Lecture on 29 October 2012



Lecture on 29 October 2012Some practiceBefore we go back to the forward FX problem I’d like to do a bit of FX practice. Here are some FX rates. 1.6150 - 1.6200 USD/GBP1.2920 – 1.2960 USD/EUR8.6500 – 8.8500 ZAR/USDHere are some items that I might want to buy1 South African House 1,000,000 RandHow many USD do I need to have to buy the house?You need to figure out which exchange rate to use. The easiest thing to do is to think about the round-trip. So pretend that you are going to buy ZAR and then sell it back immediately. If you start with 100 dollars, you buy 865 rand and then you sell the 865 rand for 865/8.85 = 97.75 USD. The other way you take 100 dollars, buy 885 rand and then sell it back for 885/8.65 = 102.31. Given that you are always going to lose if you buy ZAR and sell it back immediately it must be that you buy rand for 8.65 and sell it for 8.85. So if I need to buy 1,000,000 ZAR I need1,000,000/8.65 = 115,606.94 dollarsHow many EUR do I need to have to buy the house?To do this transaction I need to buy 115,606.94 USD with my euros. In this case the exchange rates work the same and if I want to buy USD I take the smaller of the two exchange rates so I need115606.94/1.2920 = 89479.05 EUR1 House in Paris worth 1,000,000 EURHow many USD do I need to have to buy the house?Again we need to figure out what exchange rate to use. Another way to figure this out would be to say which rate is going to give us more USD. In this case we need to multiply the million EUR by the exchange rate to figure out the dollars. Thus we need to take the larger exchange rate to figure out the amount.1,000,000EUR x 1.2960 USD/EUR = 1,296,000 USDHow many GBP do I need to have to buy the house?Now I have to take my USD and turn it into GBP in the most expensive way. I am going to divide by the smaller exchange rate.1,296,000 USD/1.6150USD/GBP = 802,476.78 GBPWhat are the bid/offer exchange rates for ZAR/GBP, ZAR/EUR and GBP/EUR?In an illiquid pair like ZAR/EUR you would probably find that you have to change EUR into USD or GBP first and then that currency in ZAR. Note ZAR/GBP is probably a relatively liquid currency pair because of the historical connection between the countries.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/USD Are 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?Law of One PriceNow 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 essentially assumes that there are no trade barriers between countries and transportation costs are zero. The example the book gives is great, steel costs quite a bit to transport and thus this law will never precisely hold. On the other hand 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 an equilibrium. Theory of Purchasing Power ParityThis 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. There 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 RatesWith 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 LevelsWhen prices of domestic goods rise relative to foreign goods this will cause the domestic currency to depreciate relative to foreign goods.For this consider our USD and EUR example. If there is only one good to buy in each country worth 100 dollars and 100 EUR at the beginning. If the cost of this good changes to 200 dollars with the EUR price staying the same at 100 EUR then people will buy euros to take advantage of the cheaper cost of the good. This will cause the EUR to rise versus the USD.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. Bring up graphWe can start with supply and demand curves. Let’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 do a simple example – Let’s assume that the current exchange rate between USD and EUR is 1 EUR/USD, the expected forward exchange rate is 1 EUR/USD and there is one asset to be purchased in each country – a bank account that pays 2% interest.So one thing that would increase demand for domestic goods relative to foreign goods is that the US bank account would start to pay more interest. For example it could start to pay 3% rather than 2%. As we saw before:Thus there will be more demand for US assets relative to European assets. This demand will increase the value of the USD against the EUR and should cause the USD to appreciate versus the EUR.Which way will this cause the exchange rate to move?The following factors cause shifts in the demand curve.Increase in the Domestic interest rateAs we’ve just seen this will increase demand for US assets and will strengthen the dollar.Increase in the Foreign interest RateThis 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 rateThis 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. ................
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