forex markets and abnormal returns...

Forex Markets and Abnormal Returns

Abstract

This study tests whether individual Forex (foreign exchange) investors can predict future returns,

time the market and generate alpha after transaction costs. Using a sample of 1,231 Forex trading

accounts and 72,072 trades, the results show that individual Forex investors can predict future

returns up to eight days after trade execution, even after controlling for volatility. The results of

return predictability are significant because it supports the idea that linear independence is rejected

as well as provides empirical evidence that private information is available in the foreign exchange

market.

Key Words: International Finance, Exchange Rates, Foreign Currency, Foreign Exchange, Money

Price, Peg, PPP, Risk Premia, Spot Rate, Forecasting Exchange Rates

JEL classification codes: F31, F310, F370

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1. Introduction

In the past decade, there has been a revolution in the field of individual investing and a rapid

increase in short-selling. Prior to the advent of the internet and online trading, numerous financial

instruments and trading strategies were unavailable to individual investors. In the current

environment, transaction costs have decreased due to the increased growth of online brokerages

and investment products that were once only available to professionals and institutional investors

and are now accessible to individuals. The role of short-selling and online Forex (hereafter, “FX”)

trading has experienced significant growth (Luke 2005), yet no studies have investigated this

sophisticated and advanced field.

Prior studies have investigated currency managers’ performance against benchmarks factors

(Melvin and Shand 2010; Pojarliev and Levich 2008) and the style performance of currency fund

managers (Pojarliev and Levich 2010). This study investigates if individual FX short sales trading

predicts future returns, which in turn would demonstrate an individual FX investor’s ability to

predict future returns. In addition, this study investigates an individual FX investor’s performance.

We obtained proprietary transactional data for 1,231 individual investors’ FX accounts that

included data regarding short sale transactions. The data also included information regarding when

the trade was open, when the trade was closed, the open price and the close price for the trade. We

verified the data using Bloomberg Terminals and the Thompson Reuter’s database.

We propose that online trading is an ongoing future trend and individual investors play a vital

role in the FX market. The novelty of this study is that individual FX investing is a field that has

not yet been explored by research and this investigation of individual FX investors will be highly

valuable.

Studies such as Silber (1984) and Kuserk and Locke (1993) discussed floor investors. Locke and Mann

(2000) and Pojarliev and Levich (2008) examined professional investors and currency managers. Barber

and Odean 2011 examined the behavior of any individual investor and their trading patterns but did not

examine the behavior or returns of individual currency investors. Christopher J. Neely (2011) examined

technical analysis for foreign exchange markets without investigating individual investor’s behavior.

Bakshi et al. (2013) examined the predictability of foreign exchange trading strategies, but not in

relation to individual investors.

The inquiry of this study differs from prior studies because prior studies investigated currency fund

managers and not individual FX investors. Furthermore, prior studies have not investigated short-selling

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transactions, the ability of individual FX investors to predict future returns or individual investors ability

to generate pure alpha. This paper investigates individual FX investor performance, their ability to

predict FX returns, their ability to generate pure alpha and timing the market. Therefore, this paper

provides new lens on the FX market by focusing on individual FX investors.

The results of this study demonstrate that the mean percent of winning trades made by

individual FX investors was 52.975 and the average percent of losing trades was 47.03. Investors

executed an average of 29.2 trades per month and 350.39 trades per year. In addition, the percent

of long winning trades was 56.7 and the percent of winning short trades was 56.26. Moreover, the

results revealed that individual FX investors were able to predict returns for up to eight days, even

after controlling for volatility. This discovery supports the argument of prior studies such as Ito,

Lyons, and Melvin (1998) and Evans and Lyons (2004) in that individual customer trades contain

pieces of new information regarding the underlying macroeconomic fundamentals that affect the

exchange rate. Moreover, our results support the evidence of both Brock, Hsieh, and LeBaron

(1991) that the linear independence of FX prices is rejected. Therefore, our discovery of return

predictability is significant because it not only supports the concept that linear independence is

rejected but also provides empirical evidence that private information exists in the FX market. In

addition, this study provides additional empirical evidence that may be used to predict future

movements in the FX market.

This study demonstrates that certain individual FX investors are able to time the market,

produce positive alpha after transaction costs and their future alpha is not related to the prior year’s

alpha, which is additional evidence of their market timing ability. Consequently, the ability of

these investors to time the market cast doubts on the proponents of market efficiency.

The outline of this paper is as follows. Section 2 provides a literature review, and Section 3

provides a detailed description of the data. Section 4 develops the methodology used and presents

the results, and Section 5 presents the conclusion.

2. Literature review

Short-selling stocks have been examined extensively in prior studies regarding finance. To date,

all prior empirical research and theoretical models that addressed short-selling have solely

analyzed equities; financial instruments such as foreign exchange contracts have been unexplored,

which presents an opportunity for empirical exploration.

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Short-selling theoretical models that address equities have relied on the theory that mispricing

occurs due to the divergence of price from fundamentals because of constraints on selling stocks

short (Miller 1977). Diamond and Verrechia (1987) hypothesized that short sellers are informed

of the true value of stocks and are thus able to exploit divergences from fundamental value.

Empirical studies that have investigated short-selling remains mixed although the majority of prior

studies support Diamond and Verrechia’s hypothesis that short sellers are informed. Aitken et al.

(1998) analyzed Australian Securities and determined that short trades that occurred near

information events were associated with larger price reactions. Christophe, Ferri, and Angel (2004)

investigated short sale transactions during the five days before the earnings announcements of 913

Nasdaq-listed firms and provided evidence of informed trading in pre-announcement short-selling.

Asquith, Pathak, and Ritter (2005) demonstrated that high-short-interest predicts negative

abnormal returns and that this relationship is strongest in stocks with low institutional ownership.

