9035-.8535)/.8535 = 5.9%. We can also find out how much the dollar depreciated against the yen by using the same formula in reverse. Rather than finding out the percentage increase as we move from .8535 to .9035, we simply find the percentage decrease by moving from .9035 to .8535. We find the dollar depreciated against the yen by (.9035 - .8535)/.9035 = 5.5%.
The percent of appreciation and depreciation are usually close to each other but never exact. The reason is that you are comparing the percent changes to different bases. As an example, if you own a stock that rises from $100 to $110 then that’s an increase of ($110 - $100)/$100 = 10%. The formula is just saying that the $10 increase relative to the $100 starting point is 10%. However, if the investment fell from $110 to $100 then that would be a decrease of ($110 - $100)/$110 = 9.1%.
For the percent increase, we’re comparing the $10 change to the $100 base. For the percent decrease, we’re comparing that same $10 change to a $110 base. Equal moves on different bases will yield different results and that’s exactly what’s happening with our currency formulas. If you’re in doubt, you can always check it by considering the yen price of the dollar. In this example, if the yen rose from .8535 to .9035 then the dollar move (in terms of yen) was falling from 117.16 to 110.68, which is a 5.5% decrease in value.
The Force of Interest Rates
Interest rates are another form of a product or service. As Americans demand these financial products they will have an impact on exchange rates. If interest rates are higher in Japan than in the U.S. then American investors should be willing to shift dollars to Japan to earn the higher rates. Interest rates play a major role in determining the flow of capital and therefore affect the price of currencies. To understand the force of inflation and interest rates better, we need to take a little detour and talk about a fundamental rule of International Finance: The law of one price.
The Law of One Price
This law is an economic theory which says that in an efficient market all equal assets should cost the same. We saw an example of this earlier when we considered a share of IBM trading on the New York for $100 and on the Philadelphia Exchange for $100.10. A share of IBM is a share of IBM regardless of where you buy it so there’s no reason for the prices to differ. Arbitrageurs corrected for this discrepancy by purchasing it cheap on the New York and selling it dear on the Philly. Their actions eventually make IBM shares trade for one price on both exchanges.
This law should hold for any asset where it is possible to buy it for a relatively cheap price and quickly sell it for a higher price. If oranges cost $1 on side of the street and can be sold for $2 on the other we should expect that people will buy oranges for $1 and walk them across the street to collect $2. As with the IBM example, tremendous buying pressure will result on the $1 oranges causing their price to rise. Meanwhile, the ensuing large supply across the street will cause their price to fall below $2.
But as long as there is a discrepancy between prices, people will continue to buy on one side and sell on the other. Their actions will stop when orange prices are the same on both sides of the street. In fact, it is this very reason that most stores require receipts when returning merchandise. Otherwise, savvy shoppers could buy up goods from a lower priced store and exchange it for cash at the higher price store. Some stores do offer better service and may be justified in charging higher prices for the same item. The only way they can guard against the “market” forcing them to have the same price is to require a receipt for exchanges.
Packaged goods are not exempt from the law of one price and must be priced according to the individual goods. If oranges can be purchased for $1 on one side of the street while baskets of 10 are sold for $12 on the other side, people will make their own baskets for $10 and sell them for $12 on the other side thus collecting an additional $2 for their efforts.
On the other hand, if the baskets sell for only $9 then people will buy the basket, break out the 10 individual oranges, walk them to the other side and collect $10. The ability to profit from packaged goods is the reason you see the mysterious “not labeled for individual sale” labels on many goods. Look at the ketchup bottle the next time you’re in a restaurant and you’re likely to see this label. Restaurants buy ketchup in very large quantities from the manufacturer and receive substantial discounts for doing so. Because of the large break in price, there is an incentive for restaurants to break apart the packages and sell the bottles individually (rather than using them for their own use) thus unfairly competing with other retailers. These labels are placed on bottles to flag potential violators.
