国际金融考试题

Problem Set

1. Exchange Rate Forecasting

Assume that Company A owes Company B 1,000,000 GBP in 90 days. The current (spot) exchange rate is 1.50USD/GBP, and the 90-days’ forward exchange rate is 1.53USD/GBP. Suppose that Company A can enlist the services of two forecasting companies, C and D. Company C predicts that the exchange rate will be 1.65USD/GBP 90 days later, whereas Company D predicts that the exchange rate will be 1.51USD/GBP. After 90 days, the exchange rate turns out to be 1.55USD/GBP.

Question:

(a) How do we measure the accuracy of forecast, and which forecast is more accurate? (b) But which forecast is more economically “valuable” for Company A, and why?

2. The Real Exchange Rate and the Real Interest Rate Differential

Most of the time we will give a time series graph of the real exchange rate and the real interest rate differential, to convince the readers that there should be a strong relationship between these two variables.

For instance, if the real exchange rate is defined using the nominal exchange rate expressed as foreign currency per domestic currency (USD, for instance), increases (decreases) in the real exchange rate represent real appreciations (depreciations) of the dollar relative to foreign currencies. Usually, it will be apparent that when the dollar is relatively strong (weak) in real terms, the U.S. real interest rate seems relative high (low) compared to foreign real interest rates.

Question:

(a) Why should the level of the real exchange rate be related to the differential between the real interest rates on different currencies? (Hint: convert the uncovered interest rate parity from a relationship between nominal interest rates and nominal rates of depreciation into a relationship between real interest rates and expected real rates of depreciation.)

Even though the link between the expected real interest rate differential and the expected rate of change of the real exchange rate being established, we have not yet generated the relationship presented in the graph, i.e., the level of the real exchange rate and the real interest rate differential.

Assume that the real exchange rate moves around over time, but it is expected to return eventually to its unconditional mean. We can model the real exchange rate experiencing transitory deviations from its unconditional mean as an autoregressive process, which can be represented in the follow equation:

11ln (ln ), 1.t t t q q q q ρερ++=+?+< (1) In the above equation, q represents the long-run equilibrium of the logarithm of the real exchange rate, which is its unconditional mean. The innovation in the real exchange rate is 1t ε+. This innovation represents the change in the real exchange rate that is due to new

information between period-t and period-1t +, and it consequently has a mean of zero. The coefficient ρ, which is between 0 and 1, tells us how fast the real exchange rate converges to its unconditional mean. When ρ is close to 1, deviations of the real exchange rate from its long-run equilibrium can be quite persistent.

Question:

(b) For the AR(1) real exchange rate process, how can we interpret the result derived in (a)? (c) How do we test the relationship between the Real Exchange Rate and the Real Interest Rate Differential, and why does this link appear to be so weak empirically?

3. An Asset Market Approach to Exchange Rate Determination

The asset market approach to the exchange rate determination recognizes that the exchange rate is the relative price of two monies, which makes the exchange rate an asset price, since monies are assets. Hence exchange rates should fluctuate randomly, and the value of the exchange rate of, say dollar per euro, should be determined by people’s willingness to hold the outstanding supplies of dollar- and euro-denominated assets. These demands, in turn, depend on the expectations of the future values of these assets.

We can capture these reasoning in a simple equation:

1[],t t t t e f aE e +=+ (1)

where t e is the logarithm of the current nominal exchange rate expressed as domestic

currency per foreign currency, t f is the value of market fundamentals at time-t , and a is a coefficient less than but may be close to 1.

Equation (1) states that the nominal exchange rate depends on its expected values prevailing in the next period and on the current fundamentals.

Question:

(a) Derive the relationship between the current exchange rate and all information about current and expected future fundamentals. What is the economic intuition?

In the monetary exchange rate model, there are distinct demands for non-interest-bearing domestic and foreign currencies; the demand for nominal money arises from the demand for real money balances. That is, people are only concerned with the real value of the nominal money they are holding.

Suppose that equilibrium in the domestic money market can be described as:

0,t t y t i t m p b b y b i ?=++ (3)

where ,

t t m p and t y are the logarithm of the domestic money supply, price level, and real income, while t i is the domestic nominal interest rate. The foreign money market

equilibrium can be defined analogously using an asterisk to denote the foreign variables:

0.t t y t i t m p b b y b i ?????=++ (4) For simplicity, assume that the positive b parameters are the same in the two countries. Question:

(b) Derive the relation under the monetary theory of the exchange rate determination. And what is the economic intuition?

The flexible-price monetary approach (exchange rate determination) model assumes that the prices of goods are fully flexible and that PPP holds at all times using a broad price index. These are extreme assumptions given that the validity of PPP has been questioned. One natural modification is to assume that PPP holds, but only for tradable goods.

Assume that the domestic composite consumption goods, C , can be written in a Cobb-Douglas form:

1,01,T N C C C ααα?=<<

where T C and N C denote the consumption of tradable and non-tradable goods, with

weights (i.e., expenditure shares) α and 1α?, respectively. The foreign composite consumption goods, C ?, can be defined in the same way:

1,01,T N C C C ααα?

??????=<<

with “*” variable denotes the foreign analog.

Question:

(c) Show the result that the consumption-based price index, P , can be written as:

1,N N P P P αα?=

where P is the minimum nominal expenditure, T T N N Z P C P C ≡+ such that

11T N C C C αα?==, given prices of the tradable and non-tradable goods. In this case, what is

the relationship between the logarithm of nominal exchange rate and those fundamental variables?

4. Here is our (short-run) open economy model: (i) UIP: e E E R R E ?

?=+; (ii) Money Market Equilibrium: (,)M L R Y P

=, with 0R L < and 0Y L >; (iii) Goods Market Equilibrium: Y D =; where ()(,)D C Y T I G CA q Y T ≡?+++? is the aggregate demand for domestic goods and services, with 01Y C << and 0Y CA <,

respectively. The nominal exchange rate is denoted as E, and the real exchange rate, q, is

defined as:

EP

q

P

?

≡. That is to say, the nominal (real) exchange rate is defined as the price

of foreign currency (basket) in terms of the domestic one.

Question:

(a) We have assumed that a real depreciation of a country’s currency improves its current account, or 0

q

CA>. But the validity of this assumption depends on the response of export and import volumes to real exchange rate changes. Please derive the condition, i.e., the Marshall-Lerner condition for the assumption as above to be valid.

(b) Derive the slopes of the DD and AA equations in the (,)

E Y space, respectively. (c) Assume that the XX curve shows all of the combinations of the exchange rate and output at which the current account balance would be equal to some desired level, say (,)0

CA q Y T

?=. Show the result that the XX curve slopes upward and is flatter than the DD curve.

(d) Assume that the economy starts at the long-run equilibrium. At time-

t, there happens to be a permanent increase in labor productivity in the domestic country. Describe the effects of a permanent increase in labor productivity on all of the endogenous variables, and explain why.

(e) Suppose that there is a permanent increase in R? at time-

t. Redo all of the jobs as in part (d).