Boehmer, Jones, and Zhang (2008) used proprietary NYSE order data and determined that heavily

shorted stocks underperformed lightly shorted stocks. Diether, Lee, and Werner (2007) determined

that short sellers increased their trading following positive returns and correctly predicted future

negative abnormal returns. Conversely, Daske, Richardson, and Tuna (2005) examined short sale

transactions that occurred shortly following significant news events and discovered that evidence

did not support the notion that short sale transactions increased prior to bad news events.

A literature review of empirical studies that address foreign exchange (“FX”) trading reveals

that short-selling has yet to be addressed. The majority of studies regarding currency have focused

on traders’ characteristics and the performance of currency fund managers. In prior studies

regarding traders’ characteristics, Silber (1984) and Kuserk and Locke (1993) examined the

trading characteristics of scalpers for future floor investors and market makers. Manaster and

Mann (1996) studied market-maker inventory positions and trading activity. Manaster and Mann

(1999) analyzed the trading profits of futures market makers from liquidity trades and price

movements. Locke and Mann (2000) determined that future professional investors exhibited a

disposition effect in which they held losing trades longer than winning trades and the position sizes

for losing trades were larger than for winning trades.

Pojarliev and Levich (2008) examined the returns of professionally managed currency funds

and a subset of returns from thirty-four individual fund managers and demonstrated that currency

fund managers earned excess returns that averaged twenty-five basis points per month. In addition,

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their study investigated the relationship between fund returns and four trading differentiating

factors: Carry, Trend, Value, and Volatility and discovered four factors that explain the variability

in returns. This study seeks to determine if individual FX investors are able to predict future

returns, time the market, and produce alpha.

2.1 The retail FX market

The retail FX market (RFM) is less than a decade old and thus warrants a review. The RFM

evolved from the foreign exchange market that arose from developments in the early 1970s when

the fixed exchange rate system changed to a floating exchange rate. Today, the FX exchange (FX)

market is one of the largest and most liquid markets in the world. Historically, the majority of

currency trading occurred between central banks, governments, corporations and other large

institutions. Individual investors were excluded due to the complexity of the instruments and

significant capital requirements needed to trade currency instruments. In the 1990s, a revolution

began in the FX markets, and retail trading was introduced, which made the FX market accessible

to individual investors. The stock market crash of 2000, along with an increase in the number of

online FX brokers, attracted a multitude of investors seeking new and innovative instruments to

trade. These events resulted in explosive growth rates of individual investors that trade FX

instruments (Luke 2005). It is estimated that the daily trading turnover of the retail FX trading

market is approximately $50–60 billion and continues to grow.

2.2 Retail FX trade systems

The retail market has evolved rapidly and numerous professional and individual investors have

developed “trading systems”. Trading systems permit individual investors and professional

investors to create computer-based programs that transmit their trading signals via the internet to

other investors. A recent development is the evolution of paid-for subscription systems where

individual investors pay trade system developers (“Developers”) for their services. Developers

may be persons or institutions that manually manage investor’s trades and/or develop trading

systems and offer access to their trades or systems for a fee. Developers promote their systems on

the internet and in trade publications. Developers sell access to their accounts and other investors

are able to earn a profit from this process. Individual investors may subscribe to these automated

trade systems and receive trade signals via E-mail, instant messaging or receive signals routed

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directly to their broker through computer programs that link the trade system Developer’s account

to an individual investor’s personal online brokerage account.

The unique sample analyzed in this study consists of proprietary data obtained from an online

trade system hosting company (“Trade System Host”). For a monthly fee, Developers may join

the Trade System Host and offer their trading system to the public. The Trade System Host records

all trades entered by Developers, provides summary statistics for each system, and ranks all

systems based on profitability. Individual investors visit the Trade System Host’s website, which

contains thousands of trade systems. Individual investors are able to search through the various

systems and subscribe to systems that suit their investment needs. Once an individual investor

subscribes to a system, complete, real-time access to all trades executed by the Developer is

available. For example, individual investors receive “trade signals” every time a trade is made.

These signals are transmitted by using instant messaging or e-mail or are directly routed to the

investor’s home computer, then to their broker through software add-ons. In effect, the individual

investor’s personal brokerage account is managed over the internet by the Developer.

A compelling advantage of this trading system is that individual investors are able to subscribe

to numerous trading systems and develop their own individual trading strategy. The Trade System

Host used in this sample contains 6,735 trade systems from developers around the world. These

systems trade a variety of financial instruments including stocks, futures, options and spot FX.

Because the primary objective of this study is to investigate the retail spot FX market, the sample

of this article consists of 1,231 accounts that have conducted at least one FX trade.

Prior studies have demonstrated that short sellers, who are considered to be sophisticated

investors, have the ability to identify mispricing and exploit market inefficiencies (Boehmer,

Jones, and Zhang 2008; Asquith, Pathak, and Ritter 2005). Empirical studies that have investigated

the trading patterns of individual investors have demonstrated that these investors are unable to

beat the market (De Long et al. 1990; Lee et al. 1991). Certain studies have indicated that a small

percentage of investors earn significant positive abnormal returns (Coval, Hirshleifer, and

Shumway 2005).

Diamond and Verrechia’s (1987) conclusion that short sellers are capable of exploiting drifts

from fundamental value arises from the assumption that short sellers are informed and able to

obtain exclusive non-public information regarding firms. Currencies are not financial instruments

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that possess unique informational advantages such as corporations. Thus, there should be little, if

any, private information available for FX short sellers to exploit.

The sample used in this study is unique because we obtained proprietary transactional data for

1,231 individual investor FX accounts that contain short sale transactions data including

information regarding when the trade was open, when the trade was closed, the open price and the

close price for the trade. This study investigates if individual FX investors are able to predict future

returns, possess market timing ability, and produce alpha after transaction costs.

3. Data

The primary data set consists of a proprietary database of individual FX investing accounts

obtained from an American internet-based data FX trade System Host from the time period of

April 2005 to March 2015. The secondary data sets used for the return analysis and benchmarking

include daily FX spot prices and return data obtained from MLDownloader, a program that

downloads FX, future, and stock data from multiple online resources including Yahoo! Finance.

