# Finance Essays - Market Exchange Rate

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## Market Exchange Rate

### The concept of efficiency and implication for empirical tests

Empirical methodologies for testing market efficiency have been carried out using different econometric measures. Bleaney (1998) employed econometric tools to determine whether the spot exchange rate behaves as a random walk.Wesso (1999) and Zacharatos and Sutcliff (2002) examined whether the forward exchange rate is an unbiased predictor of future spot exchange rate.

Sanchez-Fung (1999) and Speight and McMillan (2001) observed whether there is a co-integrating relationship among a set of spot exchange rates. Methodologies used by Levich (2001) have mainly aimed at testing the availability of unusual or risk-adjusted opportunities, the spot market efficiency and the forward market efficiency.

Conventional tests for efficiency classically involve testing the restrictions implied by the efficiency hypothesis on time series properties of equilibrium prices. In the exchange rate literature these restrictions were originally taken to mean that the spot exchange rate should follow a random walk. According to Harris and Purvis (1981) recent developments have stressed restrictions in terms of the forward exchange rate: either that the forward rate be equal to the expected future spot rate or that the interest differential equal forward premium.

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For instance, Fama (1976) proposed in finance literature it is eminent that the “random walk” property of equilibrium returns is neither a necessary nor sufficient condition for market efficiency. What in fact is required is that the actual returns from equilibrium returns only randomly. Equilibrium returns, and hence actual returns can reveal systematic time series properties.

Most of the empirical studies for testing the foreign exchange market efficiency use conventional OLS and univariate alongside with multivariate co-integration techniques. Fama (1984) examined the efficiency of nine currencies (exchange rates) against the US Dollar. He studied monthly data from 1973 to 1982 and the resulting OLS estimation showed that the market efficiency hypothesis is not accepted because of a time-varying risk premium. Naka and Whitney (1995) performed a similar test for efficiency hypothesis of seven exchange rates against the US Dollar using monthly observation from 1974 to 1991. The subsequent OLS estimation rejects reject the FRUH. However, using the same data set, they manage to accept this hypothesis through Non-Linear Squares Estimation.

Further research made by Hakio (1981), who studied the behavior of five exchange rates against the US Dollar from 1973 to 1977, confirmed that the unbiasedness hypothesis cannot be accepted. Taylor (1989) observed the US Dollar/ UK Pound exchange rate from January 1981 to July 1985 and he discovered the presence of significant risk premium and hence there is evidence of risk-averse behavior.

### The Joint Hypothesis nature for testing market efficiency

Testing for market efficiency involves testing two hypotheses simultaneously: the first being the hypothesis about the structure determining equilibrium prices or return; and the second is the hypothesis about the information used in formulating expectations and the ability of agents to set current prices to conform with their expected values. In fact, the first hypothesis will test if actual returns differ from their expected values only randomly while the second one measure whether equilibrium market returns are defined as a function of the information set Ψ_{t.}

_{}Thus efficiency is a concept that must be defined relative to both a given model and to given information set.

Aron (1997) argued that this joint hypothesis may be rejected for reasons such as investors do not maneuver available information efficiently, although the have the appropriate equilibrium model, or investors have an inaccurate measurement of the relationship linking equilibrium returns to information set, although they have rational in forming the price expectations.

Base on the above counter argument from the author on the joint hypothesis, forecasting exchange rate may not be fully rational in the sense that expectations among traders are not homogeneous, with one group building rational forecasts on future fundamentals, while a second group bases their expectations on technical analysis of recent exchange rate behaviors.

In the foreign exchange market literature, there are various model-based rationalizations that reject the joint hypothesis. These encompasses different conceptual models of exchange rate such as including, (a) a time varying risk premium, (b) rational learning in the presence of incomplete information, (c) rational speculative bubblesand, (d) the endogeneity of the interest rate differentials, which macro economic policy may adjust to offset undesired movement in exchange rate. The most important of the above factors may be the risk premium. For instance Aron (1997) debated that while the assumption of a constant risk premium in an equity market is still quite common, in the currency market it seems less justifiable.

