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Exchange rates, forecasting and arbitrage

Can you give me some thoughts/pointers on what this lecture is talking about?
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In an earlier note I shared some thought on business in the international environment. An important, and challenging, aspect of that is dealing with multiple currencies and the changing exchange rates among them.

Let's discuss exchange rate systems and how governments intervene into the foreign exchange markets. We will also go into the topic of arbitrage paying specific attention to Interest Rate Parity. I also want to show the relationships among inflation, interest rates and exchange rates.

From 1949 to 1970, the exchange rates between the major currencies were fixed. The countries were required to maintain a parity rate with the US dollar around which the daily exchange rate could vary a very small amount. Governments, in order to effect a major adjustment, would officially devalue the currency (decrease its worth against the dollar), or revalue it (increase its worth against the dollar). These were overt, announced, acts. In turn, the U.S. dollar had a fixed value in terms of gold. This scheme was put in place as part of world economic reconstruction following World War II and was called the Bretton Woods Agreement (named after the place the agreement was consummated). The World Bank and International Monetary Fund are also part of this reconstruction process, although created through other agreements.

As you have already observed, governments do not have enough reserves to withstand to consistent pressure on their currency. Although the amount of "hot money" (the term for these flows) was much less back then, it was usually still enough to cause most governments to not succeed in defending their currencies. Consequently, huge speculative profits could be made once traders began to attack a currency. These traders acted "in concert" with each other, but not as a conspiracy per se. Once a currency was under attack, everyone jumped in - like sharks around a wounded fish.

Selling vast amounts of a currency (including short sales) increased the supply of that currency ultimately causing its value to drop. The speculators would then buy at the lower price to close their positions. For a currency ripe to appreciate, the process is reversed. However, because the speculators needed financing to buy such large amounts of currency, attacking over-valued weak currencies was much more profitable than attacking under-valued strong ones. It was the very rigidity of the rates that made this possible. The price at which currency was traded did not move much at first as the government defended it. When the government stopped defending it, there would be a sudden large devaluation that signaled the speculators to close their positions.

We saw something like this in the 1997 crises in which certain currencies that had been pegged to the dollar suffered sudden devaluations. It was the reluctance of those governments to change their exchange rates to reflect current economic realities that created the situation. Contrary to the assertions of at least one government minister in that region, there was no great conspiracy -- just a lot of smart people who realized the currencies were over-valued and saw an opportunity to make money by selling those currencies. Once a few bold, well-known traders began to sell, it signaled to the rest of the world that an opportunity for unusual profit was present.

In today's world of floating rates, change occurs somewhat immediately, but usually in small amounts. Furthermore, for the most part speculators today "bet" against each other rather than against a government. Although quite large, the profits available today do not approach those of the fixed rate era. Further, speculators today face far more downside risk than under the fixed rate scheme.

Since 1973, the exchange rates have been allowed to "float." We are not in a true floating exchange rate system. We use a modified form called a managed-float rate (sometimes called a "dirty" float). In contrast to floating rates are pegged exchange rates. In this system, a country "pegs" its currency to a major foreign currency (Hong Kong and the PRC are current examples). As a practical matter, this is the same as the old fixed rate system. It has all of the weaknesses of that system, unless a country readjusts the peg rate as economic circumstances change. Some countries are successful at doing this. Many others do not adjust the rates in a timely manner - usually due to internal political considerations.

Those that don't adjust as conditions change will find the market adjusting it for them - the latter is usually more painful in economic terms because it tends to be more sudden. A pegged currency tends to float with the currency to which it is pegged. Each country has some sort of central finance organization that may intervene in the foreign exchange market to control its value.

The country that serves as the peg has no influence over being selected as the peg and, often, little control over the peg rate. That's because peg currencies tend to be in much larger economies than pegged currencies.

Don't confuse a pegged currency with a supranational currency. At the moment there are two true supranational currencies - the Euro and the Central African Franc (which itself is actually two currencies with the same nsame that are closely related). Each serves a collection of countries that accept it as their currency and manage it through a multi-lateral central bank structure of some sort. A supranational currency has its own exchange rate and is treated, financially, as a national currency within the participating countries and in financial markets..

