What Does Undervalued or Overvalued Currency Mean?
Parity means...
How does parity come about in theory?
Does parity come about in fact?
Absolute Purchasing Power Parity (PPP)
The Law of One Price Applied to Exchange Rates
Absolute PPP condition: Pus = S x Psoc
Simply stated: a dollar spent in one country should buy the same quantity of goods as that dollar spend in another country - at the existing exchange rate.
Example 1:
PPP1
Example 2: Assume that absolute PPP exists. If the Price level in the US is 90 and the price level in SOC is 60. What should be the spot rate of exchange?
Pus/Psoc = Spot
Pus/Psoc = $/SOC
90/60 = $1.50/SOC
The Role of Arbitrage in Maintaining One Price
Arbitrage: buying in one market and selling in another market to take advantage of price differences.
PPP2
The dollar price of a cup of coffee in SOC should be: Pus = S x Psoc
Pus is the price of coffee in the US
Psoc is the price of coffee in SOC
S is the spot exchange rate
If these are cups of coffee, is there a problem?
Can we generalize for all goods? We can try.
If all goods are counted, P becomes the price level of all goods
The relationship is now: Pus = S x Psoc
Transposing: S = Pus / Psoc
The spot exchange rate is a ratio of the US price level to the SOC price level.
If the price level in the US = 1 and in SOC the price level is 3, the exchange rate will be 1/3 dollars per SOC.
Problems with PPP (PPPP - purchasing power parity problems)
Are all goods traded?
Are there transportation costs?
Are there tax differences?
People don't necessarily buy the same mix of goods - so the price levels won't be measuring the same goods.
The real exchange rate - adjusted for price level differences.
Only when the spot rate is equal to the ratio of price levels will PPP exist.
How good is the concept of PPP in explaining exchange rates?
In the short run it is not a good indicator of PPP
In the longer run, it is better.
The Big Mac Index
Big Mac Jan, '06
The ratio of the SOC price to the US price is the implied spot exchange rate.
The actual spot exchange rate is ...
The percent overvalued or undervalued...
Another look, 2003 data:
BigMacIndex
Relative Purchasing Power Parity
More general concept but it avoids the problems with absolute PPP
People buy the same basket of goods and services
Instead of some absolute relationship of the price levels in a country, it just uses relative changes in the price level as an indicator of changes in the exchange rate.
In words: The PERCENTAGE change in the exchange rate for two countries equals the difference in their inflation rates.
Relative PPP says: %∆Pus = %∆S + %∆Psoc
Example: If the rate of inflation in the US is 6% and the rate of inflation in SOC is 2%, assuming that RPPP holds, what can we expect to happen to the SOC?
6 = 2 + 4. We would expect the value of the SOC to appreciate 4%.
Useful for "back of the envelope" calculations
If you know that the Argentinean rate of inflation will be about 10% and that of the US to be about 2%, you can expect the Peso to depreciate about 8% in the coming year.
Evaluation of PPP
It is, at best a LONG RUN explanation of how exchange rates adjust.
Evidence suggests that once a deviation in PPP takes place, it takes 3 to 7 years to move HALFWAY back to PPP!
What this means is that in the short run, the effects of other variables play a larger role in determining exchange rates.
Relative PPP explains better than absolute PPP.
As trade becomes more open, PPP should be a better indicator.
If PPP is not a good indicator of ex∆ rate movements, is hedging more important?
International Interest Rate Parity
Foreign exchange rates and interest rates are related.
PPP adjustment takes place because of arbitrage activity.
Hinderances to trade in goods reduces PPP
There are fewer restrictions on financial assets (and the costs of trading assets are lower).
Therefore we should see more interest rate parity.
Realized return - depends on changes in the exchange rate
Covered Interest Rate Parity
Rate when all exchange rate exposure is covered
The condition for CIP:
Rus = Rsoc + (F-S)/S
The difference in the interest rates must equal the forward premium or discount.
Example 1: A covered interest rate transaction:
If the US person buys a 1 year asset for $1m that will pay 7% in British pounds (when they could get 5% in the US)
The person buys $1m/S pounds asset - buying pounds in the spot market.
The person earns $1m/S (1 + Ruk)
The person hedges by selling pounds in the futures market 1yr. This assures the return.
Example 2: a. The spot rate is $1/SOC and the forward rate is $1.04. Is there a forward premium or discount for the SOC and what is the percent?
b. If the Rate of interest in SOC is 2% and the rate of interest in the US is 7%, what is the covered rate of return for an American investor who places covered funds in SOC?
c. Does CIP hold in this case? If not, which way will funds move?