### Foreign exchange market versus equity market

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With reference to contrasting models for equilibrium returns, Levich (1985) suggested that there is an important difference between the foreign exchange market and the equity market. In contrast to the security market, where there are several conceivable equilibrium returns, there are as yet no commonly agreed models for the determination of equilibrium exchange rates.

Harris and Purvis (1981) constructed a simple model of exchange rate determination, which supplies an explicit example of an equilibrium exchange rate which exhibits systematic serial correlation, to point up a central point: that standard test of market efficiency, derivatives from studies of the equity market, are inappropriate in the context of the market for foreign exchange. Much of the empirical work on testing currency market efficiency has proceeded by adopting the same framework as used for the equity market.

They put forward two reasons to argue why this framework may not be suitable. Firstly, the market for exchange rate is not directly similar to stock market and second, the efficiency tests used in equity markets generally assumes all investors have full information. However, this assumption does not fit in as far as the currency market is considered. For instance, information as to real trade opportunities is not known to all agents, but is rather scattered across different sectors of the economy.

Harris and Purvis (1981) concluded that in the currency substitution theory of exchange markets, if agents cannot differentiate between movements in the exchange rate due to permanent or transitory disturbances then the properties of equilibrium exchange rate will be different than if all agents had full information. Hence, with incomplete information, exchange rate changes will tend to be positively serially correlated as agents do not fully incorporate permanent shocks into expectations about prices. Harris and Purvis (1981) also put forward the fact that there exists a private-social discrepancy in agents’ decision to invest and observed that a change in the set of information encourages a change in the equilibrium model of exchange rate determination. Hence, agents in making informational decision will lapse the effect their decisions have on the model.

### Market efficiency with Certainty and Risk- Free Investment

Arbitrage is a concept usually encountered in the foreign exchange market. The essence of an arbitrage condition in a financial market is that “each and every observation is a potential arbitrage opportunity.” Aliber (1973) argued that most empirical work about the exchange market is geared towards identifying agents as speculators or arbitragers on the basis of their position towards exchange risk.

Aliber (1973) pointed out three types of explanations which are generally proposed for an apparent unexploited profit opportunity for arbitrage- transaction costs, default risk and a composite of “non-monetary returns, default risk, non-unitary correlation of returns, and premature repatriation” These costs and risks encountered by arbitragers, however, are only a sufficient condition for an unexploited profit opportunity. The necessary condition is that someone pays a higher price for foreign exchange in the forward market than in the spot market- someone must provide arbitragers with a profit opportunity.

Under the context of certainty or risk- investment, empirical studies are performed to test for the presence of unusual or risk-adjusted profit opportunities instead of testing whether return in the foreign exchange match their expected equilibrium values. In arbitrage, the equilibrium-expected return is zero. Therefore, profit opportunities are expected to be eliminated under arbitrage.

Studies reviewed by Levich (2001), who relate arbitrage to the spot and forward foreign exchange market, emphasizes that test for efficiency of arbitrage pricing relationship demand the examination of a market price in relation to an arbitrage boundary condition. Thus, any figure, representing return on a currency transaction, which rest within the boundary generates no arbitrage profit and hence, implies efficiency. Accordingly, any figure outside the boundary implies profit opportunities and hence, market inefficiency. Under this theory, the foreign exchange market is said to be efficient when (a) a large percentage of observations are captured within the boundaries, (b) the outliers represent a small fraction away from the boundaries, and (c) when those outliers area scattered widely over time. In the case of certainty or risk-free investment, for the market to be efficient, the presence of arbitrage opportunity must be small and rare.

### Interest rate parity theorem and foreign exchange market efficiency

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Examples of our workStein (1962) and Glahe (1967) ascertained that analyses of behavior in the foreign exchange market usually rely on the interest rate parity theorem. Interest rate parity (IRP) establishes the relationship between interest rates, spot rates and forward rates and the principle behind IRP is that, in equilibrium two investments exposed to the same risks must have the same returns. There is an interest rate parity condition when the percentage forward premium is equal to the percentage interest differential. The exact formulation for interest rate parity condition is illustrated below:

F_{t, 1 }- S_{t = }i_{$ - }i _{£}

S_{t }1 + i_{£}

% forward %interest

premium = differential

Test for interest rate parity condition requires data on the forward and spot exchange rates as well as interest rates on foreign currency and domestic currency denominated currency. Studies in this line reveal that the IRP condition is applicable if a high percentage of observations lie within the boundary condition generated by the transaction cost. Therefore, considering the cost of performing arbitrage transaction is fundamental when testing the IRP condition. On the whole, if the percentage of observations inside the neutral band is high and the percentage of figures outside the boundary is relatively small, then the IRP condition holds meaning that there are few opportunities to profit from covered interest arbitrage transactions.

