# Intraday spot foreign exchange market. Analysis of efficiency, liquidity and volatility.

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3 has to hold if the market is efficient. This relationship is also called covered interest rate parity. The market efficiency however has been put in a serious doubt, also in the aspects concerning the interest rates parity (Nguyen, 2000). An arbitrage attempt is sometimes made through the so called carry trades. It consists in borrowing currency generating low interest rate and investing in high yielding currency, assuming the exchange rate does not change over time or at least change less than necessary to turn a potential profit into a realized loss. To test how profitable carry trades can be, we take an example of trading conditions of one of forex brokers: Figure 1.1. Overnight rates charged by FXCM broker. Source: 17th June The columns 6 and 7 on the figure above show interest rates charged for overnight positions on the respective currency pair, i.e. the difference in overnight exchange rates. These interest rates are simply meant to reflect the difference between interest rates for each of two exchanged currencies, and thus are meant to be symmetric. In practice, negative rates have higher absolute value which constitutes another part of trading costs. In attempt to find an evidence if carry trades are susceptible to generate significant positive income, we run hypothetic carry trades for one month on 23 currency pairs, for each month over two year from January 2007 till December We assume each time a position of 1 lot was

4 placed the first day of the month and closed the first day of the next month. Each time the carry position is taken in the direction that generates positive overnight rate. All pip values are converted in USD at the average rate, and thus the generated profit is also expressed in US dollars. The monthly generated income is calculated as = + h =30 + h The results of calculations are shown in the table below. Currency pair Pip value (USD) Monthly profits in /07 02/07 03/07 04/07 05/07 06/07 07/07 08/07 09/07 10/07 11/07 12/07 EURUSD USDJPY GBPUSD USDCHF EURCHF AUDUSD USDCAD NZDUSD EURGBP EURJPY GBPJPY CHFJPY GBPCHF EURAUD EURCAD AUDCAD AUDJPY CADJPY NZDJPY GBPAUD AUDNZD EURNZD Currency Pip value Monthly profits in 2008 Average pair (USD) 01/08 02/08 03/08 04/08 05/08 06/08 07/08 08/08 09/08 10/08 11/08

6 distinguish rational trades following the news announcement, and those that are non rational and have to be rather studied using market psychology. Contrary to strong form of market efficiency, semi-strong and weak forms of this hypothesis are less restrictive. Semi-strong form claims that all public information is incorporated in prices, which exclude any privately known information. In other words, if a market is proved to be efficient in semi-strong form, neither fundamental nor technical analysis can consistently produce abnormal returns. The weak form of market efficiency states that all past prices are reflected in the today's price on the market. This basically means that is it not possible to get any significant advantage on the market by analyzing pas prices only, as it is done in the case of technical analysis. However, fundamental analysis can be successfully applied. Tools used to test market efficiency are dependent on the form of efficiency to be tested. Weak form may be detected using unit root tests. Semi-strong form is analyzed using cointegration, Granger causality and variance decomposition analysis. To define whether the foreign exchange market is efficient in semi-strong form, we are going to test: If the spot exchange rate behaves as a random walk, and If there is cointegration among a set of spot rates. If this analysis does not provide us with a positive answer, we will run a unit root test to check if the foreign exchange market is efficient in a weak form over short period of time. Methodology. To test if there is cointegration among spot rates, we do a two step analysis: 1. We find the order of integration of the variables, i.e. the number of times is differentiated before becoming stationary. For this, we use the Augmented Dickey-Fuller (ADF) test, which we expect to be confirmed by Phillips-Perron (PP) test. The reason of this step is that the test for cointegration should be done only among variables with the same degree of integration. 2. We apply Engle and Granger method to define if variables are cointegrated. In this method, one variable is regressed on the other, and we test if the residuals are stationary. Again, the Augmented Dickey-Fuller and Phillips-Perron tests are used to test for stationarity. Data. The analysis is first run on the minute-by-minute exchange rates on a set of currency pairs for the period from 1 st March 2009 until 31st May Because of the extensive second step of the analysis, our attention is restricted to only the exchange rates of USD vs. major currencies: EUR, GBP, CHF, JPY, CAD, AUD, NZD.