Benchmark data is also obtained from the Deutsche Bank web-based index portal, which provides

their proprietary Investible and Benchmark indices.

The sample includes 1,231 individual FX investors’ accounts, 72,077 trades, and all active

accounts during the sample period that have recorded at least one transaction. The 72,077 trades

constitute all trades that have been opened and subsequently closed by the trader. Trades that were

still open were not available because only paid subscribers to these systems have access to this

information. The total number of trades used for this analysis is 72,072 because five transactions

contained corrupted data. We verified the data using Bloomberg Terminals and Thompson

Reuter’s database.

The sample is very detailed and includes investors’ names, the number of trades, the type of

FX instruments traded, and transaction specific data. Transaction specific data includes a unique

trade identification number for each trade, the date, the time (in seconds) that the trade was opened

and closed, the type of trade (short or long), the open and close price of the trade in US dollars,

the quantity of contracts traded, and the FX symbol. Furthermore, the data includes information

regarding whether stops or limits were used and descriptions of individual accounts that provide

insight regarding the types of trading strategies used. Tables 1 and 2 provide descriptive statistics

of these investors.

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Table 1 indicates that the average account age is 0.27 years. Age is defined as the length of

time that an account is held open and is measured in calendar days. This average time, 0.27, reflects

that individual investors are extremely short term investors such that their trading accounts only

remain open for approximately three or four months out of the entire year.

The aggregate data provides return and win/loss data for all accounts. The total dollar mean

gross gain (loss) for each account was $55,261.91 (-$55,071.61), respectively. Overall, the dollar

average net gain for each account over its lifespan was $190.30. Furthermore, the total gross

maximum dollar gain (loss) was $1,824,780 (-$1,557,940), and the total net maximum dollar gain

(loss) was $937,220.00 (-$99,964.10), which reveals that certain investors won or lost a significant

amount of money. The average account executed 350.39 (29.20) trades per year (month), which

demonstrates that these investors are frequently trading.

< Insert Table 1 here>

Table 2 provides summary data for the 72,072 individual transactions in the transaction portion

of the database. Panel A indicates that out of 72,072 trades, 34,982 (48.54%) trades were short

sales and 37,090 trades (51.46%) were long positions. The magnitude of short-selling in the FX

market appears to be quite large when compared to prior studies that analyzed short-selling

equities. For instance, Boehmer, Jones, and Zhang (2008) examined a daily panel of NYSE short

sales from 2000 through 2004 and demonstrated that shorting consisted of 12.9 % of the NYSE

volume. Diether, Lee, and Werner (2007) reported slightly greater amounts of short sales of 24

percent for the NYSE and 31 % for the NASDAQ over the time period from January 2, 2005, to

December 30, 2005. Furthermore, Table 2 Panel B demonstrates that 56.73 % of long trades were

profitable, 41.66 % lost and 1.6 % broke even (zero gain/loss) on a pre-transaction cost basis. Out

of the 34,982 short sales, 56.26 % of shorts were profitable, 42.16 % lost and 1.58 % broke even

on a pre-transaction cost basis.

Table 2 Panel C provides a frequency distribution table of all forty-one FX traded by this

sample. The top five contracts traded consisted of nearly 70% of all contracts traded. The top five

contracts included the GBP/USD (21.6%), EUR/USD (21.27%), USD/JPY (11.4%), USD/CHF

(10.22%) and the GBP/JPY (7.93%). In summation and according to our calculations, this sample

demonstrates that these accounts were short-lived, traded actively, and were owned by relatively

successful investors when considering the win/loss percentages.


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4. Methodology

4.1 Predictability of Returns

The hypothesis used for this study tests if individual FX short sales are unable to predict future

returns. This test is performed by regressing a series of windows of returns on the individual

investors’ trade activity. Prior studies that analyzed equities focused on a five-day event window

(Deither, Lee and Werner 2007); however, this study analyzes FX, and we use detailed transaction

data that allows us to conduct a more detailed analysis of the predictability of returns by focusing

on a series of alternative windows.

To investigate if individual FX short sales predict future returns, we used Model (1), which

regresses a dummy variable, Trade, that assumes the value of one if the transaction is short and

zero if the trade is long, on the cumulative raw returns after transaction costs r (window: x1, x2)

over the event window. The event windows used in the analysis consist of cumulative raw returns

after the transaction expenses of all FX contracts from (0,1) to (0,10), where zero signifies the

execution day and the beginning of the return window calculations and one or ten signifies the end

of the return windows calculations days after the implementation of the trade. According to our

hypothesis that FX investors cannot predict future returns, the coefficient of “Trade”, which is a

binary variable and regressed against the return window (0, 10), should be positive (because it is

a short sale variable) and statistically insignificant. Model (1) is as follows:

𝑟(𝑤𝑖𝑛𝑑𝑜𝑤: 𝑥1,𝑥2) = 𝛼𝑡 + 𝛽1𝑡𝑟𝑎𝑑𝑒𝑡 + 𝜀𝑡 (1)

Table 3 provides the results of this analysis. Overall, the results do not support the hypothesis

that FX short sale trades or short sellers are unable to predict future returns. The coefficients of the

trade variable are negative and statistically significant (p-value ranges from 0.01 to 0.0062) for the

windows of (0, 2) to (0, 8), which suggests that these investors are able to predict returns up to

eight days in the future. Furthermore, the results demonstrate that the investors’ ability to predict

future returns drops off nine days (0, 9) after the date the trade is executed. Although the

coefficients continue to be negative for trades nine (0, 9) and ten (0, 10) days after the date of

execution, the statistical significance is no longer present for the ten-day window. It is notable that

the model has a relatively small coefficient of determination, yet this significantly increased once

additional control variables were used in Model (2), which follows and is described in equation

(2) below.