Considering the various factors, in the like of transaction costs, exchange controls, political risks and taxes, covered interest arbitrage profit opportunities are more obvious than real. More specifically, when taking these additional factors into consideration, most profit opportunities are either nonexistent or not risk free. Work done by Aliber (1973) and Frenkel and Levich (1975, 1977, and 1981) validate that “deviations from interest rate parity in the Eurocurrency markets are small and that a high percentage of deviations are smaller than transactions costs. Hence, analysis of their studies exemplify that the relations between the foreign exchange and short term Eurocurrency markets are efficient given that few openings for risk- free arbitrage exists.

Frankel and MacArthur (1988) conducted further analysis of the covered interest rate differentials. They extended their research to a larger group of countries, including both industrialized and less developed countries, and collected data for the year 1982 to 1987. Their final reviews reported that deviations from interest rate parity fall within a reasonably narrow range for most industrialized countries including Hong Kong and Singapore.

For instance, studies by Hilley, Beidleman, and Greenleaf (1981) held that rates quoted by banks for three to fives year forward contracts were inconsistent with interest rate parity. The authors argued that the cost for keeping capital tied up for three to five years, the adverse impact on balance sheet ratios, and the credit risks transaction, all together, can make the opportunity for banks to earn a small arbitrage profit go unnoticeable. Hence, banks will engage in arbitrage only if it generates a competitive rate of return.

Aron (1997), in his study of foreign exchange market efficiency tests in South Africa, found that equilibrium in the currency market, given a degree of capital mobility, and a deep and liquid market in short term interest bearing security, by hypothesis of uncovered interest parity (UIP) augmented by a time varying risk premium, the expected returns is given by:

E (DŜ_{t+1 }/ Ψ_{t)} = (r – r*)_{t }+ ξ_{t }

Where r – r* is the domestic and foreign interest rate differential for the period t to t+1 and ξ_{t }is the risk premium.

If agents are risk neutral, the risk premium will be equal to zero and assuming rational expectations, the ex post spot rate will differ from its rational expectation only by a random term U_{t+1 }with a mean zero. These combine assumptions yields the well-known condition for testing foreign exchange market efficiency

DS_{ t+1 }= (r – r*)_{t }+ ξ_{t +1 }

_{}

Where the term ξ_{t +1 }is independent of all information Ψ_{t }. Thus only unanticipated arrival of new information will trigger changes in prices.

_{}The hypothesis that interest rate differentials are unbiased predictors of future exchange rate movements has been almost universally rejected in empirical studies. One important fact in international finance literature is that interest rate differentials fail to predict subsequent movements in exchange rate in relation to the “unbiasedness hypothesis”. Many studies reported that exchange rate moves in a manner opposite than forecasted.

For instance, Froot and Thaler (1990) observed few cases where interest rate differentials in exchange rate prediction equations consistent with the unbiasedness hypothesis. Chinn and Meredith (2004) spotted one noteworthy feature of almost all published studies: the unbiasedness hypothesis has been examined using financial instruments with relatively short maturities, generally of 12 months or less.

Later, Chinn and Meredith (2005) tested this hypothesis using interest rates on longer-maturity bonds for the U.S., Germany, Japan and Canada. They confirmed that the relationship between interest rates and exchange rates is a feature of the short- horizon data that have been used in almost all previous studies. While employing longer horizon, the standard test for uncovered interest parity yields different results. These results hold up against a number of robustness checks, and support the earlier assumptions of Froot and Thaler (1990) that the unbiasedness hypothesis may better apply at longer horizons.

### Market efficiency with Uncertainty and Risky Investment

An investor holding a net position in foreign currency when the future spot rate is considered a random variable, the latter is exposed to foreign currency risk. Given the test for market efficiency is a joint hypothesis; the specification of the expected equilibrium return for taking the currency risk is significant.

