PPP, this and that

When it comes to exchange rates, we have one, spot exchange rate and two, forward exchange rate. 

It would be obvious that forward exchange rates are used to hedge the risk arising from foreign exchange rate fluctuations.

Hedging to safe guard from exchange rate risks can be done in three ways . As told above, forward market is one. The rest are Money markets and Options markets.

Suppose you are a US citizen dealing with a british company. Well, the british company has to pay you 10 million british pounds after one year. Obviously, there is a risk involved. Because, after one year, you may get less, equal or more dollars per pound due to fluctuations in exchange rate.

1. Better you fix the future rate (called forward rate) to be paid after an year. 

2. You take pound loan, convert and invest in dollars and repay in pounds (money market hedging)

3. Do similar thing as above, but use Option.(Options gives right to buy or sell but not obligation)

Let us see about how japanese wives made millions by Peso trade in some other post

Cross exchange rate helps in finding exchange rates of those currencies which are not commonly traded. 

Example, E(chinese yuan/malaysian ringgit) = E(Chinese yuan/ $) x E($/Malaysian ringgit) 

It is imp to note that cross exchange rate sometimes gives rise to arbitrage opportunities, which however are short lived because of shrewd arbitrageurs waiting for such opportunities. 

Covered interest parity(CIP) and Uncovered Interest Parity (UIP)

Chetan says

CIP refers to situation when the exchange rate risk (henceforth called risk) is hedged by trading in forward market that we have discussed earlier

UIP is when no hedging is done to mitigate the risk

Let us suppose, you want to invest 1$ in US. Let i$ be the interest rate in US. So after one year, you will get (1+i$) dollars.

Now, in another case, if you want invest this 1$ in europe (say) where interest rate is iE. You will first convert it into Euro and invest for an year for which you will get interest. This euro sum after an year will have to be converted in to dollars for your consumption. 

One of the key cornerstone in international macro economics at this point of time, as Chetan says, is that both returns (either you invest in US itself or you convert your dollars into Euros, invest and then convert back to dollars) are equal. This is because, if they are unequal, there is arbitrage opportunity which will be exploited soon and hence short lived. 

Thus, (i+i$) = (1/E($/Euro))*(1+iE) x F ($/Euro) .................. In CIP------------- (1)

This F($/Euro) is the forward rate that you use to hedge the exchange rate risk.

Similarily , we have  (i+i$) = (1/E($/Euro))*(1+iE) x Ee($/Euro)............. In UIP---------(2)

This Ee($/Euro) is the expected future spot market rate.

It follows from (1) and (2) that ... F($/Euro) = Ee($/Euro)

This shows that forward exchange rate is a good indicator of expected future spot market rate. If they are not equal at any point of time, there is an arbitrage opportunity.

Broadly and intuitionally......... Domestic interest rate = Foreign interest rate + Expected depreciation of domestic currency.

It is interesting to note that, there are huge capital inflows into china. One of the major reasons is because its currency is highly undervalued and investors expect it to rise in the future. On contrary note, we frequently hear news that capital has gone out of India because its currency is valued high and is expected fall in the future. ( To 100 INR??!! I wonder :) )

It is surprising to know that it is estimated that all prices converge to a single price in the long run. This is called Law of One Price (LOOP) . And the speed of convergence is about 15% per annum. Note that we are talking about a single individual good here. However, if this logic is extended to a BASKET of goods, it is called Purchasing Power Parity (popularly pronounced PPP ). And this is in absence of transaction frictions (perfect world.. ha ha ..!!) and perfectly free capital flows exist between countries.

So, in our relative prices formula that we discussed in other post, if LOOP is to hold good, relative prices equal to Q(E/US) = 1 (since all prices converge to the same price)

All this is fine. HOW DO YOU FIND EXCHANGE RATE ?

PPP is simply LOOP extended to basket of goods. Therefore if PPP (absolute) is to hold good,

Q(E/US) = 1 => E($/Euro) x Prices in Europe = Prices in US

So, here we are....!!! Exchange rate = Prices in US/ Prices in Europe . It is simply ratio of prices.

This PPP exchange rate is good estimation in the long run. Why?!!!

This is because PPP is based on LOOP, LOOP is based on Price convergence (which essentially means transportation costs and trade barriers slowly vanish) and this price convergence happens ONLY IN THE LONG RUN. 

In the above calculation we have used absolute price levels. However, if we use Change of price levels instead of absolute price levels, we arrive at something called Relative PPP. 

Mathematically Relative Change in Exchange rate at any given time between two countries  = Inflation differential between those countries.

Fore example, suppose inflation in US is 10% and in Europe is 9%. Now exchange rate between US and Europe changes at 10%-9% = 1%. 

The Big Mac Index : Got to see The Economist for more info on this index.