Another wrinkle in this is multinational currencies ... that is the situation in which one country simply adopts the currency of another to be its own. The adopting country gives up all ability to manage its monetary policy, relying on the country of issue to do so. The adopting country has no say in how the issuing country manages monetary policy. The usual reason for a country to do this is a demonstrated inability to control its own monetary policy. The U.S. dollar is a multinational currency ... it has been adopted by Panama, Ecuador and some other places.

The final condition is that of parallel currencies. That happens when two currencies both move in the same economy. The usual cause is lack of confidence by local folks in their own currency ... so they unofficially begin to use a more stable currency to do their transactions. When I was in Ukraine, the U.S. dollar and German Mark were both parallel currencies to the local currency. The local currency was rapidly depreciating. The local currency had lost so much value that folks did not even key the last 3 zeros in prices into cash registers ... it was assumed that everyone was working in thousands ... just as we assume everything is priced in multiples of 1 cent. Folks used dollars and DM to protect themselves against loss of purchasing power. The actual physical currencies circulated freely in the economy.

Those are the types of transactional currencies. There's one more type of currency ... but we individuals can't use it, only countries can. It's called "Special Drawing Rights" and it's a currency issued by the International Monetary Fund. For a good overview, go to http://www.imf.org/external/np/exr/facts/sdr.HTM.

Arbitrage:

Arbitrage is simply taking advantage of the difference in quoted currency rates and interest rates in different markets and/or times. You've probably heard that there is no such thing as a "free lunch." That means that every benefit has a cost. Well ... guess what ... there is a free lunch -- and true arbitrage is it. Arbitrage is the one riskless way to make a profit. With arbitrage, we take advantage of small discontinuities in the market and then structure our affairs to capture the profit in that discontinuity.

There are a variety of types of arbitrage that happen in international finance. I have provided you a PowerPoint file that walks you through the most common. That will supplement the stuff in Madura.

Covered interest arbitrage is one type. It takes advantage of a small discontinuity between the interest rate difference implied in a forward rate and the actual difference. The interest rates are usually short-term government securities - T-Bills here in the US. Sell a security (usually a short sale) in one market, exchanging it at the spot rate for the other currency, buy the same maturity issue of the other government and lock in the redemption FX rate with a forward contract. No investment, no risk, pure profit :-).

Because of the very high degree of market efficiency in currency markets, the opportunity for covered interest arbitrage is rare and when it does happen is fleeting. Generally, only wholesale traders are able to take advantage of it. Today, there are computer programs used by major currency trading organizations that are used to spot these opportunties. You and I are very unlikely to be able to engage in covered interest arbtrage

Covered Interest Arbitrage is based on a concept called Interest Rate Parity. Interest Rate Parity means that there is a necessary relationship among the interest rates, spot rates and forward rates for two countries. When that relationship occurs, no profit from Covered Interest Rate arbitrage is possible. It also means that an investor will earn approximately equal returns from investing in either the domestic or foreign security. Therefore, there is a bias towards domestic investment (in both countries) because a domestic investment has less risk than a foreign one. Interest Rate Parity is enforced through Covered Interest Arbitrage and is one parity condition that can be counted upon in both the short-run and long-run.

For example, if 1-year interest rates are 6% in the U.S. and 8% in the U.K. and today's spot rate is $1.65/pound. The 1-year forward rate of the pound must be $1.6194/pound. If it is not, we can structure our affairs through covered interest arbitrage to make a profit. Let's say that parity conditions exist. If they do, we could invest in the U.S. at 6%. If we do that and invest $1,000,000, at the end of one year we will have $1,060,000. Or ... we could take the $1,000,000 and exchange it for pounds. We would get $1,000,000/$1.65 = 606,060.61 pounds. Invest that at 8% and at the end of 1 year we have 654,545.46 pounds. Using the forward rate of $1.6194, we would have $1,059,970.92 ... allowing for some rounding error (less than $30), the same $1.06 million we got by investing in the U.S.