It is a matter of fact that uncertainty put in complexity and moreover reflects the reality for testing foreign exchange market efficiency. Thus, Levich (2001) put forward that there is no suitable model that has been derived to determine the equilibrium price of foreign exchange risk and for that reason test for efficiency under uncertainty will not produce any perfect results. Spot speculation and forward speculation are techniques that can be used for bearing exchange risks.

### Spot Market Efficiency

Most of the studies for testing spot market efficiency are to some extent limited to “weak form” test, which simply examine the hypothesis that all information contained in the past history of exchange rates is already reflected in the current rate. The principal method for testing spot market efficiency has been to work out the profitability of various trading strategies.

Levich (2001) identified two technical trading rules for testing spot market efficiency: the filter rule and the moving average crossover rule. The application of any methodology, including the above two mention techniques, involves two steps: (a) identifying trends in exchange rates and (b) establishing market positions to profit from the continuation of that trends.

For instance, no profits should be earned when using these techniques when analyzing the trends. Hence, the null hypothesis of market efficiency is that the cost for taking on position in the foreign exchange market should offset the resulting exchange rate change such that no net excepted profit is gained.

Dooley (1976) and Shafer (1983) performed empirical studies using the filter rules to analyze profitability of the foreign exchange market. They examined daily spot rate of nine currencies for the period 1973 to 1981. They reported that small filters (f= 1, 2, or 5 per cent) would have been profitable for all currencies over the entire sample period. For larger filters (f= 10, 15, 20, or 25 per cent) the results were more variable, but still these rules were profitable in more than one-half of the sub-periods.

For instance, they argued that basing their study over a period of 8.5 years of daily data, resulting in more than 2,200 observations, the profitability of the small filters rules was a persistent phenomenon in the floating rate period. A further research conducted by Sweeney (1986) who also used the filter methodology to study daily exchange rate of 10 currencies over the period 1973 to 1980 reported similar conclusions. He concluded that results for small filters were again superior

Following a systematically analysis of the $/DM rate conducted by Schulmeister (1987, 1988) for the period 1973 to 1986, he proposed that most of technical models (filter, moving average and momentum models) would result in a gain even after adjusting for interest expense and transaction costs. However, based on his study the filter rules did not hold. The results of small filter were positive but not significant.

Levich and Thomas (1993) added more significance to the evidence on the working mechanism of the filter rules and moving average crossover rules. They used a larger sample consisting of 3,800 observations from January 1976 to December 1990 and also added currency futures prices in their observations. The resulting conclusion of their analysis was that the filter rule and the moving average crossover rules showed evidence of profitability and that profits for the moving average crossover rules were higher than filter rules.

Levich and Thomas (1993) came up with a new technique to measure the statistical importance of technical trading rule. Their aim was to determine whether their profit figures are unusual or not. They produced random series of exchange rate and applied each technical rule to each random series they have generated. Hence, profit was measured. They repeated the same procedure 10, 000 times to generate an empirical distribution of profits.

They then compared the original series of profits to the randomly generated series. The null hypothesis would be where the profit obtained in the original series does not differ from the profit of observed in the random series significantly. From their analysis Levich and Thomas (1993) deduced that significant patterns occur in the original exchange rate series such that profit is higher than in the randomly generated ones.

### Forward Market Efficiency

Techniques for testing the forward market efficiency are normally centered towards the relationship between current forward rates, the expected future spot rate, and the actual future spot rate. In fact, the forward exchange market is efficient when the forward prices fully reflect available information. Levich (2001) employs the term Simple Efficiency Hypothesis for testing the forward market. According to him, simple efficiency hypothesis reflects the following two hypotheses:

- Rational expectation

E (S _{t + n} I _{t}) = S _{t + n}

- Forward rate pricing.

F_{t, n} = E(S _{t + n }I _{t})

Other economic models showed that the equilibrium forward rate integrate a currency risk premium. Levich (2001) termed it the General Efficiency Hypothesis. The general efficiency hypothesis reflects the following two hypotheses.