The law of one price is a powerful theory and holds for all goods whether they are located across the street or across the globe. Therefore, a Toyota Camry should cost the same whether it is purchased in Japan or in the United States. Equal assets should cost the same price. If a Camry costs $23,000 in the U.S. it should cost 2,691,000 yen in Japan if the dollar price is USD/JPY = 117. If the car were more expensive, say 2,925,000 yen then enterprising individuals or corporations would buy the Camry in the U.S. and ship it to Japan and collect 2,925,000 yen for it. Most corporations involved in shipping cars are acting as arbitrageurs as they would have purchase and sale agreements already in place before shipping the cars thus guaranteeing the profit. Once they sell the car in Japan, they would exchange those yen in the open market and receive 2,925,000 /117 = $25,000 thus receiving $2,000 more than what they paid for the car.
One of the obvious assumptions of the law of one price is that it only holds after accounting for other costs. A $2,000 gain is not a profit if shipping, insurance, tariffs, etc. cost more than that. The law of one price also assumes that there is a competitive market in both countries for the product and that the product can be transported. Housing markets and specialized local services will not necessarily adhere to the law of one price.
Therefore, it is possible to see the same product trading for different prices but that is usually due to shipping, international taxes, import quotas, political barriers, or other market frictions. Not counting these costs, the law of one price says that the home price should equal the foreign price when accounting for exchange rates:
Home price = Foreign price * exchange rate
For this Toyota example, we should expect to see:
Price in U.S. = Price in Japan * JPY/USD, or
$23,000 = 2,691,000 yen * .008547
The law of one price shows how basic arbitrage creates equal prices between equal assets. There are five key economic relationships that follow from the law of one price:
Purchasing Power Parity (PPP) Fisher Effect (FE)
International Fisher Effect (IFE)
Interest Rate Parity (IRP)
Forward Rates as Unbiased Predictors of Future Spot Rates (UFR)
Purchasing Power Parity (PPP)
At the end of World War I, Swedish economist Gustav Cassel argued for new sets of official exchange rates that would allow countries to resume their normal trade relations. His argument rested on the theory of purchasing power parity (PPP) which was basically a broad perspective of the law of one price. Rather than focus on individual goods, Cassel felt that the overall price level in each country should be identical after allowing for exchange rates. There are two versions of purchasing power parity and Cassel’s version later became known as absolute purchasing power parity. Thus, absolute PPP says that prices levels across countries should be the same if we compare them in the same unit of currency.
The second and more common version is called relative purchasing power parity which just says that the exchange rates between two countries will adjust to reflect changes in the price levels of each country. In other words, if absolute PPP is true, then exchange rates should move to equalize the difference in the rate of change of those goods. By definition, the rate of change in prices is inflation so absolute PPP states that exchange rates should move to equalize the differences in inflation rates.
For example, if the inflation rate in the U.S. is 5% while only 3% in Japan then the U.S. Dollar has a net inflationary pressure of 5% - 3% = 2%. This means that the yen must appreciate by about 2% against the dollar (or that the dollar must depreciate about 2% against the yen). It is only when this occurs that the dollar price of goods in both countries will equalize and will return to purchasing power parity.
The reason we say the yen must appreciate by “about” 2% is that it is not mathematically exact to just subtract the two inflation rates, which can be better demonstrated by an example. Assume two goods cost $100. At the end of the year, one rises 5% to $105 while the other rises 3% to $103. Did the first rise by 2% more than the second? To answer this question, we must realize that the first rose by a factor of 1.05 while the second rose by a factor of 1.03. The way to solve this is to realize that both ending prices were arrived at by multiplying the beginning price by 1+inflation rate as follows:
$100 * 1.05 = $105
$100 * 1.03 = $103
No matter which prices we start with, these ratios will always differ by 1.05/1.03 = 1.019, or about 1.9%. Although it is not too far off, you can see that 1.9% is not equal to 2% and this difference will only compound if you forecast the exchange rate further into the future.
