[MUSIC] So, in this video, we're going to have a look at how we may define the real value of a currency. And assert where it's over or undervalued, and we will see there's actually only one way to do so. Indeed, when I first started my career as an economist I started in a private bank here in Switzerland, and I was a currency economist. I realized how difficult it was to come with conclusions whether a currency should go up or down based on economic fundamentals. Because of this lack of measures, of yardsticks, where you can say if you compare a currency to that level then you can say a currency is under or overvalued. So, by the end of this video, you will be able to explain the only yard stick which we know, and it's called purchasing power party, and we will see how you may define that. And you see that there are two ways of defining purchasing power party, the absolute way, the relative way. And we will see how there are some, a major problem when constructing an estimation were based on PPP. And we will see also another funny example of a measure relating to purchasing power parity, which is called the Big Mac parity. Okay, so defining purchasing power parity. Basically, the idea is quite simple here. The idea is that, if you have a currency and you're going to abroad, so you're going to the United States, and you're based in India. And you're going to the United States, and say the cost of living is higher in the US than in India then the idea of purchasing power parity is that you need a stronger currency, a stronger rupee versus the US dollar. To compensate for the fact that prices are higher in the US, and if that condition is fulfilled then we say that PPP or purchasing parity holds. So in this example, we can say that PPP is an estimation of a theoretical exchange rate. It's actually not an observed exchange rate but it's very commonly used. So let's see this with one example. Let's take a representative basket of goods in the US which cost 100 US dollar, and let's assumed that in Switzerland the same basket of goods cost 110 Swiss Franc. So if PPP holds then the dollar should be worth 1.1 Swiss Franc, and if that condition holds, then you would be indifferent to buy the basket of good in the US or in Switzerland. You would have the same purchasing power. But if the exchange rate is not 1.1 Swiss Franc per US dollar but, say, parity, 1 US dollar equals 1 Swiss Franc. Then the Swiss Franc would be overvalued by 10% because the basket is actually cheaper in the US than in Switzerland. It would cost $100 in the US, and it would cost $110 in Switzerland. So, we're going to have a illustration of what PPP, how PPP can be measure, and I'm sure you've heard of this example. It's the example of, are they ready? Yes, they are. The example of the Big Mac parity. So take a look, we have here, very practical example how we can define PPP. Basically, the idea is to compare the price of a Big Mac. Okay, so here we don't have Big Mac, we just have simple hamburgers, but you'll see why in a minute, but let's assume these are Big Macs. Okay, this is the Big Mac which was bought in New York early this morning. It cost $4.79 to buy this, let's assume its a Big Mac again, okay. Now, this is the same, it was also bought in Beijing also early this morning, it cost 17 Yuan. Okay, this was bought here just next door in Switzerland and it cost 6.50 Francs. And last but not least, this was bought in Bombay, but you see it somewhat different from the others, it's not exactly the same and for one main reason actually in India, you don't find Big Macs made of beef, but of other meat like lamb or chicken. Okay, do what's the idea now here? The idea is to compare the price of the Big Macs in the various country. And derive from it the true value of the currency. So we know that $4.79, and let's compare that to Switzerland, 6.50 Franc, okay. So let's assume that we could buy this $479 with the current value of the Swiss Franc, which is roughly 0.99 Swiss Franc per dollar. So, which means that we paid this Big Mac in the US something like 4.7 Swiss Franc. Okay, so there would be a very easy way to make a lot of money, is actually to purchase a lot of these Big Macs in New York, bring them back very quickly here to Switzerland, and sell them, say, for 5.50 Francs, as opposed to 6.50 in the shop, in the McDonald's. We could sell them cheaper, and still make 1 Franc gain per Big Mac we sell, okay? So, to avoid this arbitrage that we buy these hamburgers in the US and sell them here and make a profit, an easy profit. Basically, these profits are cancelled if the currencies are at their PPP rate measured by the comparison between the price in the US and the price in Switzerland. And we see basically, if we divide 6.50 by 4.79 we get 1.36 and 1.36 Swiss Franc per dollar is the correct estimation of where the Swiss Franc should be according to the Big Mac theory. And now comparing this 136 versus the current exchange rate, he would take 0.95, we see that the Swiss Franc is overvalued by more than 42%. And on the same yardstick, using the same kind of calculation, we can see that the Chinese Yuan or MNB is undervalued vis a vis the dollar by also 42%, some 42%. And the India rupee is actually even more undervalued, by more than 60% versus the US dollar. With this example, we just find out that the rupee is actually massively undervalued vis a vis the dollar at more than 60%. We saw the Big Mac parity as an example of absolute purchasing power parity, and now we're going to have a look at the concept which is related of relative purchasing power parity. Here we're not comparing the price of one good, or a basket of goods, but we're actually comparing the price evolution of a basket of goods, and this is the inflation rate. So let's take one example. Let's assume that we're comparing the eurozone and Switzerland. And let's assume that we have 11% inflation in the eurozone and 1% inflation in Switzerland, and let us assume that we have, we are starting in January 2000, which is when the Euro came into existence. At that time, the currency of Euro for Swiss Francs was 160. So you had to pay 160 Swiss Franc to purchase 1 unit of Euro. So according to the theory of PPP given that the prices, the inflation rate is higher in the eurozone than in Switzerland. Basically, you need an appreciating Swiss Franc to compensate for these higher prices when you go into the Eurozone. So, you see here the formula, and you see that