Dr. P.V. Viswanath
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# Exchange Rate Determination

### Foreign Exchange Market Quotes and Inferring Cross Quotes

Suppose we have bid and ask quotes for one currency in terms of two other currencies. How can we use this to infer the cross bid and ask quotes for those two currencies?

Example 1: Suppose the following quotes are available:

 Bid Ask AUD/USD 0.7733 0.7738 USD/JPY 108.81 108.86

That is, you can sell A\$1 for US\$0.7733 and buy A\$1 for US\$0.7738; similarly, you can buy US\$1 for 108.86 yen and sell US\$1 for 108.81 yen. The question is, what is the cross-quote for the Australian dollar against the yen? That is, at what price (in yen) can you buy and sell Australian dollars.

Let us consider them one by one. Take the case of selling Australian dollars for yen. This can be accomplished by selling A\$1 for US\$0.7733 (bid price) and then converting the US\$0.7733 into yen at the rate of 108.81 yen per US\$ to get (108.81)(0.7733) or 84.14277 yen.

Similarly, you can buy A\$ for yen by buying A\$1 for US\$0.7738; the necessary dollars can be obtained by buying US\$0.7738 at the rate of 108.86 yen/\$ or a total of (0.7738)(108.86) = 84.23587 yen. That is, the cross rate is 84.14277/84.23587. In other words, simply multiply the bid rates together and the ask rates together. However, before you do that, make sure that the quotes are in the appropriate form -- thus, above, we have the quotes in AUD/USD format (US\$ per A\$) and USD/JPY format (yen per US\$). In this case, multiplying the formats (so to speak), we get AUD/JPY or yen per A\$, which is what we're looking for. This allows us to apply our rule.

Example 2: Take the following example from Shapiro, Multinational Financial Management (7th ed., page 253).

The quotes are:

 Bid Ask USD/Real 0.9955 1.0076 USD/Baht 25.2513 25.3986

We need the Real/Baht rate, that is, the rate at which Reais can be bought at sold using Bahts. We first recast the table in the desired form:

 Bid Ask Real/USD 1/1.0076 1/0.9955 USD/Baht 25.2513 25.3986

This is accomplished by flipping the first line from a USD/Real format to a Real/USD format. In so doing, we need to take the reciprocals of the original quotes; furthermore, the original bid becomes the ask in the new format and vice-versa. This should be clear because the original quote of 0.9955 indicates that a person can sell US\$1 for 0.9955 reais, which is the same as saying that he can buy 0.9955 reais for US\$1 or 1 reais for \$(1/0.9955). This is another way of saying that the dealer is willing to sell reais for \$(1/0.9955), or that \$(1/0.9955) is the ask price for reais in US dollars.

In any case, now that we have the rates in the desired format, we can get the bid and ask Real/Baht quotes as (1/1.0076)(25.2513) and (1/0.9955)(25.3986) or B25.0608/Real and B25.5134/Real, which is the solution that the textbook provides.

### Foreign Exchange Market Intervention

Sterilized vs. Unsterilized Interventions:
Interventions can be sterilized or unsterilized. In a sterilized intervention, the central bank offsets the purchase or sale of foreign exchange by selling or purchasing domestic securities so as to keep the domestic interest rate at its target. The idea is to somehow affect the exchange rate, but still not affect interest rate. However, many argue that, since the domestic interest rate usually is considered the main determinant of the value of the domestic currency, it must change in order to influence the exchange rate. A sterlized intervention seeks to affect exchange rates without affecting fundamental factors. In other words, the intervening authority is trying to have its cake and eat it, too.

Suppose you begin with the demand and supply curves DD and SS. At this point, the equilibrium exchange rate is e0. Now the government decides that it wants a lower interest rate and therefore increases the money supply. This causes the supply curve to shift inward, because at the higher level of money supply, US prices will start to move up. Hence, at a given exchange rate, investors will be willing to supply fewer euros. On the other hand, the demand for euros at each level of the exchange rate will be greater, also for the same reason. Consequently, the new demand and supply curves will be DD' and SS' with the new equilibrium exchange rate being e1.