Let’s take a look at an example. If the current exchange rate is JPY/USD = 0.8535 and the U.S. inflation is 5% while only 3% in Japan then what can we expect the equilibrium exchange rate to be? To answer, we must multiply the current exchange rate by the ratio of the relative rates of inflation:
Equilibrium = 
With these inflation rates, we should expect the JPY/USD exchange rate to rise from 0.8535 to 0.8700. Note that the spot exchange rate has also risen by 0.8700/0.8535 = 1.019, or 1.9% as well. So another way we can view absolute PPP is to say that the relation to the future and current spot rate should equal the ratio of the relative inflation rates. In this example:
Alternatively, we can say that the percentage change in the currency spot prices will approximately equal the differences in inflation rates. In this example:
What can we expect the exchange rate to be after three years if these two countries are consistently running these inflation rates? We can predict the exchange rate three years from now by multiplying .8535 by (1.05/1.03) for the first year, multiply that answer by (1.05/1.03) to get the answer for the second year, and multiply that answer by (1.05/1.03) for the third year. In effect, we have multiplied the initial exchange rate (.8535) by (1.05/1.03) three times, which is mathematically the same thing as raising it to the third power. Our expected exchange rate in three years is then JPY/USD = .9042, which is found as follows:
Equilibrium = 
Empirical evidence shows that relative purchasing power parity holds reasonably well in the long run especially when there are large differences in interest rates. Despite this fact, relative purchasing power parity does not hold in the short run. Most exchange rate movements are driven by news which ultimately affects the relative rates of inflation but purchasing power parity is a long-term event. It is often very slow to react and can take 5 to 10 years before the exchange rates equalize according to the theory.
Although relatively simple in concept, purchasing power parity is difficult to determine in practice. The reason is that you must compare identical baskets of goods between countries and that rarely exists. On a simple level, The Economist magazine publishes the “Big Mac” index to show the relative prices of McDonald’s Big Macs across the globe. But even in this case, McDonald’s changes the recipes slightly to suit local tastes so comparisons are still not truly being made on identical products.
The Organization for Economic Cooperation and Development (OECD) publishes data twice a year on the relative exchange rate differences based on purchasing power parity. The most recent update was in March 2006 and is shown in Figure 4-7:
Figure 4-7:
The solid bars indicate currencies that are overvalued relative to the U.S. Dollar by the percentage shown and are therefore expected to depreciate against the dollar. The shaded bars are those that are undervalued relative to the U.S. Dollar and expected to appreciate against the dollar. The appreciations and depreciations are a long run phenomenon and may take years to develop. Notice the bars in Figure 4-6 are nearly symmetrical around zero. The longest bars extend to about +45% and -45% while the other bars taper off at about the same rates. This shows that the overvaluation or undervaluation of currencies follows a bell curve and that currencies are fairly valued on average, which is really what purchasing power parity tells us.
Fisher Effect (FE)
If you deposit money at your bank and are told you will receive 5% on your money that is called the nominal interest rate. The word “nominal” just means “name” so the nominal interest rate is simply the “name” or the stated interest rate. However, what really matters to investors is the interest rate after accounting for inflation. High interest rates don’t mean a thing if they are followed by high rates of inflation. The reason is that interest is only beneficial if you are rewarded for saving money by being able to purchase more goods at a later time.
You may be able to purchase wine today but purchase wine and cheese tomorrow if you deposit your money and earn interest. Your increased purchasing power (the ability to buy cheese) makes you better off and provides an incentive for saving money. However, if the price of wine or cheese rises faster than the interest you’re earning on your money then you will be made worse off tomorrow. For instance, assume that wine costs $2 per unit and cheese $1 per unit. If you have $100 today, you could buy 50 units of wine or 100 units of cheese or some combination between the two. Specifically, you could buy any combination that falls on the budget constraint line shown in Figure 4-8:
Figure 4-8
For example, let’s look at the endpoints of this line. The left endpoint shows 50 units of wine and no units of cheese. This is just showing that for $100 you could purchase 50 units of wine and no cheese since 50 units * $2 per unit = $100. The endpoint on the lower right shows you could also purchase 100 units of cheese and no wine since 100 units * $1 = $100. But you could also buy varying quantities in between. One such choice is shown by the dashed lines showing you could buy 40 units of cheese for $40 and 30 units of wine for $60 thus spending a total of $100. The budget constraint line is a graphical depiction of the maximum number of the two goods you could buy given the $100 budget.