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Our multivariate regression takes into consideration the effect of daily Volatility as a proxy for

Volume. There is a need to control for Volume because recent data indicates that the FX market

amount has risen to $1.20 trillion per day and a fee is charged for executing the exchange

transactions that ultimately affect profits. Furthermore, retail FX investors and large institutions

trade spot contracts on different markets and the contracts for individual currencies often trade at

various prices due to the characteristics and sizes of lots that are purchased and sold. This implies

that we are unable to identify a single fee structure for individual currency investors. Additionally,

even if a clearing house were available to provide the data, the effect of institutional volume may

not be a proper measurement for the retail market because the retail market consists of only two

percent of the market.1 To address this issue, Volatility is used because data are available, and it

is recognized in current studies regarding currency to be positively associated with volume and

has been used as a control variable in prior FX studies (Chaboud and LeBaron 2001).2

The proxy for FX Volatility in this study is the intraday (high—low), where each day t high

and each day t low for the return windows (0, to 10) is denoted as 𝑣(𝑎𝑣𝑔 𝑤𝑖𝑛𝑑𝑜𝑤: 𝑥1,𝑥2), which has been

used in prior studies (Chaboud and LeBaron 2001); this variable is then averaged over the period

window to measure the average FX Volatility.

𝑟(𝑤𝑖𝑛𝑑𝑜𝑤: 𝑥1,𝑥2) = 𝛼𝑡 + 𝛽1𝑡𝑟𝑎𝑑𝑒𝑡 + 𝑣𝑡(𝑎𝑣𝑔 𝑤𝑖𝑛𝑑𝑜𝑤: 𝑥1,𝑥2)+ 𝜀𝑡 (2)

The regression results reported in Table 4 remain similar to the univariate regression results

that rejected the hypothesis that individual short sellers FX investors are unable to predict future

returns. The variable trade retains its negative sign and statistical significance for windows (0, 2)

to (0, 7). Similar to Model (1), the statistical significance decreases after the eighth trading day at

window (0, 8) (p-value=0.05) and is not statistically significant at windows (0, 9) (p-value=0.14)

and (0, 10) (p-value=0.55).


In summary, both models demonstrate that individual FX short sellers possess the ability to

predict future returns up to eight days after they execute a trade. Prior studies such as Ito, Lyons,

and Melvin (1998), and Evans and Lyons (2004) argued that individual customer trades contain

pieces of new information regarding the underlying macroeconomic fundamentals driving the

exchange rate. Recent studies have demonstrated that there is little linear dependence between past

and future returns. However, strong evidence exists that supports the idea linear independence

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should be rejected (Brock, Hsieh, and LeBaron 1991). Therefore, our discovery of return

predictability is significant because it not only supports the concept that linear independence is

rejected but also provides empirical evidence that private information exists in the FX market. In

addition, this study provides empirical evidence that may be used to predict future movements in

the FX market. This discovery provides an alternative method for predicting FX rates, rather than

the Artificial Neural Networks (ANN) and the Recurring Neural Networks (RNN) that were

utilized in other studies (Logar, Corwin, and Oldham 1993; Fang, Lai, and Lai 1994).

4.2 Performance of individual FX investors

The results thus far demonstrate that individual FX investors, on average, conduct more

winning trades than losing trades and are able to predict future returns eight days after a trade has

been executed. Next, an analysis of the performance of these investors is warranted because if

these investors are able to predict future returns, then they should also earn abnormal returns. The

aggregate summary data (Table 1) provides information regarding all closed and open positions

for the 1,231 accounts and indicates that, on average, investors earned $190.30 in post-transaction

costs to their accounts. However, according to Table 1, the total gross maximum dollar gain (loss)

was $1,824,780 (-$1,557,940), and the total net maximum dollar gain (loss) was $937,220.00 (-

$99,964.10), which reveals that certain investors either won or lost a significant amount of money.

This section analyzes the monthly returns of accounts to determine whether individual

investors earned positive and statistically significant abnormal returns. Table 5 provides the

aggregate summary data for accounts that were 60 days and older and included ten or more

trades. We used the accounts that were 60 days and older and that had ten more trades to

determine if consistencies existed in abnormal returns among individual FX investors. Table 5

indicates that 153 trades were conducted, of which 56.29 % were winning trades. In addition,

this table indicates that 305 (25.49) trades were conducted per year (per month). Furthermore,

Table 5 indicates that the mean total dollar gain (loss) was $132,676.07 ($-131,751.97),

respectively, and the average net gain was $924.11.


The previous results indicated that individual FX investors earned and lost large sums of

money and, on average, earned $924.11 per trade after transaction costs. To analyze the

performance of individual FX investors, we relied on the methodology developed by Pojarliev and

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Levich (2008), who used a four-factor model that explains returns based on four distinct styles of

currency trading.

𝑟𝑗,𝑡 = 𝛼𝑗,𝑡 + ∑ 𝛽𝑖,𝑗4𝑖=1 𝐹𝑖,𝑡 + 𝜀𝑡 , (3)

where

rj,t = the excess monthly return generated by the individual FX investors at time t,

𝛼𝑗,𝑡= the individual FX investor’s skill,

𝛽𝑖,𝑗= the coefficient that measures the sensitivity of the individual FX investors’ returns to the

factor,

𝐹𝑖,𝑡 = the Beta factor that requires a systematic risk premium in the market and

𝜀𝑡 = i.i.d., a random error term.

Excess returns are the daily returns for individual FX investors after transaction costs on day t

minus the daily returns on the one-month London Interbank Offered Rate. We used the four factors

proposed by Pojarliev and Levich (2008) which include the following: (1) the Carry factor

measured by the Citibank Beta1 G10 Carry Index, (2) the Value factor measured by the Citibank

Beta1 G10 Purchasing Power Index, (3) the Trend-following factor measured by the AFX

Currency Management Index, which is consistent with the AFX Currency Management Index that

Pojarliev and Levich (2008) used for the Trend-following factor and ( 4) the Volatility factor

proxied by the average of the one-month implied Volatility for the EUR/USD exchange rate and

the USD/JPY exchange rate.

