The Relationship Between Exchange Rates Essay Example for Free

The Relationship Between Exchange Rates EssayThe alliance amidst swap rolls, busy invests In this lecture we will learn how convert cast accommodate equilibrium in nancial markets. For this purpose we examine the relationship between engagement come ins and metamorphose marks. Interest judge ar the run off to acquiting interest-bearing nancial assets. In the previous lecture we have pointed pop out that as being a nancial asset central rates tend to adjust more quickly to new info that legals prices. Like exchange rates, interest rates ar also the prices of nancial assets and hence adjust quickly to new information. The mastert-seeking arbitrage activity will bring about an interest resemblance relationship between interest rates of ii countries and exchange rate between these countries. A U.S. investor deciding between investing say in new-fangled York and in Tokyo must(prenominal) consider some(prenominal) things the interest rate in the U.S., i$ , (interest rate in aU.S dollar denominated bond, or rate of authorize in a U.S. dollar denominated US stock etc), interest rate in Japan (iY the secernate exchange rate, S and the future exchange rate for maturity date, anterior rate, F . If the investor did not lock in a future exchange rate now, the unknown future bonk exchange rate would make the investment guessy. The investor sens eliminate the uncertainty over the future dollar determine of the investment by covering the investment with a foregoing exchange contract. If the investor covers the investment with a previous contract the arbitrage between two investment opportunities results in a covered interest parity (CIP) tick off (1 + i$ ) = (1 + iY ) 1 F S (1) which may be rewritten as (1 + i$ ) F = (1 + iY ) S (2) The interest rate parity equation corporation be approximated for small interest rates by i$ iY = F S S (3) This later equation says that interest dierential between a US denominated investment in strument and a Yen denominated investment instrument is affect to the forward amplitude or discount on the Yen. Example i$ = 5%, iY = 3%. Suppose S = 0.0068 dollars per Yen. What should be the 90-day forward rate? 0.05 0.03 = F 0.0068 0.0068F = 0.0068 + 0.02 0.0068 = 0.00694 Thus we expect that a 90-day forward rate of $0.00694 to give a 90-day forward pension equal to the 0.02 interest dierential. If the forward exchange rates were not consistent with the respective interest rates, then arbitrageurs could prot by immediately changing currency in the spot market, investing it and locking in the protable forward exchange rate.These actions in the market would attach the spot rate and lower the forward rate, bringing the forward premium into line with the interest dierential. Suppose the actual 90-day forward rate is not 0.00694 dollars per yearn exactly 0.0071 dollars per yen. Then prot-seeking arbitrageurs could buy Yen spot, then invest and sell the Yen forward for doll ars, since the forward price of Yen is superiorer than that implied by the covered interest parity relation. These actions will tend to increase spot rate and lower the forward rate, thereby bringing the forward premium buns in line with the interest dierential. 2 The interest rate parity condition (CIP) can be workd to compute eective draw on a foreign investment. Re-write (3) as i$ = i Y + F S S (4)This latter equation says that the return on a US dollar denominated asset (US dollar interest rate) is disposed(p) by the Nipponese interest rate plus the forward premium or discount on Yen. If CIP holds then equation (4) will hold as well. What happens when an investor does not use the forward market? Then we can not expect eective return on US dollar denominated asset be addicted by (4) as the investor in question will not be able to loaf the premium on Yen (or lose the discount). In this case, we say investor has an uncovered investment. The eective return then will be dete rmined by the Japanese interest rate plus the change in the spot exchange rate between today and say 90 days from now. Letting it be the domestic interest rate on a domestic currency denominated asset, say US Dollar, between date t and t + 1, and similarly i stands for foreign interest rate, t the eective return on a domestic currency denominated nancial asset will be given by it = it + St+1(5)Which in our example will be i$ = iY + S without judgment of conviction subscript. Suppose in the example we have been considering so far, the US investor did not use the forward market. After 90 days when the investor go to change Yen back to dollars, she nds that the Yen has appreciated against US dollar say by 1 percent. This means that your Yen buys 1 percent more dollars than they did before. This means that eective return on Yen investment then will be given by iY + S = 0.03 + 0.01 = 0.04. 3Hence, the return on a foreign investment plus the expected change in the exchange rate (in the repute of Yen) is our expected return on a Yen investment. If the forward exchange rate is equal to expected future spot rate (Mathematically this means that E St+1 given all the available information = Ft ) then the forward premium/discount is also equal to the expected change in the exchange rate. In this case we say that uncovered interest parity, (UIP) holds. More formally UIP condition says that the expected change in spot exchange rate is equal to interest dierential. E(St+1) St = i t i t St (6)where for E denotes the expectation doer. At this level you dont need to worry about what this operator means, you can simply think ESt+1 denoting the expected future value of spot rate. As above analysis indicate forward exchange rates incorporate expectations about the future spot exchange rates. If the forward exchange rate is equal to the expected future spot rate, then the forward premium is also the expected change in the exchange rate. In this case, UIP is said to hold. Empirical studies indicate that there ar small deviations from CIP. These deviations are possible cod to presence of transactions cost, dierential taxation across countries on the returns from investing in nancial markets, government control, and political risk involved in investing in dierent countries. However, these deviations are small enough to assume that CIP holds true almost exactly in the real world data. on that pointfore, we can say that prot-seeking arbitrage activities eliminate prot opportunities in the exchange rate markets. Hence, CIP condition can be viewed an equilibrium condition that characterizes the relationship between spot exchange rate, forward rate and interest rates of two countries.4 The problem arise in showing if the UIP holds or not in the data. Extensive studies have shown that UIP does not hold in the data especially for the industrialized countries. This means that percentage change in expected future spot rate is not equal to interest dierential . Or, forward rate is not equal to expected future spot rate. Mathematically, this implies that there are deviations from UIP condition stated in (6) above. That is, it i t ESt+1 St =0 StThis means that eective return dierential is not equal to zero. There are several explanations given in the literature. there