Rather than purchasing one (or both) of these goods, you could choose to invest your money and earn interest. Assume that you deposit $100 in a bank at 10% and receive $110 in one year. If wine and cheese prices remained the same, you could now buy any of the following combinations on the budget constraint line shown in Figure 4-9:
Figure 4-9
Notice that the budget constraint line has shifted outward and that you could now buy 110 units of cheese or 55 units of wine or other combinations in between. The important point to understand is that you are better off since you can now purchase a bigger basket of goods. This, of course, assumes the prices of those goods stay the same.
What would happen if the price of wine and cheese rose faster than the rate of interest on your money? For example, what if wine rises to $2.30 per unit and the price of cheese to $1.20 per unit? Figure 4-10 shows that the budget line now falls inward meaning that you can now purchase fewer goods than you could before. Notice that the line falls below zero for 100 units of cheese which is showing that you must now borrow money to buy 100 units of cheese. You are worse off by investing your money and deferring consumption.
Figure 4-10
American economist Irving Fisher used the above argument to show that what really matters to investors is the real rate of interest (also called the inflation-adjusted rate of inflation). In other words, what really matters is the rate at which current goods can be converted into future goods. A high nominal interest rate means nothing if you are worse off in terms of purchasing power once you collect your money.
Think of it like investing in a stock that has gone down dramatically in price but then goes through a reverse split. Imagine that you have been given 1,000 shares of stock trading for $10. At this point, you could sell those shares and receive $10,000 cash. Now assume that the stock falls to $2 and then undergoes a 10:1 reverse split. You will then be left holding 1/10 as many shares at 10 times the price, or 100 shares of stock trading for $20.
Notice that in nominal terms the investment has risen from $10 to $20, which makes it appear that you are far better off in terms of purchasing power. However, if you were to cash in those shares, you’d only receive $2,000 so you are far worse off than was apparent. Even though the stock price is twice as high, it would be hard to convince you that you’re better off and that’s exactly what Fisher argued about nominal rates of interest.
The Fisher Effect states that interest rates are really made up of two components. One component is the true (real) interest rate required by the investor. The second component compensates the investor for inflation. If your required interest rate is (r) and inflation is expected to be (i) then you really need an increase on your money of (1+ r) * (1+i). If we factor this out, we find the required rate of return is:
1+r = (1+r) * (1+i) = 1 + r + i + ri
Therefore, the nominal interest rate should be:
Nominal rate = required interest rate + inflation rate + (required rate * inflation rate)
For example, if you require 10% on your money but inflation is expected to also be 10% then you should really seek a nominal rate of 10% + 10% + (10%*10%) = 21%. If you get a nominal rate of 21% and inflation does turn out to be 10% for the year then you will be better off by exactly 10%. In this example, the cross product term at the end (10% * 10%) adds one full percentage point to the nominal rate making it 21% (otherwise the nominal rate would be 10% + 10% = 20%). However, if inflation is relatively low then this cross product becomes very small and can be ignored, which means the Fisher Effect reduces to:
Nominal rate = interest rate + inflation rate
The Fisher Effect therefore tells us that the difference in interest rates equal the difference in the expected rate of inflation. In this example:
10% interest (U.S.) – 8% interest (Japan) = 5% inflation (U.S.) – 3% inflation (Japan)
The real rate of return is equalized once the two interest rates are separated only by the expected inflation rate differential. The Fisher Effect tells us that currencies with high inflation should bear higher interest rates. The higher interest rate is only higher in nominal terms and not in real terms. It is there to compensate investors for the higher expected inflation. In the end, if inflation rates are accurate then investments in either country should make an investor equally well off. According to Fisher, long run real interest rates remain stable and it is only the nominal rates that adjust to account for inflation.