Forward premium of 4%
The covered rate of return is 6%: a 2% interest return plus a 4% premium.
CIP does not hold 7 ≠ 2 + 4 Since the yield is higher in the US, funds will move to the US.
If the rates of return are not equal (after the forward discount or premium), arbitrage opportunities exist.
If the realized returns are greater in the UK:
In the foreign exchange SPOT market the ₤ demand rises, exchange rate rises.
In the foreign exchange Futures market the ₤ supply rises, the forward rate falls.
This equalizes the realized returns
Thus, the return will be F/S(1+ Ruk)
Covered interest rate parity holds quite well.
Uncovered Interest Rate Parity
When people do not cover exchange risk exposure
Assuming ceteris paribus
equal risk, taxes, terms to maturity, & liquidity
Uncovered parity exists when Rus = Ruk + %∆Se
In words: the investor will be indifferent when the return in the US is equal to the return in the UK after adjustment for exchange rate changes.
The term %∆Se will be positive if the dollar is expected to depreciate.
The term %∆Se will be negative if the dollar is expected to appreciate.
Example: Assume that the US interest rate is 6% and the interest rate in SOC is 8%. The spot rate is $1/1SOC and the expected future spot rate is $0.97/1SOC. What is the uncovered rate of return for an American investor who places funds in SOC? Does UIP hold? Which way will money flow?
The uncovered rate of return: Rus = Rsoc + %∆Se, 8+(-3) = 5%
UIP does not hold, 6≠5, money will flow to the place with the higher return.
Does UIP hold?
Quite well - normally especially if there are unrestricted investment flows.
One big problem - risk
If the value of a country's currency if highly variable, there will be a risk associated with determining the expected %∆Se
The real UIP condition is Rus = Ruk + %∆Se + RP (where RP is the risk premium).
The risk premiums may explain some of the deviations from UIP
Other restrictions: capital controls or limits on foreign ownership
Foreign Exchange Markets and Efficiency
Being able to anticipate reliably matters
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Adaptive Expectations
Looking only at past history to anticipate the future
Trend lines
Statistical best- fit trend lines
Simple guesses
All methods have costs
Problems with adaptive expectations
Ignores new (current) information about the future
Difficult to know which technique predicts best.
There is an issue with Data Mining - you can always find a PAST explanation for why something happens - spurious correlation problems.
Rational Expectations
Uses all past and current information as well as relevant information about how markets work
Advantages
Besides historical information it uses current info and how markets work
Generally better at anticipating future market changes
Disadvantages
Simplifying assumptions show the weaknesses
People have the same information
People have the same understanding of how the market in question works
This is an attempt to deal with the fact that each individual will anticipate differently - forcing participants to anticipate the all the different individual anticipations.
Efficient Market Hypothesis
Prices and rates of return on assets reflect all relevant information -
including past and present information and
information about how markets function.
If this were not true profitable arbitrage opportunities exist.
Implications of efficient market hypothesis (EMH)
1. actual returns are related to expected returns
2. some factors are more relevant in these expectations than others
3. it is very difficult to consistently earn higher than average returns (given the risk level)
CIP and UIP will hold only if the forward premium is equal to the expected appreciation or depreciation
(F-S)/S = %∆Se
and, after transformation, this condition holds if F = Se (Forward = Expected Spot)
Evidence - Generally this condition holds that the forward rate = the spot rate but...
Risk premiums can cause a divergence.
Real Interest Rate Parity
So far, only nominal value have been analyzed but
Real values matter
Real values are nominal values adjusted for price level changes.
If I expect 5% nominal R in the US and 2% inflation. In the UK I expect a 10% nom return and 4% inflation, then...
Do Real Interest Rates Move Toward Parity over Time?
RIP will hold if both Relative PPP (%∆Pus - %∆Psoc = %∆Se)
and if UIP holds (Rus - Ruk = %∆Se)
So, RIP exists if Rus - %∆Puse = Ruk - %∆Puke
If Real ius = Real iuk
Example: Assume that RIP holds:
US nom i = 8%
UK, nom i = 10 and the expected inflation rate is 6%
What is the expected inflation rate in the US?
8 - x = 10 - 6
4%
Real Interest Rate Parity and International Integration
The more integrated are the financial markets, the more real interest rate parity holds.