Now, let's say the forward rate was $1.63/pound. At the end of one year, we would have the same 654,545.46 pounds. But because we entered into the forward contract, we can now get ($1.65/pound) x 654,545.46 pounds or $1,066,909. In other words, with the forward contract we would make a risk-free $6,909 over investing in the U.S. It is risk-free because we locked in the repatriation exchange rate at the time we made the investment by using the forward contract. Without the forward contract, we do not know when we make the investment what the repatriation exchange rate will be -- therefore we would be assuming a risk. We've just done covered interest arbitrage. J

But, that's why the forward rate must be determined by the interest rate differential. Arbitragers will engage in the covered interest arbitrage until the interest rate in the U.K. is forced down (increased supply of funding for U.K. securities) and the forward rate adjusts (increased demand for pound). There will also be impacts on the spot rate (pound will increase) and on domestic rates (rates will tend to increase).

Note also how the signs work algebraically. ($/L) * L = $ -- that's why I encourage you to show FX rates as so much of one currency per unit of the other. If you do that and work the signs algebraically, you will get the correct currency in the answer. If you don't get the currency you wanted, you have not done the calculation correctly. That's a way to "idiot check" your answers. J

Another type of arbitrage is called locational arbitrage. It is based on small discontinuities in quotes from different sources for the same currency. Suppose you are a trader at a currency trading firm. When you are called by another trader or call another trader yourself, both the bid and ask quotes are always given (that's the standard ondustry practoce abd a trader must be prepared for either to be accepted). So ... let's say you get two calls. From Firm A you get a bid of E1 = US$1.0457 and an ask of E1 = US$1.0465. The spread is $.0008. Firm B quotes you bid $1.0460 and ask of $1.0469. In this case, there is no opportunity for arbitrage even though the quotes are not identical. Firm A's bid price (what they will buy at) is less than Form B's ask price (what they will sell at).

But, if Firm B had quoted bid = US$1.0468 and ask of $1.0475 you have an opportunity for riskless profit if you act decisively. You would buy from A at $1.0465 and simultaneously sell to B at $1.0468. Your profit is $.0003 per Euro. Doesn't sound like much does it? But, run millions of Euros through it and you can make some money. Run 25 million Euros through it and you've made $7500 ... not bad for 15 seconds work. As you'd guess, this opportunity does not happen very often ... but sharp traders do take advantage of it when it does happen. The arbitrage will cause firm A to raise its ask price (increased demand) usually dragging the bid price along. Firm B will lower its bid price (increased supply) usually dragging its ask price as well. Through the arbitrage, the exchange rates of the firms will tend to come back together. Locational arbitrage is most common during movements of exchange rates when one firm may not be quite on top of the movement or has erred in spotting an inflection point.

Triangular arbitrage is yet a third. Think about cross-rates. They have to work out as they did because of arbitrage. Lets say that the Euro is quoted at $1.0456 and the Yen at $.009756. That infers that E1= 107.1751 yen. But let's say the quote is E1 = 106.9000 yen. Something is wrong. We could make a riskless profit by selling US$1,000,000 for yen getting yen 102,501,025. We then sell yen for Euros getting E getting E958,849.63. Finally we sell the Euros for dollars ending up with US$1,002,573.17. We've made over $2,000 risk free in about 15 seconds without any investment. Triangular arbitrage today is often spotted through computer programs that constantly compare currency quotes being received by the trading floor. As a practical matter, each trader may be looking at different currencies, so using the computer to link things makes it easy (and fast).

That arbitrage is not a frequent opportunity is what we'd expect. Arbitrage is available only when there is a discontinuity in the market. Given the high degree of market efficiency, that ought to be rare. As traders have become more technologically sophisticated, arbitrage opportunities have become increasingly scarce.