7 Results. The results of the Augmented Dickey-Fuller and the Phillips-Perron tests are in the table below. At this first step, if there is a unit root of a series, it is considered to be non stationary, and it is differentiated once again. The procedure is repeated until the p-value of at least one of two unit root tests is below 5%. The table presents the tests statistics along with p- values, as well as the number of times the series was differentiated until became stationary. Currency pair Times diff. ADF (p-value) PP (p-value) USDCHF (0.01) -217 (0.01) EURUSD (0.01) -206 (0.01) GBPUSD (0.01) -192 (0.01) USDJPY (0.01) -214 (0.01) USDCAD (0.01) -209 (0.01) AUDUSD (0.01) -204 (0.01) NZDUSD (0.01) -224 (0.01) Table 1.2. Statistics and p-values of the Augmented Dickey-Fuller and the Phillips-Perron unit root tests, minute data. As seen in the table 1.2, all the series became stationary after one differentiating. Thus, the Engel and Granger method can be run on the second step, and the table 1.3 presents, for each pair of exchange rates, the statistics and the p-value of the Augmented Dickey-Fuller and Phillips- Perron rests for residuals of regression of one series of exchange rates on another. USDCHF EURUSD GBPUSD USDJPY USDCAD AUDUSD NZDUSD USDCHF (0.01), -304 (0.01) (0.46), -2.35(0.43) (0.21), (0.17) -2.5 (0.34), (0.35) (0.21), (0.12) (0.51), (0.47) (0.53), (0.50) EURUSD (0.25), (0.23) (0.32), (0.33) (0.39), (0.35) (0.74), (0.68) (0.55), (0.50) GBPUSD (0.41), (0.40) (0.05), (0.02) (0.09), (0.08) (0.24), (0.20) USDJPY (0.21), (0.19) (0.30), (0.34) (0.51), (0.55) USDCAD (0.43), (0.34) (0.51), (0.49) AUDUSD (0.58), (0.48) Table 1.3. Results of the Engel and Granger method applied to daily exchange rates: statistics and p-values of ADF and PP tests, for residuals of the regression of price series of one currency pair against another, minute data. The results obtained in the table 1.3 are consistent with previous studies: the market is not efficient in a semi-strong form. This time the proof of it has been given for the foreign exchange market, on the minute-by-minute exchange rates of the major currency pairs. We can finally check if the market is efficient in a weak form. As was seen during the conducted analysis using high frequency minute data, for every series, the null hypothesis of unit root could

9 Figure 2.1. Spreads on currency pairs of MIG Investments SA, 20th June Time-Varying Liquidity The trading on the foreign exchange market is not uniform over time. Central Banks interventions decrease forex market liquidity and increase costs borne by traders (Pasquariello, 2002). Evans, Lyons (Evans, Lyons, 2004) investigate if trades have more influence on the price around the moments of news announcements, and come to a positive conclusion. During the day, the level of trading activity is variable. If we schematically split the 24-hour period of trade into "Japanese", "European" and "American" sessions, corresponding to business hours in each respective part of the world, we can expect significant movements of currencies in

10 periods of business hours of its home region. For example, the EURUSD currency pair would most move during the European and American session, but very little during Japanese business hours. Figure 2.2. Calendar of news announcements affecting the foreign exchange market, 22nd June The figure 2.2 shows an example of forex news announcements calendar. The announcements of medium to high importance are susceptible to temporarily affect market operations. To test it, we will compare the market liquidity between the time around a news announcement and all the other trading time. We analyze the announcements of medium and high importance as indicated and scheduled on publicly available calendars, e.g. or Following statistics will be analyzed:

13 It is a common practice that small orders are typically processed automatically, while important trades can be verified by a dealer before they are being approved. If we assume that trading system can automatically handle any volume the market generated at any conditions without changing the processing time, we narrow the analysis to positions processed after a dealer's approval. The results are presented in the table 2.4. Average time, s Standard deviation News time (major news) News time (medium news) Non news time Table 2.4. Time required to complete a market transaction (manual order processing only). The results above do not witness for any significant difference between the processing time. We attempt to make only the distinction between major news and no news, as well as restrict the definition of news time to 1 minute prior and 5 minutes after the news announcement. The results are in the table 2.5. Average time, s Standard deviation All transactions News time (major news) Non news time Manual processing only News time (major news) Non news time Table 2.5. Time required to complete a market transaction (important news only). From the results above, we conclude that the orders processing time as a measure of forex market liquidity does not change in the period of news announcements. Hot Potato Trading Evans and Lyons (Evans, Lyons, 2001) analyze the market liquidity using the orders flow. A particular attention is paid to the hot potato" trading, when positions are passed many times between traders and dealers, for risk management purposes. Hot potato trading generates increases the number of transactions, i.e. a certain volume of demand and supply. On the other hand, repetitive transactions in both directions are susceptible to compensate themselves, thus having the resulting signed order flow to remain the same. The model is described by two equations below: = ( + ) + = + +