Carry trades consist of borrowing a low interest-rate currency and investing in a high-interest-

rate currency. Trend-following consists of following patterns or reversals. The value factor is used

when investors have a long-term view and need an underlying benchmark to identify over- and

undervalued currencies. Volatility is used because currency investors generally trade on currency

Volatility, and the frequency distribution of FX instruments traded in this sample revealed that

only 32% of all trades were EUR/USD and USD/JPY contracts. Thus, the Volatility proxy used in

this study was the Deutsche Bank FX Volatility Index, which consists of a basket of nine currencies

that are better representatives of the currencies traded by the individual FX investors included in

this sample.3

To examine the performance of individual FX investors, we used the four previously described

factors (Carry, Value or PPP, Volatility, and Trend) in Equation (3), and then we calculated the

Information Ratio and an alternative measure of the Information Ratio that depends on alpha. The

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Information Ratio is used to gauge the skill of an individual FX investor because it determines the

active returns achieved by individual investors and divides it by the risk taken by the investors. A

high Information Ratio implies superior skills of the individual FX investors. The Information

Ratio in equation (4) is defined as the proportion of annual excess returns to the standard deviation.

𝐼𝑅𝑗,𝑡 =𝑅𝑗,𝑡

𝜎(𝑅𝑗,𝑡) (4)

We used an alternative measure of the Information Ratio that captures alpha directly, as

demonstrated in equation (5).

𝐼𝑅𝑗,𝑡∗ =

𝛼𝑗,𝑡

𝜎(𝛼𝑗,𝑡) (5)

Table 6 provides information regarding the Excess Annual Returns, Standard Deviation, and

Information Ratio using equation (4). In addition, Table 6 provides the rank of each FX investor

based on the Information Ratio (IR) using equation (4), the Annual Alpha, the Tracking Error, the

Information Ratio using equation (5), and the Rank of individual FX investors based on IR*

(Information Ratio based on equation 5).

Table 6 indicates that not all individual FX investors produced positive alpha, and the mean of

IR is -0.01633 but the average IR* is 0.009588. Moreover, Table 6 demonstrates that the ranking

of individual FX trader changed according to the method used to calculate the Information Ratio.

For example, individual FX investor M60 produced an annual alpha of 0.102 with IR 0.555 and

ranked number one, while the same individual M60 IR* was 0.622 and ranked number three.

Conversely, individual investor M162 produced an annual alpha of 0.075 with IR 0.401 and was

ranked number two, while the same investor M162 with IR* 0.776 was ranked number one.


4.3 Market Timing of Individual FX investors

These results prompted us to investigate whether individual FX investors produced pure alpha

through market timing or if the results were due to the exposure to factor Betas. To analyze this

issue, we ran the cross-sectional regressions on each of the four market factors in the FX markets

and used the following equation developed by Pojarliev and Levich (2010). The concept behind

this analysis is to determine if significant or non-significant Beta coefficients exist for the four

factors.

𝛽𝑘𝑗,𝑡

= 𝛾0 + 𝛾𝑡−1𝛽𝑘𝑗,𝑡

+ 𝜕𝑗,𝑡 (6)

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Table 7 Panel A to Panel D demonstrates that the Beta coefficients for all four factors are not

significant with a t-stat ranging from 0.011 to 1.478. Therefore, we conclude that individual FX

investors do not have significant exposure to the four FX market factors Betas, which leads us to

theorize that individual FX investors produced an alpha without relying on passive exposure to

market factor Betas.

To further investigate the exposure of an individual FX by the four FX market factor Betas,

we investigated the percentage of individual FX investors that were passively exposed to the four-

factor Betas. This investigation provided more robustness to the previous analyses because a low

percentage of individual FX traders passively vulnerable to the four-factor Betas lends more

evidence to the theory that FX investors may produce pure alpha.


Table 8 provides the percentage of individual FX investors that had significant exposure to

each particular factor over multiple year time periods. Table 8 reveals that only 3.85% of the

individual FX investors had significant exposure to the trend factor during the year 2009–2010,

and approximately 4%-6% of individual FX investors had significant exposure to all four factors

during the year 2010–2011. The results indicated that 11.7% of the individual FX investors had

significant exposure to the Carry factor, 8.51% had significant exposure to the Volatility factor,

and 9.57% had significant exposure to both the Value and Trend factors during the year 2012–

2013. During 2013–2014, 13.13% had significant exposure to the volatility factor, 16.16% to the

Trend factor, 4.04% to the value factor and 7.07% to the Carry factor. The analysis provided in

Table 8 reveals that a small portion of the individual FX investors had significant passive exposure

to the four factors, which implies that the performance of certain individual FX investors depended

on that passive exposure; however, a larger percentage of the performance did not depend on

passive exposure to the four factors. This leads to the conclusion that the investor’s ability to time

the market, rather than exposure to the factor Betas, enabled them to produce alpha.


We investigated if individual FX investors possessed timing ability. We utilized the procedure

used by Pojarliev and Levich (2008) that explored timing ability by separating the style factors

into positive and negative returns and then explored if individual FX investors were able to time

the changing returns. Therefore, we ran regressions of the following form for every single FX

investor.

14

𝑟𝑗,𝑡 = 𝛼𝑗,𝑡 + ∑ 𝛽𝑖,𝑗4𝑖=1 [𝐹𝑖,𝑡|𝐹𝑖,𝑡 > 0] + ∑ 𝛾𝑖,𝑗

4𝑖=1 [𝐹𝑖,𝑡|𝐹𝑖,𝑡 < 0] . (7)

Then, we calculated alpha for each FX investor and followed the identical procedure used in

table 6 to compute the Information Ratio. Table 9 indicates that individual FX investors produced

an average alpha of 0.0366. In addition, individual FX trader M60 produced an annual alpha of

0.188 with IR 0.555 and IR* 0.932 and ranked first for both IR calculations methods. These data

support the concept that certain individual investors produced alpha because of their timing

abilities.