- Rational expectation

E (S _{t + n} I _{t}) = S _{t + n}

- Forward rate pricing

F_{t, n} = E(S _{t + n }I _{t}) + RP_{ t, n}

In the above forward rate price RP _{t, n }represents the currency risk premium at time t for maturity n.

Most tests for forward efficiency require regression methodology to observe the relationship between the future spot rate and the past forward rate. However, it is complicated to link regression results to conclusions about market efficiency since of the complexity regarding a currency risk premium.

Elliot and Ito (1995) recently held that regression methodology has further limitations because there is no simple relation between results and profit opportunities in the forward market. Thus, Levich (2001) argued that more direct test of forward market efficiency rather study whether unusual profit exist in the forward market, or whether it is possible to surpass the forward rate as a predictor of the future spot rate.

Nevertheless, the existence of currency risks will make the profit earned through forward speculation compensate only for additional risk incurred. Hence, a counter argument for the efficient market is that surpassing the forecasting performance of the forward rate need not be an indication of market inefficiency.

Levich (2001), from his results obtained from the regression analysis, showed that there is a strong rejection of the forward premium as an unbiased predictor of the future exchange rate change. He also put forward that expectational errors are the other main explanation behind the forward rate bias. As a matter of fact, expectational errors arise naturally in the world of uncertainty.

In the evolution of the exchange rate regime, from the floating exchange rates to other regime shifts, it is typical to expect a slow learning process since investors need time to comprehend new policies and able to persuade themselves that the are permanently organized. Further studies devised by Lewis (1989) embodied that even when slow learning process is integrated into market agent’s expectations of the U.S. money supply process, nearly half of the forward rate bias observed in the 1980- 1985 US$ appreciation is still unaccounted for.

Many empirical studies have been conducted to reveal whether other variables can used in regressions that can notably enhance the forecasting performance of the forward exchange rate. Most of these studies can be grouped under the assessment of whether the forward rate can be considered an unbiased predictor, or the best available predictor of the future spot rate. Levich (2001) briefly examined some of the variables used in these studies namely: (a) Historical forecast errors, (b) Multiple forward rates, (c) “Large” or ‘Small” contemporaneous forward premiums, (d) A contemporaneous professional forecast and (e) The contemporaneous PPP spot rate.

### Efficiency of Black Markets in Foreign Currencies

Gupta (1981) mentioned that there has been much literature pertaining to explain the efficiency of the currency markets with considerable work supporting the hypothesis that the foreign exchange markets are weak efficient. However, there are countries where foreign currencies trading take place in black market. The presence of black markets is the result of restrictions placed on the foreign sector.

The importance of these markets in sustaining the illegal import and export of goods and assets, as well as illegal capital flows, has been growing in the past few years. However, it is feasible that black market may not be efficient because the information about prices and market participants is generally imperfect. Certain factors, in the like of thin market and transaction costs, hinder efficient adjustment of exchange rate to new information.

In his study, Gupta (1981) performed market efficiency tests on the black market exchange rates for India, Taiwan, and South Korea. Empirical tests were carried out on both monthly and weekly black market exchange rates in for these countries. In fact, Gupta (1981) defined the black market exchange (EB_{t}) as the price of a US$ in domestic currency in the black market, usually for unlicensed transfers.

Base on autocorrelation functions, Gupta (1981) observed that the results were considered to be supportive of independence since very few coefficients were found to be significant and these did not display any systematic patterns in terms of signs and lags. The implication of the latter is that the probability of relatively large or small changes from one week to the next is greater than would be expected under a normal distribution. Therefore, the significance tests which assume normal distributions could be misleading.

### Cointegration and market efficiency tests.

It is frequently of interest to test whether a set of variables are co-integrated. This may be desired because of the economic implications such as whether some system is in equilibrium in the long run, or it may be sensible to test such hypotheses before estimating a multivariate dynamic model.

The relationship between cointegration and error correction models was first suggested by Granger (1981). The concept of cointegration deals with the analysis of long run equilibrium relationships between non-stationary tine series. The error-correction models play a major role in formulating both the change in the nominal exchange rate and, to some extent, the change in the price level. Later, Granger (1987) applied the concept of cointegration and the associated error-correction representation to the purchasing power parity relationship between the Canada and the United States. He observed that the results were supportive of purchasing power parity as a long run equilibrium relationship between Canadian prices, American prices and the Canadian dollar/American dollar exchange rate.

