Models Used for Exchange Rate Determination

The models that try to explain current value of currency are usually based on simple economic facts. The most prevailing and widely know theory is Purchasing Power Parity (PPP). This theory was first introduced by Swedish economist Gustav Cassel in 1922. Cassel's PPP is based on the law of one price which argues that goods expressed in the same currency should have the same price. This rule allows us to make a direct comparison between different currencies. For example if the price of one barrel of oil is $15 in the U.S. and it is 30CHF in Switzerland then the exchange rate between these two countries should be 0.50 USD/CHF. Therefore spot rate is given by following formula:

St = Poil,US / Poil,SWIT = $15/CHF 30 = 0.50 $/CHF

There is a wide criticism of this version of PPP since it ignores transportation costs, tariffs, or other obstruction to the free flow of trade. Hence the relative version of the PPP has been suggested. Relative PPP states that the rate of change in the prices of products should be similar when measured in a common currency, as long as transportation costs and trade barriers are unchanged. The following formula reflects the relationship between relative inflation rates and changes in exchange rate:

St+T /St = (1 + Id) / (1 + If)

where,

If = (Pf,t+T / Pf,t ) - 1

(foreign inflation rate from t to t+T)

and

Id = (Pd,t+T / Pd,t ) - 1

(domestic inflation rate from t to t+T.)

Theory of Interest Rate Parity states that the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate. Interest rate parity plays an essential role in foreign exchange markets, connecting interest rates, spot exchange rates and foreign exchange rates. The relationship can be seen when you follow the two methods an investor may take to convert foreign currency into U.S. dollars. Option A would be to invest the foreign currency locally at the foreign risk-free rate for a specific time period. The investor would then simultaneously enter into a forward rate agreement to convert the proceeds from the investment into U.S. dollars, using a forward exchange rate, at the end of the investing period. Option B would be to convert the foreign currency to U.S. dollars at the spot exchange rate, then invest the dollars for the same amount of time as in option A, at the local (U.S.) risk-free rate. When no arbitrage opportunities exist, the cash flows from both options are equal.

A Theory of Foreign Exchange Rates that states that the expected Future spot foreign Exchange rate t periods from now equals the current t-period forward exchange rate. This theory simply asserts that forward rates exclusively represent the expected future rates.

There is another important theory called as the International Fisher Effect (IFE) named after the economist Irving Fisher. It uses nominal interest rate differentials rather than inflation rate differentials to explain exchange rate movements, but it is closely related to the PPP theory because nominal interest rates are highly correlated with inflation rates. It states that in the long run, inflation and nominal interest rates move together, implying that real interest rates are stable in the long term. The change in the spot exchange rate hence given by the following equation:

St+T /St = [1 + id(T/360)] / [1 + if(T/360)]

where,

i_f = foreign interest rate for T days;
i_d = domestic interest rate for T days.

Another approach is Balance of Payments (BOP) which sees foreign currency as the price of any commodity. In the simplified version of BOP the capital account of a country is defined as the difference between exports and imports as follows:

CA = X - M

where, X is exports and M is imports.

In general, at higher real exchange rates we should expect more exports and fewer imports, and higher current account surpluses; while at lower real exchange rates, the opposite should occur. According to the balance of trade approach, the exchange rate moves in the required direction to compensate a trade imbalance. For example, suppose the trade balance is in equilibrium. An increase in domestic income leads to an increase in demand for imports causing a trade deficit. Then, we should expect the exchange rate to depreciate to correct this imbalance. Using a similar argument, we should also expect a depreciation of the domestic currency, following an increase in domestic prices, a decrease in foreign prices, or a decrease in foreign income.

In the Monetary and Portfolio Approaches, exchange rate movement is thought to eliminate any monetary disequilibrium resulted from changes in money supply and demand. In the pure monetary approach following equation is used to explain to exchange rate behavior,

MS V = P Y

where, V is the velocity of money, P is the price level, Y is real output and MS is the supply for money, Using this equation with the PPP theory one can simply drive the following to explain spot rate changes:

St = (Vd/Vf) x (Yf/Yd) x (MSd/MSf)

Taking an example of an increase at domestic money supply (MS_d) as oppose to foreign money supply (MS_f), one can expect an increase in the spot exchange rate.

The portfolio approach expands the monetary approach by including other financial assets. The portfolio approach postulates that in addition to the domestic money supply, the exchange value is determined also by domestic and foreign financial securities. In this approach, the wealth (W) is distributed across money (M) holdings, domestic bonds (B), and foreign bonds (B*), which is expressed by following formula:

W = M + B + SB*

Supposing the monetary authorities decide to increase the money supply, the domestic interest rate falls. With a lower interest, households are no longer satisfied with their portfolio allocation. The demand for domestic bonds falls relative to other financial assets. Households shift out of domestic bonds. They substitute into domestic money and foreign bonds. Because of the increase in demand for foreign bonds, the demand for foreign currency rises. All other things constant, the increased demand for foreign currency causes the domestic currency to depreciate.

All the theories above simply try to explain the movements in the exchange rate basing on the rule that economies are tend to balance back to equilibrium point in response to the drifts at any particular economic parameter. The movement towards the equilibrium point is the result of the actions of traders who are buying and selling currencies for arbitraging purposes. We will now see whether these theories can be utilized for forecasting purposes.