Then, we investigated the details regarding how each FX investor timed the market. To clarify,

we investigated if individual FX investors produced alpha by being exposed to each of the four

factors; this exposure is a reflection of their ability to time the market. Therefore, we used the

identical model previously used: monthly data regarding individual FX returns on Carry, PPP or

value, Momentum or Trend and Volatility were analyzed. Each factor was separated into

observations of positive and negative returns, and separate coefficients were estimated on each

factor to test if the individual FX investors were skilled in loading positively (negatively) on factors

when factor returns were positive (negative). Significant t-statistics are reported in bold. This is

the identical model used in Table 9; however, in this case, we analyzed the data in greater detail.


Table 10 indicates, for example, that three individual FX investors had positive Carry or had

positive (long position) exposure on positive Carry. In addition, four had negative Carry or had

negative (short position) exposure on negative Carry, and two had positive PPP or had positive

(long position) exposure on positive PPP. Furthermore, three had negative PPP or had negative

(short position) exposure on negative PPP, and three had positive Volatility or had positive (long

position) exposure on positive Volatility. In addition, three had negative Volatility or had negative

(short position) exposure on negative Volatility, two had positive Trend or had positive (long

position) exposure on positive Trend, and two had negative Trend or had negative (short position)

exposure on negative Trend.

This analysis leads to another question regarding the existence of style persistence for

individual FX investors. To clarify, if we noted that individual FX investors did not follow an

identical trading pattern, then they did not possess style persistence that would provide additional

evidence regarding their timing ability. An example of timing the market would occur when an

15

individual FX investor who was exposed to one of the factors in period t-1 was unlikely to maintain

the same significant exposure in period t.

To perform the analysis, we first ran a regression on alpha, where 𝛼𝑗,𝑡 represents the excess

return for individual FX investor j that is not explained by the four factors.

𝛼𝑗,�̂� = 𝑅𝑗,𝑡 − ∑ 𝛽𝑖,𝑗4𝑖=1 𝐹𝑖,𝑡 (8)

Then, we ran a second regression to investigate if the individual FX investors that performed

well in the past continued to perform well in the future. The purpose of our investigation was to

determine if the future alpha was not related to the previous alpha because if the alphas were not

linked, this would provide additional evidence that individual FX investors possessed market

timing ability. Therefore, we used the model developed by Aggarwal and Jorion (2010) and the

following regression equation.

𝛼𝑗,𝑡 = 𝜑0 + 𝜑1𝛼𝑗,𝑡−1 + 𝜇𝑗,𝑡 . (9)

Table 11 demonstrates that the regression did not yield a significant coefficient on the previous

year’s alpha, which implies that past performance measured by alpha was not related to future

performance, supports the concept that individual FX investors vary their exposure from year to

year and is additional evidence of their timing ability.


5. Robustness

In the previous analyses we have shown that individual FX investors produce pure alpha

through their timing ability. In the following analyses we used other analytical equations to check

if our findings still hold. If individual FX investor is able to increase (decrease) reliance on factor

𝐹𝑖 when returns on 𝐹𝑖 are rising (falling) then that shows positive timing ability. To test this

possibility, we ran regressions of the following for each individual FX investor:

𝑟𝑗,𝑡 = 𝛼𝑗 + ∑ 𝛽𝑖,𝑗4𝑖=1 𝐹𝑖,𝑡 + ∑ 𝛾𝑖,𝑗

4𝑖=1 𝐹𝑖,𝑡

2 + 𝜇𝑗,𝑡 (10)

Table 12 shows the factor loadings for each individual investors. Each factor was separated

into positive and negative returns and separate coefficients are estimated on each to test of whether

individual FX investors possessed the skill in loading positively (negatively) on factors when

factors returns are positive (negative).

16


Table 12 shows that individual FX investors Load positively ( negatively) on factors when the

factors are positive ( negative) and the loadings are significant Then we calculated Information

Ratio using equations (8, and 9)


Table 13 shows that running a different regression specifications still produce the same results

as explained in table 9. For example, M60 rank according to IR ratio is 1 and according to IR* is

2. The above results support our findings from table 9.

Finally, we checked for the relationship between individual FX investor Alpha and the

predicted Alpha. We regressed the intercept (Alpha) for each individual FX investor against the

R2 from the time series regression using each of the following specification that were used in the

paper

𝑟𝑗,𝑡 = 𝛼𝑗 + ∑ 𝛽𝑖,𝑗4𝑖=1 [𝐹𝑖,𝑡|𝐹𝑖,𝑡 > 0] + ∑ 𝛾𝑖,𝑗

4𝑖=1 [𝐹𝑖,𝑡|𝐹𝑖,𝑡 < 0] (7)

< Insert Figure 1 here>

𝑟 = 𝛼 + ∑ 𝛽𝑖4𝑖=1 𝐹𝑖,𝑡 + 𝜀𝑡 (3)


𝑟𝑗,𝑡 = 𝛼𝑗 + ∑ 𝛽𝑖,𝑗4𝑖=1 𝐹𝑖,𝑡 + ∑ 𝛾𝑖,𝑗

4𝑖=1 𝐹𝑖,𝑡

2 + 𝜇𝑗,𝑡 (10)


We found that there is an inverse relationship between Alpha and R2 which supports our

analysis that individual FX investor have timing ability because the inverse relationship means

that Alpha was produced through individual FX investors ability to time the market and doesn’t

depend on the market factor loadings that explains returns in the FX market.

