Lecture on 31 October 2012 - Leeds School of Business



Lecture on 31 October 2012The examA couple of quick comments:I tend to give longer exams. Pace yourself. Start by going through the exam, if you can answer a question easily then do it. Otherwise go to the next one. If there are 5 questions remaining and you’ve taken 10 minutes to do the above exercise then you have 8 minutes per question. Pace yourself through the questions. The goal is to maximize points. You lose if you get problem 1 correct but take 25 minutes to do it. You won’t even get to see the last problem.Don’t cheat. I take the honor code seriously and so should you.After the examWe are going to do chapter 16 next. International Financial Systems which ties together FX markets and central banking.Today I want to start with some of the material in the book. If there is time then I’m happy to work through some more spot/forward problems for those that want.Appendix to Chapter 15Just as a side note as it’s easy to miss it. There’s an appendix to chapter 15 called Interest Rate Parity. This appendix basically tells you that the return from a foreign asset cannot be greater than the return from a domestic asset because there are very few restrictions on exchanging money and buying the foreign asset. Another way of expressing this relationship (not in the book) is – show slide on FX forwards.Law of One PriceNEXT SLIDENow we are going to head into supply and demand arguments for foreign exchange. We start with the law of one price. This states that the price of an identical good will be the same throughout the world. Clearly this is never going to be strictly true – it assumes that there are no trade barriers between countries and transportation costs are zeroIn order for the law of one price to hold what is the exchange rate between USD and JPY in JPY/USD?I like this example the book because it illustrates the problems with the law, steel costs quite a bit to transport. And periodically there have been quotas and tariffs on steel.The principle is a reasonable one – namely that prices between countries can not get too far out of line. If they were then goods and possibly services would move between the countries and eventually they would reach equilibrium. Theory of Purchasing Power ParityNEXT SLIDEThis leads up to an important theory about how exchange rates are determined – The theory of Purchasing Power Parity. It states that exchange rates between any two currencies will adjust to reflect changes in the price levels between the two countries. In particular the theory suggests that if one country’s price level rises relative to another’s then its currency should depreciate and the other country’s currency should appreciate.It is the application of the law of one price to national price levels. It appears that this works in the long run but not in the short run. NEXT SLIDEThere are several issues with the PPP that mean it cannot fully explain exchange rates.International transaction costs are not zero. Namely goods and services that can be traded across borders have substantial transportation and other costs associated with this trade.Not all goods and services can be traded across borders – land, restaurants, etc.Some goods and services are not identical between countries. A Mercedes Benz is not the same car as a Toyota.Drivers of Long Term Exchange RatesNEXT SLIDEWith these ideas as background let’s think about what affects exchange rates in the long run. We are going to consider the following principle: anything that increases the demand for domestic goods relative to foreign goods will cause the domestic currency to appreciate relative to the foreign currency.There are four main drivers for exchange rates in the long run.Relative Price LevelsNEXT SLIDEWhen prices of domestic goods rise relative to foreign goods this will cause the domestic currency to depreciate relative to foreign goods.Let’s do an example. Let’s say a basket of good costs $1000 in the United States and costs 650 pounds in the UK. What is the exchange rate? If there is inflation and the cost of good rises 10% in the United States then what does this do to the exchange rate?Trade BarriersBarriers to free trade such as tariffs and quotas will create more demand for domestic goods relative to foreign goods – this will tend to cause the domestic currency to appreciate relative to the foreign currency.Preferences for Domestic versus Foreign GoodsIncreased demand for a country’s exports will cause its currency to appreciate. Increased demand for foreign imports will cause a country’s currency to depreciate.ProductivityWhen productivity rises it tends to rise in domestic sectors that produce traded goods. Higher productivity is thus associated with a decline in the price of domestically produced traded goods relative to foreign traded goods. As a result the demand for domestically traded goods increases relatively to foreign goods and thus the domestic currency tends to appreciate.Exchange Rates in the Short RunIn the short term one can consider the exchange rate as the price of domestic assets in a foreign currency. We can start with a supply and demand analysis of foreign exchange rates.NEXT SLIDELet’s start by looking at a particular exchange rate USD and EUR. The exchange rate in EUR per USD is along the vertical axis. The horizontal axis is the quantity of dollar assets.It is assumed that the supply of dollar assets does not change with the exchange rate and thus it is vertical. The demand curve takes a bit of thought. In what follows we assume that the expected forward FX rate does not change. Thus a lower exchange rate will increase