The Efficiency of the Foreign Exchange Market - Coursework Example

?Efficiency of Foreign Exchange Market And Relation between Forward rate and Future spot rate Financial markets have been a mystical area for the researchers. The area is mystical, because over the years it has validated and invalidated numerous theories. One theory that has been validated by a group of researchers in some time frame has been proved invalid by the other researchers on a different time frame. One of the early theories of modern finance is the hypothesis of efficient markets. The efficient markets hypothesis tells that prices fully reflect information available to market participants. From the microstructure point of view, these participants are either hedgers or speculators. In efficient markets, there are opportunities neither for the hedgers nor for the speculators to make super-normal profits (Fama, 1970). In such a situation, speculative efficiency and arbitraging efficiency exist. The speculative efficiency hypothesis is the proposition that says if there is speculative efficiency in the market, the expected rate of return to due speculation in the forward foreign exchange market is zero (Hansen and Hodrick, 1980). The arbitraging efficiency hypothesis is the proposition that the expected rate of return to covered or uncovered interest arbitrage in the international capital market is zero. Interest arbitrage is a form of arbitrage where funds are taken out of home country to invest in a foreign country’s interest bearing securities. This strategy tries to make profit from the difference in interest rate of the two countries. Interest arbitrage is a central concept to understand the foreign exchange movements. Literature Review For testing the speculative efficiency of any foreign exchange market, many academicians consider the hypothesis that the forward price is the best forecast available of future spot price. For the test of arbitraging efficiency, several authors test covered interest parity (CIP), i.e. the parity between the forward discount from the expected spot and the interest differential between a pair of currencies. Since transactions costs and risk premium are there in the price, now it has become a widely known fact that, rejecting the CIP test doesn’t necessarily imply that the market is arbitraging inefficient. In the context of a simple forward market model it can be shown that arbitraging efficiency can exist even if CIP does not hold and transactions costs and risk premium are absent (Stein, 1965). In reality, prices include transaction costs and there is a presence of risk premium for the risk taken by taking position on that particular asset. Since transactions costs and risk premium exist in practice (Bilson, 1981); a departure from CIP does not necessarily imply arbitraging inefficiency. With transactions costs and risk premium, it can be shown that the null hypothesis for testing CIP differs from that for testing arbitraging efficiency. Frequent failures of the tests of market efficiency as the forward discount deviates from either the interest differential or expected depreciation; have led researchers to postulate the existence of a risk premium. There have been also a lot of cases of large difference of average holding returns across asset classes. Moreover the risk premium has been time dependent (Grauer et al, 1976). Researchers have often tested for a risk premium as a function of the variance of forecast errors or of the exchange rate movements (Domowitz and Hakkio, 1985). A usual initiative for researchers while testing for speculative efficiency is that they take for granted that speculators are risk neutral. Empirical studies for a large variety of currencies and time periods and for the recent floating experience tend to report results which are unfavorable to the efficient market hypothesis under risk neutrality (Longworth, 1981; Fama, 1984). For the period 1973 to 1979, Hansen and Hodrick (1980), using weekly data and three-month forward rates and carrying out tests involving the currencies of seven countries which are Canada, France, Italy, Japan, Switzerland, United Kingdom and West Germany versus US $, reject the null for three currencies (mark, franc and lire versus US $), but do not reject the null for the remaining four currencies. Some academicians also use ‘weak-form error orthogonality’ test (Tease, 1980). Using the gap between forward rate and the future spot rate as a proxy for the forecast error, they regress this proxy against one or more of its lagged values. This is for understanding speculative efficiency. One major problem encountered in testing either speculative efficiency or arbitraging efficiency hypothesis is that the expected rate of depreciation is not directly observable and it is difficult to find a good proxy for it. Testing Market Efficiency There are three methods for testing market efficiency. Since information on the exchange rate (in the form of its past time-series) cannot be used to improve on profits, if exchange rate truly follows a random walk without drift. Thus the first method for testing market efficiency is to carry out a simple test of the exchange rate for unit root to understand a random walk without drift. This method was quickly abandoned when it was realised that such a test of market efficiency is valid only if the interest differential is constant over time. Though there are some concerted efforts by the central banks of particular economies, like developed or emerging, to take monetary measures, but the interest rate differential generally changes. Since market efficiency implies that profit opportunity doesn’t exist, the second method for testing market efficiency is to test for the profitability of filter rules (for example, a simple rule of buying a currency whenever it rises P% above its most recent trough and selling the currency whenever it falls P% below its most recent peak). If market is not efficient, then such techniques will bring profits. This method has not been popular with economists. The