6. Conclusion

This study analyzed if individual Forex investors were able to predict future returns, time the

market and generate alpha after transaction costs. This study used a sample of 1,231 FX trading

17

accounts and 72,072 trades. The results demonstrated that, contrary to existing theoretical

literature, this group of individual investors was able to predict future returns up to eight days after

trade execution. This discovery supports prior studies such as Ito, Lyons, and Melvin (1998) and

Evans and Lyons (2004) that determined that individual customer trades contain new information

regarding the underlying macroeconomic fundamentals that impact the exchange rate. Moreover,

our results support the evidence provided by both Brock, Hsieh, and LeBaron (1991) that the linear

independence of FX prices should be rejected. Therefore, our discovery of return predictability is

significant because it not only supports the concept that linear independence should be rejected

but also provides empirical evidence that private information exists in the FX market, which may

be used to predict future movements in the FX market. In addition, this study demonstrates that

certain individual FX investors are able to time the market and produce positive alpha after

transaction costs. Moreover, these investors did not possess style persistence and their future alpha

was not related to previous year’s alpha, which provides additional evidence of their market timing

ability. Furthermore, we ran robustness check by using different specifications and methodology

and the results further support the findings that individual FX investors ability to time the market.

Finally, this study is limited because it offers no explanation as to why these investors are able

to time the FX market, which suggests that certain individual FX investors appear to act as

informed FX managers. Unlike equities, in currency markets, there should not be available

information that may be exploited by individual investors. A review of the data indicates that the

overwhelming majority of investors use technical analyses. Consequently, the ability of these

investors to time the market casts doubts on market efficiency. The study of this issue is

recommended for future research, which may be accomplished by conducting surveys and

interviews with individual FX investors to provide a richer understanding of the causes of this

phenomenon.

18

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21

Appendix

Table 1. Summary statistics of aggregate data for all systems.

This table presents the aggregate summary statistics for all 1,231 accounts. These data were precompiled by the

Trade System Host for each system, and the mean, standard deviation, minimum and maximum were calculated

from each account. The time period is from April 2005 to March 2015. The data used to compile this table consisted

of all trades, currently open and closed, and were unlike the transaction data contained in Table 2 that contained only

closed positions. The reason for this difference is that only paid subscribers had access to open positions. Age of

Account in Years measures the life of the account measured in years. Monthly Subscription Cost reflects the cost that

Developers charge for access to their system. Average Holding Time for Trades (in Hours) represents the average

time each trade is held. Opening Equity Value represents the amount of capital that each account began with on the

date of inception. Number of Trades reflects the total number of trades that are closed and currently open at the time

of the data extraction that occurred on April 2005. Some Winning Trades, Number of Losing Trades, Percent of

Losing Trades, Percent of Winning Trades, Trades per Month and Trade per Year were compiled from the aggregate

data provided by the Trade System Host and are based on all open and closed positions. Total Dollar Gain and Total

Dollar Loss represent the pre-transaction gross gains realized by each account and are measured in US dollars. Total

Gain/Loss represents the net of the Total Dollar Loss/Gain.

Variable Mean Std. Dev Minimum Maximum

Age of Account in Years 0.27 0.42 0.00 3.55

Monthly Subscription Cost $134.90 $205.34 $0.00 $2,000.00

Average Holding Time for Trades (in Hours) 1,508.48 4,541.57 0.00 41,282.77

Opening Equity Value $90,854.03 $28,944.96 $1,000.00 $400,000.00

Number of Trades 59.59 181.47 1 4002

Number of Winning Trades 33.52 102.06 0 1936

Number of Losing Trades 26.08 85.99 0 2066

Percent of Winning Trades 52.97% 29.97% 0.00% 100.00%

Percent of Losing Trades 47.03% 29.97% 0.00% 100.00%

Total Dollar Gain $55,261.91 $139,666.16 $0.00 $1,824,780.00

Total Dollar Loss -$55,071.61 $118,632.96 -$1,557,940.00 $0.00

Total Net Gain/Loss $190.30 $59,972.54 -$99,964.10 $937,220.00

Trades per Year 350.39 1176.87 - -

Trades per Month 29.20 98.07 - -

22

Table 2. Summary statistics for transaction data for all systems.

This table presents summary statistics regarding the transaction portion of the data obtained from the Trade System

Host. Unlike Table 1, Table 2 only contains data regarding closed positions because open position transaction data

are only available to subscribers. Panels A and B divide the sample into trade positions, which consist of shorts and

longs, and provides the total number of closed trades executed and the percentage of both shorts and longs for all

trades. Panel B provides the percent of the longs and shorts that are winning trades, losing trades and even trades

(realized gain of zero). Panel C presents the frequency distribution and number of trades for all sport FX contracts

that have been opened and closed by Individual FX investors.

Table 2 Panel A Table 2 Panel B

Trade Position Number of Trades Percent of All Trades

Percent of Winning

Trades

Percent of Losing Trades Percent of Even Trades

Long 37,090 51.46 56.73 41.66 1.6

Short 34,982 48.54 56.26 42.16 1.58

Table 2 Panel C

FX Symbol # of Trades Percent FX Symbol # of Trades Percent

GBPUSD 13656 21.60 USDDKK 40 0.06

EURUSD 13446 21.27 AUDCHF 36 0.06

USDJPY 7203 11.40 USDZAR 35 0.06

USDCHF 6459 10.22 EURNOK 21 0.03

GBPJPY 5014 7.93 USDHKD 19 0.03

EURJPY 4256 6.73 GBPHKD 16 0.03

AUDUSD 3073 4.86 EURSEK 15 0.02

USDCAD 2597 4.11 GBPDKK 14 0.02

EURGBP 1119 1.77 GBPSEK 14 0.02

GBPCHF 1060 1.68 GBPNOK 12 0.02

CHFJPY 870 1.38 GBPSAR 12 0.02

NZDUSD 848 1.34 USDSEK 10 0.02

EURCHF 828 1.31 USDINR 7 0.01

AUDJPY 759 1.20 GBPEUR 5 0.01

EURAUD 628 0.99 USDTHB 5 0.01

EURCAD 473 0.75 GBPINR 4 0.01

CADJPY 277 0.44 USDMXN 3 0.00

GBPAUD 114 0.18 GBPSGD 2 0.00

GBPCAD 104 0.16 USDISK 2 0.00

USDSGD 55 0.09 BAREUR 1 0.00

GBPNZD 54 0.09 BARGBP 1 0.00

USDNOK 42 0.07

23

Table 3. Regression results of returns as a function of short/long trades.

