Problem Set 4

Question 1

what is the law of one price?

Answer 1

The law of one price states that if identical products or services can be sold in two
different countries, and no restrictions exist on the sale or transportation costs of moving the product
between the countries, the product’s price should be the same in both countries. Comparing prices
across countries requires only a conversion from one currency to the other. For example,
𝑃$×𝑆 = 𝑃£

Question 2

what is absolute purchasing power parity?

Answer 2

If the law of one price were true for all goods and services, the
purchasing power parity exchange rate could be found from any individual set of prices. By comparing
the prices of identical products denominated in different currencies, one could determine the “real” or
PPP exchange rate that should exist if markets were efficient. This is the absolute version of the theory
of purchasing power parity. Absolute PPP states that the spot exchange rate is determined by the
relative prices of similar baskets of goods

Question 3

what is relative purchasing power parity?

Answer 3

If the assumptions of the absolute version of PPP theory are relaxed a
bit more, we observe what is termed relative purchasing power parity. This more general idea is that
PPP is not particularly helpful in determining what the spot rate is today, but that the relative change in
prices between two countries over a period of time determines the change in the exchange rate over
that period. More specifically, if the spot exchange rate between two countries starts in equilibrium, any
change in the differential rate of inflation between them tends to be offset over the long run by an
equal but opposite change in the spot exchange rate

Question 4

what is the Fisher effect?

Answer 4

The Fisher effect, named after economist Irving Fisher, states that nominal interest rates in each country
are equal to the required real rate of return plus compensation for expected inflation. More formally,
this is derived from (1 + 𝑟)(1 + 𝜋) − 1:
𝑖 = 𝑟 + 𝜋 + 𝑟𝜋
where 𝑖 is the nominal rate of interest, 𝑟 is the real rate of interest, and 𝜋 is the expected rate of
inflation over the period of time for which funds are to be lent. The final compound term, 𝑟×𝜋, is
frequently dropped from consideration due to its relatively minor value. The Fisher effect then reduces
to (approximate form):
𝑖 = 𝑟 + �

Question 5

how do we empirically test the Fisher effect?

Answer 5

To empirically test the Fisher effect, forecasts of future rates of inflation are needed (not what inflation
has been). Predicting the future can be difficult. Empirical tests using ex-post national inflation rates
have shown that the Fisher effect usually exists for short-maturity government securities, such as
Treasury bills and notes. Comparisons based on longer maturities suffer from the increased financial risk
inherent in fluctuations of the market value of the bonds prior to maturity. Comparisons of private
sector securities are influenced by unequal creditworthiness of the issuers. All the tests are inconclusive
to the extent that recent past rates of inflation are not a correct measure of future expected inflation.

Question 6

theory of interest rate parity

Answer 6

The theory of interest rate parity (IRP) provides the linkage between the foreign exchange markets and
the international money markets. The theory states: The difference in the national interest rates for
securities of similar risk and maturity should be equal to, but opposite in sign to, the forward rate
discount or premium for the foreign currency, except for transaction costs.

Question 7

covered interest arbitrage

Answer 7

The spot and forward exchange markets are not constantly in the state of equilibrium described by
interest rate parity. When the market is not in equilibrium, the potential for “riskless” or arbitrage
profits exists. The arbitrager who recognizes such an imbalance will move to take advantage of the
disequilibrium by investing in whichever currency offers the higher return on a covered basis. This is
called covered interest arbitrage (CIA). CIA is possible when interest rate parity does not hold. An
example of a basic CIA strategy would be to (1) convert dollars at the current spot into a foreign
currency, (2) invest the foreign currency in a risk-free investment in the foreign country, (3) simultaneously
sell the future proceeds of the foreign risk-free investment in the forward market, and finally (4) calculate
the opportunity cost of the funds at the U.S. risk-free interest rate. When done correctly, the difference
between the revenue in step 2 should exceed the cash-outflows in steps 3 and 4.

Question 8

unbiased predictor

Answer 8

An “unbiased predictor” means that the distribution of possible actual spot rates in the future is
centered on the forward rate. The fact that it is an unbiased predictor, however, does not mean that the
future spot rate will actually be equal to what the forward rate predicts. Unbiased prediction simply
means that the forward rate will, on average, overestimate and underestimate the actual future spot
rate in equal frequency and degree. The forward rate may, in fact, never actually equal the future spot
rate.

Question 9

rationale for relationship between spot and forward rate

Answer 9

The rationale for this relationship is based on the hypothesis that the foreign exchange market is
reasonably efficient. Market efficiency assumes that (1) all relevant information is quickly reflected in
both the spot and forward exchange markets; (2) transaction costs are low; and (3) instruments
denominated in different currencies are perfect substitutes for one another. Empirical studies of the
efficient foreign exchange market hypothesis have yielded conflicting results. Nevertheless, a consensus
is developing that rejects the efficient market hypothesis. It appears that the forward rate is not an
unbiased predictor of the future spot rate and that it does pay to use resources to attempt to forecast
exchange rates