14 where is the price change in the moment, is the order flow in the moment, =, =( + ), >0, =1 8, is the payoff increment in the moment, is aggregated order flow in the moment, indicates a proximity of news announcements. Evans and Lyons (Evans, Lyons, 2005) found evidence of a clear impact of news announcements on market liquidity, as well as some evidence of potato trading using hourly data. To test for presence of hot potato trading activity on minute data on forex, we are going to estimate the model for the major currency pairs using unsigned orders flow. A dummy variable takes the value of 1 one minute prior and ten minute after major and medium news announcements, 0 otherwise. The, its p-value and of the model are presented in the table 2.6. Currency pair (p-value) EURUSD 0.0 (0.122) 13.53% USDCHF 0.0 (0.002) 10.26% GBPUSD 0.0 (0.137) 18.34% USDJPY 0.0 (0.729) 11.02% USDCAD 0.0 (0.358) 10.83% AUDUSD 0.0 (0.201) 14.53% NZDUSD 0.0 (0.546) 9.35% Table 2.6., p-value and of the estimated hot potato trading model, minute data. All the coefficients differentiating between news announcements time, i.e. expected time of hot potato trading, and all the other time, are at zero. We thus find no evidence of hot potato trading on the foreign exchange market. Chapter 3. Volatilit and Risk Market volatility is a characteristic that describes how often and how much the market, in particular the price, changes. Market volatility is perceived differently by different market participants: it is desirable for active speculators, but tends to be avoided by long term investors.

15 Measures of Volatility and Risk Volatility is traditionally measured using basic statistical tools, like variance and standard deviation. According to Mandelbrot (Mandelbrot, Hudson, 2004, p. 48) this measure only reflects one part of the real market risk, "benign risk". The remaining "wild risk" is often neglected by researches, unless they use stable Pareto distributions. An alternative measure of volatility could be the number of price ticks arriving per unit of time useful information for speculators. Value-at-Risk, or VaR, at the 100(1 )% confidence level is generally defined by the upper 100 percentile of the loss distribution and is denoted as ( ), where is the random variable of loss. The VaR is a rather simplistic measure that only gives the level of loss. The investor does not know anything from VaR about the potential loss beyond this limit. An investment with VaR of USD is not necessarily less risky than that with the VaR at USD, if its potential maximum loss is USD vs USD of the second asset. This type of risk if often referred as tail risk. An extension of the VaR definition is the Expected Shortfall measure, otherwise called Expected Tail Loss. While using this measure, one assumes the loss is already beyond the VaR level. The Expected Shortfall measures the expected loss under these conditions, i.e. is the conditional expectation of loss, when the loss exceeds the VaR level (Arztner et al., 2007, 2009). In other words, it calculates how severe the average loss is, if VaR exceeded (Rachev et al., 2006): % ( ) = ( > ( ) %( )) where is the return given over time horizon, = is the loss. %( ) is also denoted ( ) %( ) meaning conditional. Three ratios are commonly used to evaluate the risk of an investment: 1. Sharpe Ratio (Sharpe, 1966) is a measure of risk-adjusted performance of an investment asset or a trading strategy. It is defined as: = ( ) The major shortcoming of this ratio is the underlying assumption of a normal distribution of residuals.

16 2. Stable-Tail Adjusted Return Ratio (STARR) (Rachev, 2006) is the ratio between expected return and its conditional value at risk: = ( ) ( ) % ( ) % 3. Rachev ratio (R-ratio) (rachev et al., 2007) with parameters and is defined as: = %( ) %( ) = (, ) where and are in [0,1]. The idea of this ratio is to maximize the level of return and get insurance for the maximum loss. It thus, out of three presented ratios, provides the most flexibility in terms of underlying distribution and desired levels of confidence, For both STARR and R-ratio, a lower absolute value negative result indicates a higher risk. The table below compares the risk of trading different currencies, on minute and daily data for the period from 1st March 2009 till 31st May ETL is calculated based on the assumption that the errors follow an -stable distribution. Currency Daily data Minute data Pair Sharpe VaR ETL STARR R (0.1,0.8) Sharpe VaR ETL STARR R (0.1,0.8) ratio (10%) (10%) (90%) ratio (10%) (10%) (90%) AUDCAD AUDCHF AUDJPY AUDNZD AUDUSD CADCHF CADJPY CHFJPY CHFSGD EURAUD EURCAD EURCHF EURGBP EURJPY EURNZD EURSGD EURUSD GBPCHF GBPJPY GBPUSD NZDCAD NZDCHF NZDJPY NZDUSD