Now, suppose that the US government desires to maintain the old exchange rate of e0. However, at this rate, there will be an excess demand for euros; hence the US government will have to be willing to supply euros by buying dollars. Typically, though, the government will buy dollars by supplying not euros, but rather euro-denominated securities because this is how it keeps its euro reserves (rather than as cash). However, if it stops at this point, then the US money supply will decrease because of the purchase of dollars. This will cause interest rates to move back up to where they were. This would be an unsterilized intervention. In this case, the exchange rate can be kept at e0, but only because it is willing to go along with fundamental factors consistent with the lower exchange rate of e0 (i.e. a stronger dollar and a higher interest rate).

However, if the government is not happy with the impact of the exchange market intervention on domestic money supply and interest rates, it will try and sterilize the impact of the intervention by open market purchases of dollar denominated Treasury bills. By buying Treasury bills and paying for them with dollars, this would increase the availability of dollars and thus offset (or sterilize) the contraction in the dollar supply caused by the foreign market intervention.

Although this sterilization is successful in maintaining the status quo in the domestic interest rate market (i.e. keep the interest rate low), the question is, what happens to the exchange rate? Will it stay at the lower value of e0 (stronger dollar) or will it move back to e1 (weaker dollar)? The answer lies in how investors react to the impact of the sterilized intervention on their asset portfolios. Before the government intervention, investors had a certain amount of dollar-denominated and euro-denominated securities. Now, after the sterilized intervention, they have fewer dollar-denominated securities (because the government has bought Treasury bills in its open-market operations) and a greater amount of euro-denominated securities (because the government has sold euro-denominated securities in its foreign market intervention).

If investors do not see any difference between holding euro-denominated and dollar-denominated securities, then the exchange rate will stay at e1. The US government effort to bring the exchange rate back to e0 will be unsuccessful. This is because from the viewpoint of investors, there is no change in the quantity of euros supplied. The only change has been in the ratio of euro-denominated and dollar-denominated securities held by investors; but if investors don't differentiate between the two, that is a change that is not a real change.

However, suppose that investors do not think of dollar-denominated and euro-denominated securities as being perfect substitutes. Then, they would find themselves holding "too many" euro-denominated securities. They will, therefore, try to sell these euro-denominated securities to rebalance their portfolio. As a result, the euro will fall in value (since there is nobody to buy these securities at the e1 exchange rate), and the dollar will be strengthened. If this happens, then the policy of sterilized intervention will have been successful, i.e. the government will have been able to influence the exchange rate without having to modify its domestic interest rate policy.

The other way in which sterilized intervention can work is if the government's intervention in the foreign exchange market convinces investors that the future exchange rate will be lower (i.e. the dollar will be stronger) because they believe that the government will act to change the fundamentals in that direction (say, by increasing the rate of growth of the US economy). If so, they will bid the dollar up on the strength of expectations of the future value of the dollar; in other words, the changed expectations will pull the demand and supply curves back to their original DD and SS values. (See the Fed publication explaining the real effects of sterilized interventions for more discussion on this topic.)

(Is this an example of sterilized intervention? Read this Economist article.)

### International Parity Relationships

Spot Foreign Exchange Markets are interconnected with Forward Forex Markets; similarly both of these are connected with the markets for loans, and all of these, in turn, are connected with the markets for goods and services, in general.  In what follows, we will try to establish the concepts that describe the nature of these interrelationships.

### Effects of Devaluation

This part is based on Paul Krugman and Maurice Obstfeld, "International Economics: Theory and Policy," 4th edition, p. 502ff:

To devalue the currency, the central bank declares itself willing to buy and sell currency to maintain the new exchange rate. A rise in the level of the exchange rate (the number of units of domestic currency needed to purchase one unit of foreign currency) makes domestic goods and services cheaper relative to foreign goods and services, assuming that domestic and foreign prices remain constant. Therefore, domestic output moves to a higher level. This increases the level of transactions, causing an increased demand for money. If the central bank does not intervene, this raises the interest rate above the world interest rate. To maintain the exchange rate at the higher level, the central bank will need to intervene and purchase foreign assets (and increase the supply of the domestic currency). This causes the domestic money supply to increase. Devaluation thus can cause a rise in output, a rise in official reserves and an expansion of the money supply.