Some other authors conducted further research in the same line of study. Mark (1987) uses the Engle-Granger time-domain approach to test PPP after 1973 between the United States and five countries (including Canada). He is unable to find support for in the Canadian-American case. Baillie and Selover (1987) and Taylor (1988), also with post-1973 data, cannot find support for PPP in the Canadian-American case. Enders (1988) considers PPP between the United States and three countries. He finds mixed evidence in favour of PPP in the Canadian-American case.

Johnson (1990) used a different approach of PPP in the cointegration framework to the Canadian-American case. In his analysis he observed that the relevant time series were cointegrated after 1950, and there is some evidence of cointegration over the post-1914 period. Over the entire 1914- 1986 period, the results of his suggest that a fully adjusted nominal exchange rate allows Canadian inflation to be independent of the American inflation. In fact, during the fixed nominal exchange rates regime in the 1960s the PPP was maintained through the adjustment of Canadian prices toward their PPP level. When the exchange rate was fixed, Canadian inflation responded directly to American inflation.

For instance, Johnson (1990) found that the flexible nominal exchange rate responded strongly to deviations from PPP after 1970. There was only a small response of Canadian inflation to deviations from PPP in the 1970s rather than the larger response in the 1950s.

Therefore, the implementation of exchange rate policy and the choice of exchange rate regime have a strong effect on the mechanism through which PPP is maintained and thus a strong effect on the domestic inflation process.

Corbae, Lim and Ouliaris (1992) used univariate and multivariate tests of the unbiasedness hypothesis in forward market efficiency studies using canonical regression procedures for cointegration systems. Canonical regression procedures for cointegrated systems are then used to test the null hypothesis of forward market unbiasedness of forward market efficiency. The procedures provide a simple test for the presence of a forward-market risk premium and are able to characterize its time series properties. The results showed that when the forward rates are not unbiased predictors of the future spot rates, the risk premium is non- stationary, comprising an I(1) permanent deviation and a transitory component. Hence, the latter is stationary and does not carry any trend.

Zivot (2000) examined the foreign exchange market efficiency for the British pound, Japanese Yen, Canadian Dollar against the US Dollar from 1976:1 to 1996:6. He compared cointegration models between the forward rate with the current spot rate and the forward rate with the future spot rate. He observed that cointegration analysis initially strongly rejected the efficiency hypothesis in all exchange rates.

Studies reviewed by Hakkio and Rush (1989), who observed the efficiency hypothesis for the UK pound and Deutsche mark from 1975 to 1986, concluded that the spot and forward rate, within a country, are cointegrated. Hence, the results were consistent with the concept of efficiency for the currency market. For instance, the estimation of the error correction model rejects the hypotheses of no risk premium and efficient use of information available by the market participants. These observations reject the foreign exchange market efficiency hypothesis.

Wickremasinghe (2004) used the cointegration model and Granger causality tests to study the efficiency of the foreign exchange market in Sri Lanka. He used the above two tests to examine the semi-strong form efficiency and unit root test for the weak form efficiency. He adopted Engle and Granger (1987) bivariate and Johansen (1995) multivariate cointegration tests, which are procedures to be carried out in to steps. The first step is to test for the order of integration of the variables, which involve observing the number of times variables have to be differenced before they become stationary. Testing the degree of integration of variables call the use of two well known: Augmented Dickey-Fuller (1979,1981) test and Phillip Perron (1988) test.

Wickremasinghe (2004) examined the monthly nominal spot rates for Japanese Yen, UK pound, US dollar, French Franc, Indian Rupee and German mark from data he collected from the Central Bank of Sri Lanka. His analyses of the unit root test showed that all the six currencies are random walks; by such reflect the efficient hypothesis in its weak form.

Hence, this result implies that market agents in the Sri Lanka’s foreign currency market cannot devise any technique to predict future movements of an exchange rate from its pass results. For instance, the cointagration test provides evidence against the semi-strong version of EMH. This means that movement of one or more exchange rates can be predicted from the movements of the other exchange rates. Hence, market participants can make profit both in the short and long run.