the implied return on US assets as the return on the US asset in foreign currency terms will gain more from the implied appreciation of the rate. This makes the demand curve downward sloping. Let’s look at this. If the exchange rate starts at 1.05 and the expected forward exchange rate is 1.05 then a move in the exchange rate to 1.0 but leaving the expected forward exchange rate at 1.05 will imply that US assets will earn an extra 5% simply by holding them. This will increase demand for US assets.The following factors cause shifts in the demand curve.Increase in the Domestic interest rateNEXT SLIDEBank accounts in the United States can be thought of as an US asset. What happens if a bank account paying 2% interest changes its rate to 3%. This will increase the demand for this asset. This should increase the value of the USD against the EUR and should the USD to appreciate versus the EUR. If the exchange rate started at 1.3 USD/EUR would you expect the exchange rate to be higher or lower afterwards?As we’ve just seen this will increase demand for US assets and will strengthen the dollar.Increase in the Foreign interest RateNEXT SLIDEThis is the opposite of the domestic interest rate and thus will decrease demand for US assets and weaken the dollar.Increase in the expected future exchange rateNEXT SLIDEThis will increase demand for US assets as from a foreign currency perspective the return will be higher. Thus this will strengthen the dollar.The factors we discussed regarding long-term movements also affect the short term.A possible contradictionWe have talked about two different effects on foreign exchange rates. These are:Increases in domestic interest rates. These tend to increase demand for local assets and strengthen the currency. Second we have increases in the domestic price level relative to foreign price levels. This tends to decrease the demand for domestic products and weaken the currency. These effects are offsetting but in the long run the PPP theory holds and thus this decreases the exchange rate in the long-term.There are really several things going on here that we are not going to spend too much time on. The subtlety that we have ignored is that it is not reasonable to assume that a change in a particular factor does not affect other factors. If we think about the changes in domestic interest rate we know that this relates the spot FX rate and the forward FX rate. If we assumed that the expected forward FX rate is always Spot *(1+R_foreign)/(1+R_domestic) then the change in domestic interest rate will have no effect on Spot because the fact that domestic interest rates yield more is completely taken account of in the forward market.Spot and Forward MarketsCurrencies trade in both the “spot” market and also the forward market. The forward market is simply a contract to exchange currency at a date in the future rather than today. There is a strong arbitrage condition that sets the forward price for currencies. The argument goes as follows.Let’s say that I have 1,000 USD today and want to end up with euros in 1 years time. I could do either of the following strategies.Strategy 1Buy Euros and put the euros in the bankStrategy 2Enter into a forward contract to sell the dollars in a year and put the dollars in the bank for a year.If I enter into either of these transactions today I should end up with the same amount of cash. If I didn’t then I could enter into the one that makes more money and do the opposite trade with someone else and I would make a riskless profit.Mathematically we haveSpot rate = F_0 EUR/USDForward rate = F_t EUR/USDInterest rate EUR is r_EURInterest rate USD is r_USDStrategy 11000 USD = 1000F_0 EUR grows to be 1000F_0(1+r_EUR)Strategy 21000 USD 1000(1+r_USD) 1000(1+r_USD)F_t EURAs these must be equivalent we have:1000(1+r_USD)F_t EUR = 1000F_0(1+r_EUR)F_t = F_0(1+r_EUR)/(1+r_USD)Note this doesn’t mean that in 1 years time the exchange rate will be F_t but simply that a forward contract entered into today for 1 years time will be done at this level.There is an equivalent to the expectations theory of interest rates that suggests that the best estimate for the FX rate in 1 years time is the forward rate today.Let’s work some examples.To make life a little easier we will get rid of the bid/offer spreads from the spot transactions. 8.7500 ZAR/USDAre interest rates higher or lower in South Africa or the United States?Here are some rough interest rates:1 year USD rate = 0.17%1 year ZAR rate = 5.96%Question 1. Is the 1 year forward Rate higher or lower than today?Question 2. What is it?8.7500*(1.0596)/(1.0017)= 9.2558 ZAR/USDThe thing you have to keep straight is which interest rate to grow the result by and which you discount it by. It is fairly easy if you know what the units of the exchange rate are. Namely 8.75 ZAR/USD. If you are going to multiply by (1+r_ZAR) then it must apply to the numerator. If you are going to multiply by (1+r_USD) then it applies to the denominator.One of the challenges to exchange rates is of course that I could have asked the above question as:The exchange rate is:0.1143 USD/ZARKeep the interest rates the same.The answer to question 1 is now lowerThe answer to question 2 is 0.1081 USD/ZARQuestion 3. Under an expectations theory of FX do you expect the ZAR to be stronger or weaker in a years time? Weaker because 1 USD will buy more ZAR.If we time let’s work another example0.6182 GBP/USD6-month rates in the US are 0.14%6-month rates in the UK are 0.33%Is the 6-month forward rate higher or lower than the spot rate?What is the 6-month forward rate? ................
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