problem for the test for efficiency for markets under this method is intellectually challenging. It is very difficult to determine the beginning and end of time-series as different time series will give different results. Also the filter rules which are numerous are difficult to investigate. By far the most popular method for testing market efficiency has been the third method which involves regressing the logarithm of the spot rate onto the lagged logarithm of the forward rate (Frenkel, 1976, Turnovsky and Ball, 1983). The third method’s null hypothesis of speculative efficiency can be rejected if the forward discount deviates sufficiently from the expected mean of the (actual) rate of depreciation and this can be the result of the fact that the supply of speculative funds is less than infinitely elastic with respect to backwardation. Backwardation is the situation when price of forward or future contract trades below the expected spot price on the date when the contract matures. Academicians maintain that the sensitivity of the speculative net position to backwardation is higher when expectations are held firmly. In period of considerable doubt, the net position is naturally poor (Stein, 1995). Results and Analysis For the sake of this paper, we are going to use the third method of testing market efficiency and this will in turn empirically test whether forward rates are in fact the unbiased estimator of future spot rate or not. There general relation between the forward price and the spot price is as follows: Ft = S0 * ert Where, Ft represents the forward price of the asset at time t S0 represents the current spot price of the asset ert represents a mathematical exponential function  and it represents cost of capital. Empirical model for testing the predictability of future spot rates is given by St+k = a + b Ft + et+k Where, St is the natural logarithm of the spot rate at month t, Ft is the natural logarithm of the forward rate at month t with k the 3 month settlement period, The terms a, b are constant parameters and e is the error term. The natural logarithm has been taken since relation between the forward and the spot price is multiplicative in nature. This equation expresses the notion of rational expectations with no risk premium. The assumption is, therefore, that market participants are risk neutral and form expectations in a "rational" manner; the expected values of exchange rate determinants are explicitly discounted to the present values. To put it differently, this means the expectation from the broader factors that determine the rates have already influenced the price and the relevant information for predicting exchange rates is fully reflected in the current forward exchange rate. Therefore, testing the hypothesis of forward market efficiency is equivalent to testing the joint hypothesis a = 0 and b = 1; a =0 invariably leads to the conclusion that there is no transaction cost and risk premium. Failure to reject the joint hypothesis implies that the forward rate determined at time t is an unbiased predictor of the spot rate for time t + k. However, statistical rejection of this hypothesis will infer either that the market is inefficient or that the specification of the model is incorrect, or both (Wesso 1999). In this segment we are going to look at the relation between the British sterling and US dollar in the light of above theory. The data for the purpose of analysis has been sourced from the Bank of England website (tables given in Appendix). The data is basically spot price and the forward price of sterling in terms of dollar. Here we are using the average monthly data. The raw data that has been taken for our analysis starts from January 1979 and ends at March 2012. We have taken spot prices, one month forward rates and three months forward rates of these dates, and properly lagged the forward rates to tally the corresponding spot rates. Let us first look at the spot price and 1 month forward data relation. Here the forward rate will be lagged by 1 month, since 1 month forward rate will be the estimate for the spot price of next month. It can be seen that, the forward price closely follows the spot price. It can be more evident from the spread chart. The charts are available as an appendix to this paper. Here the spread has been calculated by deducting the forward rate from the spot rate. The most of the time the spread is between -0.05 and +0.05. There are some moments of extraordinary spikes like that in 2008. In times of crisis the confidence falters, the volatility increases. Simple descriptive statistical analysis of the spread data gives a mean of 0.0014, with standard deviation 0.0436. Now we run the regression of natural logarithm of the spot rates on the natural logarithm of the 1 month forward rates. The regression returns intercept at a= 0.0113 and the coefficient for the natural logarithm of the 1 month forward rates b = 0.9795 with corresponding t values 2.2287 and 101.4361. These values are very near to a = 0 and b = 1. Now let us run similar methods on the data where the natural logarithm of the spot rates has been regressed on the natural logarithm of the 3 month forward rates, after lagging the forward data by a time period of 3. Here, the results are okay with the proposition but not as encouraging as the case for the one month forward rate. Here, the intercept turns out to be a = 0.04761 and the coefficient for the natural logarithm of the 3 month forward turns out to be b = 0.9103. The corresponding t values are 4.5517 and 45.5590. This deviation is more evident from the spread data of the spot price and 3 month forward data. Here the most of the data lies within -0.1 to 0.1. In case of the spread for the spot price and 1 month forward data, the most of the data laid in between -0.05 and 0.05. Simple descriptive statistical analysis of the data returns a mean of 0.0035 and standard deviation of 0.0921 which is nearly double the spread volatility for the 3 month forward spread. Clearly 3 month spread data is more volatile. The