From a public policy perspective, it is far better in an economic sense to let the market make numerous small adjustments than to resist and have the large, sudden adjustment. Think of this as the difference between climbing down an embankment versus falling off a cliff. The small adjustments tend to be easily absorbed into an economy with minimal dislocations. One reason for this is that folks in business like predictability ... if one can anticipate a trend, business can be structured to take advantage of that. If the trend is resisted, it is harder to properly structure business dealings. Does one structure for the short-run stability or for the long-term given that the timing of the inevitable adjustment is not known?

Now let's explore a couple related issues about exchange rates.

Why Exchange Rates Change:

First, exchange rates are nothing more than the price of one currency expressed in terms of another. We are all familiar with the concept of expressing the price of something in terms of a currency ... the price of a gallon of gasoline, for example, represents an exchange rate ... one gallon of gasoline in exchange for some amount of money. For most of us, that price is in US dollars, but it could be in any currency.

Changes in capital flows can have a large affect on exchange rates. The balance of trade and services also can have an affect. Underlying those are two factors that are intertwined - inflation and interest rates.

The International Fisher Effect relates these two through a version of the Law of One Price. If the required real return (the return that increases purchasing power by the interest rate) on a risk-free investment is the same everywhere in the long run (and it must be or investment would flow to where it was highest until opportunities at that rate ceased to exist), then the nominal return for a risk-free investment must be primarily based on the inflation rate. That is, the market sets the nominal rate at a level sufficient to offset expected future inflation and net the required real return. If everything is in equilibrium and parities hold, this will be true. Distortions can occur in the short-run due to barriers to capital flows and other market imperfections, but in the long run the IFE seems to hold reasonably well.

For businesses, the market adds a risk premium to reflect the possibility of default (that is, the risk that the borrower will not repay the debt). In recent years, the market also adds a default premium to some countries' government debt rates. We used to think of sovereign debt (national government debt) as being immune to default (that is, we felt sovereign debt interest rate was the nominal risk-free rate) because the governments controlled taxes or could create money through deficit spending (provided a government did not borrow to fund the deficit).

The market no longer is quite so certain of that. Looking at what happened during recent crises has caused us to rethink the old view that the only difference in government interest rates is inflation. We now apply credit ratings to Sovereign debt in much the same manner as we do to commercial debt. Countries with lower credit ratings pay more in interest -- reflecting the greater likelihood of default. We have seen default premiums added to Mexican, Russian and Japanese government debt, for example.

That suggests that, perhaps, there always was some sort of premium for the possibility of default included in government interest rates. If that were true, then inflation expectations would not be the only difference in government rates. It would also suggest that government rates are not always the "risk-free" rate.

For places such as the U.S., the U.K. and most of the industrial world (and many other countries as well) that default premium, if it exists, is probably small enough to be ignored. For some countries it probably is not trivial. This is a brand new area and, frankly, we are just beginning to understand the comparative risks of different governments.

Right now, we in the U.S. are experiencing moderate inflation (based on CPI), between 2% and 3% depending on how it is measured. Interest rates have not fully adjusted so the real rate of return available here (at least for medium term debt) is lower than normal. Current U.S. government debt yields suggest our real rate of interest is in the 1 to 2% range (go to http://www.bloomberg.com/markets/rates/index.html). Look at the yield on inflation-indexed treasuries -- that approximates the real rate of return on those securities). That is low by world standards. Despite that, capital has been flowing towards the U.S.

It is a bit curious that capital flows to the US remain strong. This may be due to equity capital flows not being as influenced by interest rate movements compared to debt capital flows. This capital inflow is likely to continue.

Adding to that is the U.S. is a "safe-haven" for capital (even considering the recent corporate accounting issues) ... one of those hard to quantify factors. Weaknesses in other economies tend to cause capital to flow out from those places to safer ones. Folks in unstable areas want to hedge against local problems by moving funds from places where the economies are collapsing. Folks seek safe-haven countries to avoid loss of wealth by political action as well. Not all of the drivers are economic ... some can be social or political.