according to this inflation differential. The Swiss Franc should be roughly 10% higher one year after the euro comes into existence. So the parity should be 145.58. And you see the formula here. How we get to this thing. Basically, we multiply by the inflation differentials in between Switzerland and the eurozone. Now let's assume that a year after, in 2001, we have still an inflation differential but lower. We have that the eurozone inflation drops to 2%, and the inflation in Switzerland remains at 1%. Then we still need an appreciating Swiss Franc to compensate for the higher prices in the eurozone, but only by roughly 1%, and you see here the formula again, but with 2% inflation in the eurozone, and we get to 1.4515. So this theory is that basically the currencies where inflation is high should be depreciating versus the currencies of countries where inflation is low. Because, again, you need a stronger currency to compensate for higher prices. So here is the formula. And you see that the PPP rate, which again, and it's very important to know, it's the only yardstick that we can think of to measure whether a currency is over or undervalued. So you see here how we can compute it. We basically, take a currency exchange rate in the previous example it was 160. And we multiply by P / P*. P is the domestic inflation rate, and P* is the foreign, inflation rate. But now there's a problem here. And the problem is this with the E. The first observation 160. You see that in the previous example, we said okay, 160. We start and then we have because of the inflation differential. Roughly 10% of precision of the Swiss Francs and we get to 1.4558. But now we need to think of a major problem that we have. We're estimating PPP and that relates to the E, the first observation or what we called the anchoring point. In the previous chart, we saw that it was 160. I.e, the first quotation of the Euro versus the Swiss Franc when the Euro came into existence in January 2000, 160, okay. And then from this point, we anchor the inflation differentials, for instance, after one year we saw it was one, 45, 58, because of the inflation differential. Okay, the problem is, who says that 160 was the correct PPP in January 2000? There's no theory which tells us that, and basically, I can show you a chart, and this is the problem illustrated here in the following chart. We see the evolution, and that's the red curve here of the Swiss Franc versus the Euro. Now, let's assume that we choose January 08 as the anchoring point. At that time, you see that the Swiss Franc was very weak versus the Euro. The Euro was strong, it was 165, this is the strongest, the Euro has been in its history versus the Swiss Franc. So if we choose that as the base period, the anchoring point you see we get this green dotted line here, and what this green dotted line is telling us is that, today, according to the slide the Euro should be worth 155 versus the Swiss Franc, okay. That's extremely high for the Euro versus the Swiss Franc. On the other hand, if we choose August 2011 as the base period, the anchoring point, this e in the previous formula I showed you. Then you see we get a completely different message because the black line here ends up the last observation at parity. So, the message here is to say if we choose that August 2011 as the anchoring point then we would say that the Swiss Franc is correctly valued versus the Euro today because the current parity is 108, and the PPP is suggesting one. Okay, but so you see here there is a major problem here, it's the aprioriness of the anchoring point, the first observation on which we hook the inflation differentials, okay. So, the way to solve this problem is through a technique which we call the regression. This is a bit technical, we will put in a glossary the details for those of you who are interested on how we can solve the problem of the aprioriness of the first period. Actually, a proxy way to solve this problem, is to take some kind of average of all the exchange rate which are observed. So here in this instance it would be from January 2000 to today December 2015, it takes some kind of average, and that becomes your anchoring point. So but the academic way to solve this problem is through what we call a regression technique, and this is with constraint parameters, an elasticity of one. Okay, I won't give you the full details on the inflation differentials you can find the details in the glossary. And once we do that, we get this blue line which we called here true PPP rate. And here we can say that the Swiss Franc is overvalued. We had already this message when we looked at the Big Mac Parity. We have the confirmation here when we look at the broader set of goods, not just the Big Mac. And we see that it should be roughly worth 128 Swiss Franc per Euro. So in conclusion, we saw that with this video that the only way to measure the correct value, the theoretical value of a currency is the so called PPP. And the two ways to measure that, one is the absolute version of PPP, Purchasing Power Parity, and we saw that with the example of the Big Mac. And then there's the relative purchasing power parity which is used when we take not just one good, the Big Mac, but a basket of goods and we compare their price evolution in history. We also saw there's a major problem when measuring PPP, the relative PPP. And that's the anchoring point and we find out the solution to this problem. It's with this regression technique. Again, it's not part of the course, it's in your recommended readings, but for those of you who are interested, this is how we get to this true value of what the Swiss Franc should be versus the Euro, and that value is 129. Now, if we compare 129, the theoretical value of what the Swiss franc should be versus the Euro to 108, which is the value of the Swiss Franc versus Euro today. Then we have an overvaluation of 17% of the Swiss Franc versus the Euro. Now this overvaluation of the Swiss Franc vis a vis the dollar this time. Remember, was really, really high, at 42%. Again, when we look at the Big Mac parities, we find that the Swiss Franc is the most overvalued currency in the world. So the burger, are they still there? Are they still around? Yes, they are. Yes, well, talking about the Swiss Franc 42% over evaluation means that this burger here must be really good. Because it's the most expensive one in the world. So, let me see if that's correct. [MUSIC] Mm-hm quite tasty.