International Fisher Effect (IFE)
The Fisher Effect and Purchasing Power Parity consider only the interest rates and inflation rates. PPP states the following two premises based on a rise in inflation for the home country:
1) Exchange rates move to offset the difference in inflation rates
2) Interest rates of home country will rise
If we combine these two effects, we get the International Fisher Effect. According to this effect, the interest rate differential between two countries should equal the exchange rate differentials. For example, assume USD/JPY = 100. Interest rates are 10% in U.S. and 8% in Japan. A Japanese investor could take 10,000 yen and invest it at 8% in Japan to yield 10,800 yen in one year. On the other hand, that investor could convert the 10,000 yen to 10,000/100 = $100. The investor could then invest in the U.S. and receive $110 in one year. However, if inflation is 2% higher in the U.S. then we should see the U.S. dollar fall by roughly 2% (1.10/1.08 = 1.01852, or 1.85% to be exact) to $98.18. If that happens, the Japanese investor will convert his $110 back to yen and receive $110 * 98.18 = 10,800 yen, which is exactly the amount he would have had he left it in Japan at 8%.
As a recap between FE and IFE, if the real interest rates in the U.S. and Japan are 3% but the U.S. expects 5% inflation while Japan expects 2% then the nominal rate in the U.S. will be 3% real rate + 5% inflation adjustment = 8% nominal rate. The nominal interest rate in Japan will be 3% real rate + 2% inflation = 5% nominal rate. PPP will predict that the U.S. Dollar will fall by roughly 5% - 3% = 2% against the yen (or that the yen will rise 2% against the dollar). PPP arrives at this conclusion by comparing the inflation rates.
On the other hand, IFE states that we should expect the exchange rate for the U.S. to fall by 8% nominal rate - 6% nominal rate = 2% fall in the dollar. Both theories arrive at the same conclusions but by considering different data.
Interest Rate Parity (IRP)
Closely related to the law of one price is the law of one expected return. Essentially this law is saying that all investments of equal risk should have the same return. Just because all investments of equal risk have the same yield does not mean they will have the same price. As the price of an asset rises its yield will fall and vice versa. In other words, there is an inverse relationship between the price of an asset and its yield. For example, assume a stock is trading for $50 and pays a $1 annual dividend. The yield on this stock is then $1/$50 = 2%. But if the price of the stock rises to $60 then any new investors at this level are earning at the rate of $1/$60 = 1.6%. As stock prices rise their yields fall. The reason for this is that the dividend rate stays the same ($1 per year) so the more you pay for the stock the lower the return on your money. Of course, dividends do not necessarily stay constant through the life of a stock but for any given dividend the more you pay to get that dividend the lower the return on your money.
Bond prices behave the same way. If a U.S. government bond is trading for $10,000 with a 5% yield then it pays a $500 interest payment to the bondholder (usually paid as two $250 payments every six months). Under this arrangement, investors are paying $10,000 for $500 worth of fixed returns, or 5% interest, which is why this is called a 5% bond. However, if the price of this bond rises to $10,500 then the yield will fall to $500/$10,500 = 4.7%. Why would investors pay more than $10,000 for this bond? If interest rates fall then investors should be willing to pay more for this bond to capture the higher 5% yield. Just as with stock yields, bond yields fall as prices rise.
Whenever two nations have different interest rates you should see a flow of funds from the country with the low interest rate to the one with the higher interest rate. According to interest rate parity, the currency associated with the lower interest rate should trade at a forward premium to that of the currency with the higher interest rate. This is just another way of saying that investors will flock to the countries with higher interest rates thus driving up the forward premiums. However, that flow of money will stop once the interest differential is equal to the forward differential.