required chart is in the appendix. The underlying assumption while running the method has been that there is no transaction cost and no risk premium. But, we have seen from the chart of 1 month forward spread, the chart bottomed near -0.15 during the 2008 crisis. The clearly the there is a high risk premium during those uncertain periods. Also, from the microstructure of the markets, we can definitely say that there is some sort of transaction cost in every market. That transaction cost may depend upon the fiscal policies by the government, but there cannot be a market where the transaction cost is purely zero. In other terms the transaction cost can be viewed as some form of institutional cost. Conclusion There has been an extensive literature on the efficient market hypothesis which tell that the all the information has already been priced in and there is no other information in the system which can help to make supernormal profits. In other words, the speculative efficiency and arbitrage efficiency both exist. Now for reflecting the price perception of information, we generally consider a uniform view among the market participants. In real life situation, when market participants invest in foreign countries interest bearing securities, they try to gauge the chance of earning a good return. From our own experiment with the data from the Bank of England, it is clearly visible that there is a time effect on the efficiency of the system. With longer contract, market participants will demand more and more risk premium. Also, the economic environment has a bearing on the risk premium. At times, it may happen that some traders in the market overreact to some events and news. This can lead to some anomaly. The same is also true for the market regulators. There can be some periods when the regulators in a country take some measures to outsmart the market. This can create serious jittery in the market. Again, it is not possible for the monetary regulators to prioritize the interest differential while framing the policies rejecting other priorities like inflation and growth, through capital inflow in terms of hot money is a major concern for the regulators. So, from purely academic pursuit, the markets can be taken as efficient and the forward price can be taken as the unbiased estimate for the future spot rate; but from the traders’ point of view, caution needs to be practiced while applying such conclusion. Appendix Figure 1: Spot Rate Vs. 1 Month Forward Rate (Bank of England, n.d.) Figure 2: Spread between Spot Rate and 1 Month Forward (Bank of England, n.d.) Figure 3: Spread between Spot Rate and 3 Month Forward (Bank of England, n.d.) Tables Findings of Regression Between the natural logarithm of the spot rates and natural logarithm of the 1 month forward rates Multiple R 0.9813 R Square 0.9629 Adjusted R Square 0.9628 Observations 398 F 10289.27372 Significance F 1.7991E-285 Coefficients Standard Error t Stat Intercept 0.0113 0.0051 2.2287 LN 1m Forward 0.9795 0.0097 101.4361 (Bank of England, n.d.) Descriptive Statistics For the 1 month spread Mean 0.0014 Standard Error 0.0022 Median -0.0003 Mode -0.0084 Standard Deviation 0.0436 Sample Variance 0.0019 Kurtosis 1.5201 Skewness -0.2993 Range 0.3397 Minimum -0.1863 Maximum 0.1534 Sum 0.5595 Count 398 Descriptive Statistics For the 3 month spread Mean 0.0035 Standard Error 0.0046 Median 0.0054 Mode 0.0384 Standard Deviation 0.0921 Sample Variance 0.0085 Kurtosis 2.0593 Skewness -0.6910 Range 0.6299 Minimum -0.3806 Maximum 0.2493 Sum 1.3771 Count 396 Findings of Regression Between the natural logarithm of the spot rates and natural logarithm of the 3 month forward rates Multiple R 0.9168 R Square 0.8405 Adjusted R Square 0.8401 Observations 396 F 2075.6254 Significance F 4.0354E-159 Coefficients Standard Error t Stat Intercept 0.04761 0.01046 4.55173 LN 3m forward 0.91028 0.01998 45.55903 (Bank of England, n.d.) References Bank of England, n.d., Statistical Interactive Database - interest & exchange rates data, available at: http://www.bankofengland.co.uk/boeapps/iadb/index.asp?first=yes&SectionRequired=I&HideNums=-1&ExtraInfo=true&Travel=NIxIRxSUx (accessed on April 9, 2012) Bilson JFO,1981, The Speculative efficiency Hypothesis, Journal of Business, Vol. 54, No. 3, pp.435-52 Domowitz, I and Hakkio, CS, 1985, Conditional Variance and the Risk Premium in the Foreign Exchange Market, Journal of International Economics, Vol. 19, No.1/2, pp. 47-66 Hansen, LP and Hodrick, RJ ,1980, Forward Exchange Rates as Optimal Predictors of Future Spot Rates, Journal of Political Economy Vol. 88, No. 5, pp.. 829-53 Frenkel, J A. 1976, A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence, Scandinavian Journal of Economics, Vol 78, No. 2, pp.200-24s Fama E.1984, Forward and Spot Exchange Rates, Journal of Monetary Economics, Vol. 14, No. 3, pp.319-38 Fama E.1970, Efficient Capital Markets: A review of Theory and Empirical Work: Journal of Finance, Vol. 25, No. 2, pp. 383-417 Grauer FR, Itzenberger RH and Stehle, R, 1976, Sharing rules and Equilibrium in an International Capital Market Under Uncertainty, Journal of Financial Economics Vol. 3, No. 2, pp.233-256 Longworth D, 1981, Testing the Efficiency of the Canadian-US Exchange Market under the Assumption of no Risk Premium, Journal of Finance, Vol 36, No 1, pp. 43-49 Stein JL. 1965, The Forward Rate and the Interest Parity, Review of Economic Studies, Vol. 32, No. 2, pp.113-26 Tease WJ, 1988, Speculative efficiency and the Exchange Rate: Some Evidence since the Float, Economic Record, Vol. 64, No. 1, pp.2-13 Turnovsky S and Ball, KM, 1983, Covered Interest Parity and Speculative efficiency: Some Empirical Evidence for Australia, Economic Record, Vol. 59, pp.271-80 Wesso G. R. 1999, The forward rate as an optimal predictor of the future spot rate in South Africa: An econometric analysis, South African Reserve Bank, Occasional Paper No.13, available at: http://www.esaf.org/internet/publication.nsf/ladv/a3c83b170d2e81b442256b6c003b8614/$file/opaper13.pdf (accessed on April 9, 2012) Read More