should be prot opportunities in the exchange rate market that are being exploited by the investors. That may be possible if the inside trading type of activities are possible and used extensively. In other words, there are informational asymmetries in the market, some investors have more information than others and they make positive prots. Although, this may explain part of the puzzle especially in the very short run, it is hard to believe that these informational asymmetries persist for a long time, especially in nancial markets where information ow is very rapid and exchange rates adjust rapidly to new information. It is possible to think that investors are systematica lly making mistakes in predicting the future value of spot exchange rate. That is, Ft = ESt+1 for a prolonged period of time. This means that forward rate is a biased forecaster of future spot rate. Here biased means that it does not correctly predicts the future value of spot exchange rate on clean. In other words, an unbiased predictor means that it predicts on average correctly the future value of a price, say exchange rate, so that over the long run the forward rate is just as likely to overpredict the future spot rate as it is to underpredict. Unbiased predictor does not mean that forward rate is a good predictor. What it 5 means is that forward rate is just as likely to guess too high as it is too low future spot rates.There is some evidence that indicates that investors in foreign exchange rate market make systematic mistakes in predicting the future value of spot exchange rate and hence causing systematic deviations from UIP. It may be possible to think scenarios where inv estors make mistakes in their forecast of future values of asset prices, but the magnitude of these mistakes shouldnt be that large to account the large deviations we observe in UIP. That is, it is hard to understand why especially over longer time periods investors make big mistakes in a systematic fashion. Over time at least we should expect these errors to shrink a level where deviations from UIP become smaller. other explanation is that there should be a premium to take a risk by not covering the investment. This idea is based on the carriage of investors in taking risk.The eective return dierential between two countries should be dependent on the perceived risk on each asset and the risk aversion of the investors. The risk aversion refers to the tendency of investors to prefer little risk. In terms of investments two investors may agree on the degree of risk associated with two assets, but the more risk-averse investor would require a higher interest rate on the more risky asset to induce her to hold it then the less risky-averse investor would. In nance, by risk we mean the variability of return from any given investment. This is because the more variable the return from an investment is, the less certain we can be about its future value. If investors dier in their risk taking behavior we may observe that deviations from UIP and hence, changes in risk and risk aversion are associated with changes in eective return dierential (that is interest dierential). That is, it i t ESt+1 St = f (risk,riskaversion) St 6The left hand side of this equation is the eective return dierential (or deviations from UIP). The right hand side can be viewed as the risk premium. Since CIP conditionit it = Ft St Stholds almost exactly, subtracting ex-pected change in exchange rate from both sides it it Ft St ESt+1 St ESt+1 St = St St St Ft ESt+1 ESt+1 St = St St(7)or it i t (8)Thus, we nd that the eective return dierential (or deviations from UIP) is equal to t he percentage dierence between forward and expected future spot exchange rate. The right hand side of (7) is usually considered to be a measure of risk premium in the forward exchange rate market. If eective return dierential is zero, then risk premium will be zero. If it is positive, then there is a positive risk premium on the domestic currency, because the expected future spot price of foreign currency is less than the prevailing forward rate. In other words, traders are oering to sell foreign currency for domestic currency in the future will receive a premium, in that foreign currency is expected to deprecate (relative to domestic currency) by an amount greater than the current forward rates.Conversely, traders wishing to buy foreign currency for delivery next period will chip in a premium to the future sellers to ensure a set future price. The relationship between interest rates and ination The real interest rate reects the nominal interest rate with an adjustment for inatio n. In other words, real interest rate is the nominal interest rate familiarised for ination. Generally, the nominal interest rate will tend to incorporate ination expectations. The relationship between interest rates and ination is given by the Fisher equation i=r+ (9) where i is the nominal interest rate, r is the real interest rate and is the expected ination rate. An increase in will tend to increase the nominal interest rate. If the real rate of interest is the very(prenominal) across countries, then the Fisher can be have with CIP equation i$ iY = U S J = F S S (10)This latter equation says that if real interest rates are the same internationally, then nominal interest rate dierential dier solely by dierences in expected ination. Note that relative exchange rate is given by the ination dierential and assuming that PPP, Fisher equation, and interest rate dierential hold then real interest rates are equalized across countries. The expected exchange rates and the interest rates The pattern of interest rates over dierent time periods for dierent investment opportunities is known as term structure of interest rates. There are several interest rates. Short run interest rates, long run interest rates, namely 1 month, 3-month, 6-months etc.There are several theories explaining the the structure of interest rates on dierent investment opportunities over time. Expectations the long term interest rates tend to equal to the average of short-term rates expected over the holding period. The expected return that will be generated from holding a 10 year bond should be on average be the the sum of holding a series of short term bonds, say 30-day bond rates. Liquidity premium Long term investment instruments must incorporate a risk premium since investors prefer short term investments. As the term of 8holding an instrument rises, the interest rate on that instrument should rise as well. Preferred Habitat There exists separate markets for short and long term as sets, with interest rates determined by conditions in each market. Under conditions of freely owing capital across countries, the term structures in dierent currencies infer expected exchange rate changes, even if forward exchange markets for these currencies do not exist. If the term structure lines for two currencies are parallel, then exchange rate changes are expected to be constant diverging, then the high interest rate currency is expected to belittle at an increasing rate over time converging, then the high-interest rate currency is expected to depreciate at a declining rate relative to the low-interest rate currency.