For example, assume that interest rates are 10% in the U.S. and 8% in Japan. We’ll also assume that the exchange rate is USD/JPY = 100. This setup alone is not enough to guarantee that funds will flow from Japan to the U.S. since astute investors would understand that the 2% differential is probably due to an expected 2% fall in the exchange rate. However, if a one-year forward contract is quoting USD/JPY = 99 then there is an arbitrage opportunity and a very big incentive to transfer from Japan to the U.S. The reason is that there Japanese investors can gain a 2% premium on their investment (receiving 10% rather than 8%) while only suffering a 1% loss (99 yen rather than 100 yen) on the future exchange rate. We could also view it as the Japanese investor gaining 10% on his money while suffering a 1% loss on the exchange rate thus effectively gaining 9% on his money, which is 1% higher than the 8% he would receive from keeping the yen in Japan. By using the forward market, a Japanese investor could guarantee the return exchange rate for yen and is thus “covering” his risk. When used in this fashion, the interest rate parity becomes covered interest rate parity.
A Japanese investor could take 10,000 yen and covert it to 10,000/100 = $100. He could invest it in the U.S. and, at the same time, enter into an agreement to sell U.S. dollars forward. The investor will collect $110 in one year and can then convert it back to yen for $110 * 99 = 10,890 yen. Had the investor left the 10,000 yen in Japan he would only have 10,800 yen at the end of one year. By investing in the U.S. and locking in the return rate with a forward contract the Japanese investor is better off by 890 yen, or nearly 1%.
These actions tend to boost the spot rate for dollars (as Japanese investors buy dollars to invest in the U.S.) and also reduce the forward rate (as Japanese sell dollars forward). This, in turn, means the forward discount will widen and gradually cause the arbitrage opportunity to disappear. In addition, as money flows from Japan, the U.S. investments will be bid higher thus causing their interest yields to fall. For Japan, investors may even sell investments so they can get the higher U.S. interest rate. The sales of these investments will drive down their interest rates. At some point, the interest rate differentials will exactly equal the differential on the forward rate and the arbitrage opportunity disappears. About the only power that can stop the equality between interest rates and forward rates is government intervention.
Forward Rates as Unbiased Predictors of Future Spot Rates (UFR)
We have shown how the spot rate and forward rates are heavily influenced by expectations of future inflation rates. The spot and forward rates move in tandem and are tied together by the force or arbitrage. We previously saw that IRP assures that, in the absence of government intervention, any discrepancies between the interest rates and forward rates will be arbitraged through covered interest parity.
Figure 4-10 shows a graphical representation of this condition. The horizontal axis measures the forward premium or discount on the currency. In the previous example, we assumed there was a 1% discount on the forward premium since the exchange rate was USD/JPY = 100 and was USD/JPY = 99 for the forward rate. It is this relationship that the horizontal axis measures. The vertical axis measures the expected change in the home currency. If IRP holds then the forward rate should reflect the expected future spot rate. In Figure 2-10, the open circle shows a condition where covered interest parity holds. Here we see the forward premium is -2 thus meaning that the forward currency is 2% lower than the current exchange rate.
If that’s true, then we should also see the home currency value on the vertical axis at -2 as well. Again, this is just saying that if the forward rate is at a 2% discount it is because the home currency is expected to fall by 2%. However, if the forward contract was trading at a 3% discount but the home currency fell by 4% then the dot would fall off the line as the solid dot does and arbitrage is possible. The important point is that there is no reason to suspect that there should be a systematic over or undershooting of these rates. That is, one would expect that they should fall on the parity line, on average. This just means that the forward rate should reflect the expected future spot rate. In other words, it should be an unbiased estimator of the future spot rate. Sometimes that rate will be a little low and sometimes it will be high. But on average, it should not be biased in one direction or the other.
Figure 4-11
