 In this session, we will try to develop relationship between spot exchange rate, foreign exchange rate and interest rates. By covered interest arbitrage means covered or protection in the event of a change in the exchange rates because of a power contract. For example, we have market info on US and Swiss currencies and that says that spot exchange rate between Swiss and US currency is equal to 2 Swiss francs and we have 360 days power rate and that is 1.90 Swiss francs against 1 dollar. A nominal interest, nominal risk free interest rate in US is equal to 10% whereas in Switzerland it is 5%. Now assuming 1 dollar we have and we need to invest this 1 dollar into some riskless investment. So would there be any arbitrage opportunity? We have an option that is option 1 where we can invest this 1 dollar in riskless US investment say pre 60 day T bills and at 10% riskless interest rate if this 1 dollar is grown over a period of 1 year then at the end of year 1 it comes to 1.10 US dollar. Now as a second alternative we have an arbitrage opportunity and let's see how this arbitrage process work. We need to take the certain number of steps like at first we need to convert 1 US dollar into Swiss franc at the rate of 2 and in this way we will be getting 2 Swiss francs then we will at the same time we will be getting a forward contract of 360 days which is 1.90 Swiss francs. We are entering into this forward contract because we need to convert our Swiss franc into US dollar at the end of the period. Then at the third step we need to invest the 2 Swiss francs in Switzerland in riskless investments let's see if we put this 2 Swiss francs into riskless investment at the risk free interest rate of 5% then this 2 Swiss francs will be grown to the amount of 2.10 Swiss francs. Now we need to convert this Swiss franc of 2.10 into a dollar at the forward contract rate of 1.90 so we will be getting 1.1053 US dollars. So in this way we see that there is a difference of 0.03 and their difference is higher than the return we have earned in US riskless investment. So we can conclude that if we have 2 riskless investments then there exists some opportunity for the arbitrage transaction. Now let's talk about interest rate parity. Assuming no covered interest arbitrage opportunities in existence then there must be in existence some relationship between spot exchange rate, forward exchange rate and relative interest rates. Now to see let's equate our earlier 2 options option 1 and option 2 to prevent any arbitrage opportunity. So we have an equation the left hand side of that equation is the 1 plus R US and that is the interest rate of US which is equal to the spot exchange rate multiplied by the relationship between interest rate of a foreign country and the forward exchange rate. We can also replace this equation for t time period in order to determine the effect over a certain period of time. As per interest rate parity the percentage forward premium or discount is approximately equal to the interest rate differences which we can see in the equation on the left hand side the equation is showing the forward premium or forward discount whereas on the right hand side the equation is showing the difference in the inflation rate of 2 countries like a domestic country and a foreign country. As per interest rate parity interest rate differential of any 2 country can offset the changes in the relative value of the currencies. This means that in this way the opportunities for arbitrage transactions can be eliminated. To understand this let's take an example we have a spot exchange rate between Japanese yen and US dollar equal to 120 Japanese yen whereas interest rate in US is equal to 10 percent and in Japan it is equal to 5 percent. So in the presence of this data what would be the forward rate to prevent the covered interest arbitrage. Now if we put this data into the equation of that we have earlier seen where we equate the model one option one with option two and putting the values into this equation we come to the value of 114 Japanese yen and at this forward exchange rate the possibilities of arbitrage opportunities is eliminated. Now how we can develop the relationship between forward exchange rates and future spot rates. We see that the there is a condition that is called as unbiased forward rate conditions and ignoring the risk this condition should hold well. This means that the consistent decline in the forward rate than the future spot rate and in that case anyone wanting currency in future would consistently get more you know of that currency but not agreeing or entering into the forward exchange. And if this is the situation then the forward rate will be increased to get anyone interested in the forward exchange rate and same is true for the opposite of this condition. For these two reasons we can see that the forward and actual spot rates should be equal to each other on average. Let's see the implications of relationship between purchasing power parity, interest rate parity and the UFRR unbiased forward rate. At first we develop the relationship between uncovered interest rate parity for that purpose we need to put international financial market relationship in one place that we have developed earlier means we have the equations for purchasing power parity interest rate parity and unbiased forward rate and if we combine the unbiased forward rate and interest rate parity we see that the unbiased interest parity is equal to and this is basically that the expected spot exchange rate after one period is equal to the spot exchange rate as grown by the differential of interest rates between the two countries. Now let's talk about international fisher effect to that purpose we now compare purchasing power parity and the UIP we have the equations of the two sides and we see that both of the equations have expected spot exchange rate on their left side and their right sides then must be equal to each other if we equalize their right side to each other we see that the difference between the inflation rate is equal to the difference between the interest rate of the two countries. So if this means if we try to rearrange this equation we see that the real rates are basically equal across the countries.