The effect of a devaluation on the balance of payments depends on several factors (this part is based partly on Carbaugh, International Economics, Chapter 15):

The elasticity approach: The extent to which a devaluation affects exports and imports depends on the price elasticity of demand for exports and imports. The Marshall-Lerner condition says that devaluation will improve the trade balance if domestic demand elasticity for imports plus foreign demand elasticity for exports is greater than 1. Simply put, if the demand elasticity for exports is high, the reduction in the foreign currency price of exports will stimulate demand, while a high demand elasticity for imports will mean that the higher domestic currency price of imports will affect demand for imports negatively. The effect on the trade balance depends on the effect of devaluation on both exports and imports.

The J-curve effect says that in the short run, devaluation will worsen the trade balance, but with time the balance will improve (3-5 years). Recognition lags, decision lags, delivery lags, replacement lags and production lags affect the amount of time for the improvement to take effect -- in the short run, prices will change, but quantities will not change; thus, for example, prices of exports will drop, but the quantity exported may not. The effect of devaluation also depends on how quickly producers pass on higher or lower costs to their customers. There is some empirical evidence for the J-curve.

The absorption effect: This approach emphasizes the impact of devaluation on the spending behavior of domestic economy. The balance of trade is the difference between total domestic output and domestic absorption (spending) (From National Accounts, we know that Y = C+I+G+X-M; defining C+I+G=A (absorption), we get X-M= Y - A). A positive balance means that the output exceed domestic spending, while a negative balance means that spending exceeds total production. A devaluation will only improve the trade balance if output rises relative to domestic absorption; if an economy is operating below capacity, a devaluation will shift resources into export production and encourage spending on import substitutes.

However, if an economy is operating at full employment, total production cannot rise; hence domestic demand will not change. This will cause a situation of excess demand, leading to a rise in the domestic price level. If, in equilibrium, the increase in domestic prices is equal to the increase in the exchange rates, there will be no effect on the trade balance, since real goods prices have not changed. On, the other hand, if the money supply does not accommodate the increase in prices, there might be an intermediate situation, where domestic prices rise, but in a smaller proportion than the rise in exchange rates. Domestic demand would probably be smaller because some money will have to be diverted from consumption to real money balances. This could, then, lead to an improved trade balance, even if the economy is operating at full employment. The trade balance would be cut by a reduction in domestic demand. This assumes, however, that restrictive monetary policy does not have a negative effect on domestic production (Michael Michaely, "Relative Prices and Income-Absorption Approaches to Devaluation: A Partial Reconciliation," American Economic Review, v. 50, no. 1, March 1960, pp. 144-147).

The monetary approach: Elasticity and absorption approaches apply only to the trade balance; the monetary approach also includes the capital account. Considered from this broader perspective, a devaluation may induce a temporary improvement in the balance of payments. Devaluation increases the domestic price level (as explained above), increasing demand for money and drawing foreign capital flows (because of higher interest rates that result; also see above). However, in the long run, the inflow of money increases domestic spending, increasing imports and returning the economy to the starting point. The ultimate conclusion of the monetarists is that devaluation affects the real economy only temporarily; the only long run effect is to raise the domestic price level.

Why devalue? So why would a country want to devalue its currency?

1. If price elasticities of demand for imports and exports are sufficiently large, a devaluation of the currency would improve the country's trade balance. This would allow the country to accumulate reserves. This might be seen as being desirable even though the devaluation would cause
2. This can improve domestic output, which usually means improving employment. Even if this devaluation is suboptimal in the sense of selling domestic goods unduly cheaply and buying foreign goods unduly dearly, the government may deem it worthwhile, given that employment improves an individual's well-being much more directly than a handout. And, in any case, the cash-handout may be difficult to implement because of the difficulty of locating unemployed workers.
3. The government is interested in stimulating the export sector and the import-substitution sector, perhaps for infant industry reasons.
4. Alternatively, stimulating the export sector and the import-substitution sector may encourage employment in those sectors, which, for reasons given in 2. above, may be the optimal way of dealing with poverty in those sectors.

Why keep a currency dear? Essentially this would involve invoking the flip side of the arguments above.