The introduction of the Euro and its acceptance as a reserve currency and as a safe-haven currency created a competition with the dollar for these functions. We can expect as the Euro takes a larger "market share" of those roles that the dollar will continue to experience some downward pressures. We have begun to see that happen and we can expect that over time it will continue to happen. The current depreciation of the dollar is likely related to a relatively weaker economy, in combination with reduced capital inflows. In addition, our real rate of risk-free return is low compared with other industrialized economies. That is a particular problem now as the Fed's response to the economic weakness is further lowering of interest rates.

The U.S. balance of trade and services has been negative for some number of years now (merchandise trade is a deficit, services trade a surplus most of the time). Ordinarily this would have put pressure on the dollar to depreciate. However, the capital flows and use of the dollar as a reserve currency have, in the past, more than absorbed the extra dollars in the global economy. We need to watch this with care in setting public policy here in the US ... it is seems reasonably clear that this is starting to change structurally

Given that things do tend towards equilibrium over time, the change in the value of the dollar vis-à-vis some other currency will tend to be at the rate of the difference in inflation rates. The interest rates will, over time, adjust to bring us back to the normal real rate of return. For folks outside the U.S., economy, the projected change in the value of the dollar must be factored into the nominal interest rate to arrive at expected return those folks will experience.

For those of us inside the U.S. economy (who face no exchange rate risk), we are faced at the moment with unusually low interest rates. That is one reason why the Fed actively manages interest rates - letting the real rate of return normalize. We would expect that lowering interest rates would also reduce capital flows towards the U.S. - perhaps we're just now beginning to see that.

That should increase pressure on the dollar to further depreciate and it would presumably cause capital to flow to other countries (which is consistent with observed reduced inflows to the US). Of course, no one can be certain that the countries to which it would flow would be those countries with the greatest need for economic development. Economic opportunity and economic need are not necessarily the same thing. As noted, this seems to be starting. The lag between interest rate change and economic effect can be 12-18 months.

Forecasting Exchange Rates:

So, can we forecast the value of the dollar? Well -- yes and no.

We can use certain parity relationships as forecast aids, but those should be viewed as "expected values" and not as realized outcomes. An expected value is the most likely outcome. The actual (realized) outcomes vary around the expected value in something approaching a normal distribution.

We can forecast its short-term value by looking at the forward exchange rates for the period that is of interest. Those rates represent the expected value of the dollar at the end of the forward contract period. If they did not, there would be an opportunity for traders to make a riskless profit through arbitrage. Remember, the spot-forward premium or discount is a function of the interest rate differentials between "risk-free" interest rates in the two countries for the same time period. Quite a few studies show that, over long periods of time, the forward rate is an unbiased estimate of the future spot rate. However, the dispersion of realized outcomes around that expected value (measured by the standard deviation) is often too large to comfortably go bare. The use of hedge tools locks in the rate.

To add to the complexity, at any given time there is likely bias in the forecasts. In the long run, the bias self-cancels, but in the short run it adds to forecast error. That is, use of the forward rate provides a systematic error - either too high or too low. If that were consistent, we could adjust the forecasts. Unfortunately it is not, the bias varies over time and we can not tell when it will change.

We can not forecast the long-range value of one currency in terms of another with great accuracy, but we can often predict the trend. The problem is that these longer-range forecasts of the trend are usually not accurate enough to make riskless decisions - the variation in outcomes is too high. For a forecast to be meaningful, it must tell us what the exchange rate will be at a specific point in time in the future. Knowing the average rate of trend really does not get to actionable information for specific transactions. It can be useful in looking at longer-term items such as economic exposure.

Solution Preview

There are a few major currencies that drive the global economy: dollar, pound, yen, etc. Exchange rates were fixed so that there was not a huge flux in the global economy. They basically all hovered around the their value against to dollar with small changes. This was to help rebuild Europe after WWII.

In the currency market people devalue a currency (selling large quantities) in groups to purchase it cheap knowing that it will balance out when it is purchased again at market value. Because countries were hesitant to adjust exchange rates made this a good buy. Now that there are floating rates (they ...

Solution Summary

Interpretation of class notes.

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