18 = ( ) + ( ) + where ( ) and ( ) are assumed to be constants. The model is estimated on the minute data. The estimated values of the coefficient along with its p-value for major currency pairs are presented in the table below. The result for cross and exotic currency pairs are of the same order. Currency pair p-value EURUSD USDCHF GBPUSD USDJPY USDCAD AUDUSD NZDUSD Table 2.8. and p-value for the Glosten-Milgrom-Harris model. For four currency pairs out of seven, there is a non negligible evidence of an increased volatility during the first and the last 30 minutes of either regional equity trading session. Chapter 4. Conclusion The present research studied such crucial properties of the spot foreign exchange market over the short term as efficiency, liquidity and volatility. In particular, it was found on minute data that the forex market market is efficient in weak form. Foreign exchange is also being extremely liquid, and its liquidity is not affected by regional equity trading sessions and news announcements. Finally, the forex market is exceptionally volatile, especially on the high frequency data. Additionally, it was noted that forex data, in spite of apparent fractals pattern, does not have same properties at different scales, in particular in terms of market volatility. The main conclusion for short term intraday trading is that investors should be particularly cautious and use specified models only, as traditional equity and long term forex models are not appropriate. In terms of future research, the intraday spot forex trading is definitely a vast domain that is still to be explored and new adequate models are still to come. Bibliography Artzner P., Delbaen F., Eber J.M., Heath D. (1997), Thinking Coherently // Risk, Vol. 10 (11), pp Artzner P., Delbaen F., Eber J.M., Heath D. (1999), Coherent Measures of Risk // Mathematical Finance, Vol. 9 (3), pp Bank for International Settlements (2007), Triennal Central Bank Survey. Foreign Exchange and Derivatives Market Activity in 2007 // December 2007.

19 Beine M., Laurent S., Palm F. (2003), "Central Bank FOREX Interventions Assessed Using Realized Moments // Journal of International Financial Markets, Institutions and Money, available at SSRN: Beine M., Lecourt Ch. (2004), Reported and Secret Interventions in the Foreign Exchange Markets // Finance Research Letters, 1(4), pp Evans M.D.D., Lyons R.K. (2001), Time-Varying Liquidity in Foreign Exchange // October Evans M.D.D., Lyons R.K. (2004), Do Currency Markets Absorb News Quickly? // Cass Business School Research Paper, June 2004, available at SSRN: Evans M.D.D., Lyons R.K. (2005), Meese-Rogoff Redux: Micro-Based Exchange Rate Forecasting // January Fama E. (1970), Efficient Capital Markets: A Review of Theory and Empirical Work // Journal of Finance 25, pp Frenkel M., Pierdzioch Ch., Stadtmann G (2002), The Accuracy of Press Reports Regarding the Foreign Interventions of the Bank of Japan // March Glosten L., Harris L. (1988), Estimating the Components of the Bid/Ask Spread // Journal of Financial Economics 21 (1988), pp Lyden S. (2007), Time of Day and Market Impact // The Journal of Trading, Summer Lyons R.K. (2002), The Future of the Foreign Exchange Market // 5th Annual Brookings- Wharton Papers on Financial Services Conference, January Mandelbrot, B., Hudson R.L. (2004), The (mis)behavior of markets: a fractal view of risk, ruin, and reward // New York: Basic Books. Nguyen T. (2000), Foreign Exchange Market Efficiency, Speculators, Arbitrageurs and International Capital Flows // Centre for International Economic Studies, Adelaide University, Policy Discussion Paper No 0033, March Pasquariello P. (2002), Informative Trading or Just Noise? An Analysis of Currency Returns, Market Liquidity, and Transaction Costs in Proximity of Central Bank Interventions // May 2002.

20 Rachev S.T., Stoyanov S., and Fabozzi F.J. (2007), Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures // Wiley, July Rachev, S., Martin D., Racheva-Iotova B. and Stoyanov S. (2006), Stable ETL optimal portfolios and extreme risk management // Decisions in Banking and Finance, Springer/Physika, Rachev, S.T. et al. (2006), Risk and Return in Momentum Strategies: Profitability from Portfolios based on Risk-Adjusted Stock Ranking Criteria // Technical Report, UCSB, Sharpe W. F. (1966), Mutual Fund Performance // Journal of Business 39 (S1), pp

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