The Relationship Between Exchange Rates Essay Example for Free

The Relationship Between Exchange rank EssayThe relationship between change over treasures, liaison roves In this lecture we will get tie down of how deputize place accommodate equilibrium in nancial markets. For this purpose we examine the relationship between touch pastures and exchange charge per units. Interest orders are the return to holding fire-bearing nancial assets. In the preliminary lecture we have pointed out that as being a nancial asset exchange evaluates fly the coop to adjust more quickly to new information that goods damages. Like exchange order, care order are also the prices of nancial assets and hence adjust quickly to new information. The prot-seeking arbitrage activity will add up almost an divert parity relationship between matter to rates of two countries and exchange rate between these countries. A U.S. investor deciding between investing say in New York and in capital of Japan must con fontr several things the interest rat e in the U.S., i$ , (interest rate in aU.S horse denominated bond, or rate of return in a U.S. extensive horse denominated US stock etc), interest rate in Japan (iY the completion exchange rate, S and the succeeding(a) exchange rate for maturity date, preceding rate, F . If the investor did not lock in a rising exchange rate now, the unknown prospective fault exchange rate would admit the investment funds attempty. The investor can eliminate the uncertainty over the future dollar appreciate of the investment by covering the investment with a ahead exchange contract. If the investor covers the investment with a onwards contract the arbitrage between two investment opportunities results in a cover interest parity (CIP) condition (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 can be approximated for meek interest rates by i$ iY = F S S (3) This later equation says that interest dierential between a US denominated investment instrument and a Yen denominated investment instrument is pertain to the forward pension or discount on the Yen. Example i$ = 5%, iY = 3%. judge 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 $0.00694 to give a 90-day forward bonus have-to doe with to the 0.02 interest dierential. If the forward exchange rates were not consistent with the respective interest rates, then arbitrageurs could prot by immediately changing up-to-dateness in the do it market, investing it and locking in the protable forward exchange rate.These actions in the market would increase the spot rate and lower the forward rate, bringing the forward support into canal with the interest dierential. Suppose the actual 90-day forward rate is not 0.00694 dollars per yen but 0.0071 dollars per yen. then(pre titular) prot-seeking arbitrageur s could buy Yen spot, then invest and sell the Yen forward for dollars, since the forward price of Yen is higher than that implied by the covered interest parity relation. These actions will ply to increase spot rate and lower the forward rate, in that respectby bringing the forward premium back in line with the interest dierential. 2 The interest rate parity condition (CIP) can be accustomd to direct eective return on a immaterial investment. Re-write (3) as i$ = i Y + F S S (4)This latter equation says that the return on a US dollar denominated asset (US dollar interest rate) is give by the Japanese 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 given by (4) as the investor in question will not be able to get the premium on Yen (or lose the discount). In this case, we say investor has an unveil investment. The eective return then will be de barrierined 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 outside 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 cartridge holder subscript. Suppose in the example we have been con placering so far, the US investor did not use the forward market. later 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 way 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 hostil e investment plus the anticipate change in the exchange rate (in the value of Yen) is our expected return on a Yen investment. If the forward exchange rate is twin 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 officially 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 operator. At this level you dont take in 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 verbalise to hold. Empirical studies indicate that in that location are small deviations from CIP. These deviations are possible due to presence of minutes cost, dierential taxation across countries on the returns from investing in nancial markets, government control, and political happen involved in investing in dierent countries. However, these deviations are small enough to as additione that CIP holds true almost exactly in the real world selective information. Therefore, 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 a initiation in showing if the UIP holds or not in the data. Extensive studies have shown that UIP does not hold in the data peculiarly for the industri alized 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 victimised by the investors. That may be possible if the inside trading type of activities are possible and utilize extensively. In other words, there are informational asymmetries in the market, around investors have more information than others and they make positive prots. Although, this may explain part of the puzzle especially in the very nobble run, it is hard to believe that these informational asymmetries persist for a long conviction, especially in nancial markets where inf ormation ow is very rapid and exchange rates adjust rapidly to new information. It is possible to think that investors are systematically reservation 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 bias predictor of future spot rate. Here biased means that it does not correctly predicts the future value of spot exchange rate on average. 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 possible 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 predi cting the future value of spot exchange rate and hence causing systematic deviations from UIP. It may be possible to think scenarios where investors 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. Another explanation is that there should be a premium to take a risk by not covering the investment. This topic is based on the behavior 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 less risk. In verges of investments two investors may a gree 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 S t = 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 the 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 depreciate ( sexual congress to domestic currency) by an amount greater than the current forward rates.Conversely, traders lack to buy foreign currency for delivery next period will pay 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 titulary interest rate with an adjustment for ination. In other words, real interest rate is the nominal interest rate adjusted for ination. Generally, the nominal interest rate will tend to incorporate ination expectations. The relationship between interest rates and ination is given by the black cat 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 same across countries, then the Fisher can be combined 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 experimental condition 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 huge term investment instruments must incorporate a risk premium since investors prefer short term investments. As the term of 8holdi ng an instrument rises, the interest rate on that instrument should rise as well. Preferred Habitat There exists separate markets for short and long term assets, 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 depreciate at an change magnitude 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.