This table presents the regression results of Model (1) that regressed a dummy variable trade and assumed the value

of 1 if the transaction was short and zero if the trade was long on the CRR r(window: x1, x2) over the event window. The

event window used in the analysis is the CRR of the FX contract traded from one (0, 1) to ten (0, 10) days after the

execution of the trade. The primary hypothesis states that FX investors cannot predict future returns and the

coefficient for trade should be positive and statistically insignificant.

𝑟(𝑤𝑖𝑛𝑑𝑜𝑤: 𝑥1,𝑥2) = 𝛼𝑡 + 𝛽1𝑡𝑟𝑎𝑑𝑒𝑡 + 𝜀𝑡

Window Variable Coefficient x 100 Std. Error x 100 t-Statistic p-value R2

(0,1) Constant 0.00036 0.00858 0.0418 0.9666

0.00024

TRADE -0.01699 0.00973 -1.7465 0.0807

(0,2) Constant 0.00633 0.01256 0.5037 0.6145

0.00057

TRADE -0.03728 0.01361 -2.7395 0.0062

(0,3) Constant 0.01289 0.01513 0.8521 0.3942

0.00043

TRADE -0.03936 0.01616 -2.4350 0.0149

(0,4) Constant 0.01524 0.01842 0.8275 0.4080

0.00057

TRADE -0.05387 0.01948 -2.7659 0.0057

(0,5) Constant 0.02944 0.01981 1.4858 0.1373

0.00090

TRADE -0.07479 0.02138 -3.4971 0.0005

(0,6) Constant 0.01887 0.02193 0.8603 0.3896

0.00065

TRADE -0.06979 0.02334 -2.9904 0.0028

(0,7) Constant 0.02026 0.02416 0.8384 0.4018

0.00064

TRADE -0.07543 0.02584 -2.9190 0.0035

(0,8) Constant 0.01880 0.02530 0.7453 0.4561

0.00048

TRADE -0.06870 0.02680 -2.5622 0.0104

(0,9) Constant 0.01884 0.02728 0.6905 0.4899

0.00031

TRADE -0.05931 0.02852 -2.0799 0.0375

(0,10) Constant 0.00828 0.02911 0.2844 0.7761

0.00013

TRADE -0.03971 0.03030 -1.3104 0.1901

24

Table 4. Regression results of returns as a function of short/long trades and volatility.

This table presents the regression results of Model (2), which regressed a dummy variable trade that assumed the

value of 1 if the transaction is short and zero if the trade is long on the CRR r(window: x1, x2) over the event window.

Furthermore, the control variable of Volatility (vt) was added to the regression to control for Volatility.

𝑟(𝑤𝑖𝑛𝑑𝑜𝑤: 𝑥1,𝑥2) = 𝛼𝑡 + 𝛽1𝑡𝑟𝑎𝑑𝑒𝑡 + 𝑣𝑡(𝑎𝑣𝑔 𝑤𝑖𝑛𝑑𝑜𝑤: 𝑥1,𝑥2) + 𝜀𝑡

Window Variable Coefficient x 100 Std. Error x 100 t-Statistic p-value R2

(0,1) Intercept 0.0065 0.0147 0.44 0.66 0.0003

TRADE -0.0169 0.0097 -1.74 0.08

V(0,1) -0.9688 2.3915 -0.41 0.69

(0,2) Intercept 0.0518 0.0235 2.20 0.03 0.0018

TRADE -0.0364 0.0136 -2.67 0.01

V(0,2) -6.9957 4.1050 -1.70 0.09

(0,3) Intercept 0.1612 0.0327 4.93 0.00 0.0071

TRADE -0.0357 0.0161 -2.22 0.03

V(0,3) -22.4176 5.5260 -4.06 0.00

(0,4) Intercept 0.2759 0.0422 6.54 0.00 0.0125

TRADE -0.0482 0.0194 -2.49 0.01

V(0,4) -39.4394 7.3096 -5.40 0.00

(0,5) Intercept 0.4175 0.0527 7.92 0.00 0.0204

TRADE -0.0664 0.0210 -3.16 0.00

V(0,5) -58.8198 8.8345 -6.66 0.00

(0,6) Intercept 0.4917 0.0640 7.69 0.00 0.0241

TRADE -0.0586 0.0228 -2.57 0.01

V(0,6) -72.2336 10.6245 -6.80 0.00

(0,7) Intercept 0.6207 0.0737 8.42 0.00 0.0320

TRADE -0.0608 0.0251 -2.42 0.02

V(0,7) -91.4966 12.2978 -7.44 0.00

(0,8) Intercept 0.7139 0.0857 8.33 0.00 0.0376

TRADE -0.0518 0.0259 -2.00 0.05

V(0,8) -105.2422 14.0045 -7.51 0.00

(0,9) Intercept 0.8234 0.0912 9.03 0.00 0.0426

TRADE -0.0404 0.0275 -1.47 0.14

V(0,9) -121.6535 14.8699 -8.18 0.00

(0,10) Intercept 0.9329 0.0969 9.63 0.00 0.0498

TRADE -0.0174 0.0292 -0.60 0.55

V(0,10) -139.8944 15.8239 -8.84 0.00

25

Table 5. Summary statistics for aggregate data for all systems 60 days and older with ten or more trades.

This table provides aggregate summary statistics for all accounts that are 60 days or older and with ten or more

trades. These data were precompiled by the Trade System Host for each system and the mean, standard deviation,

minimum and maximum were calculated. The time period is from April 2005 to March 2015. The data used to

compile this table consists of all trades, opened and closed, and is unlike the transaction data contained in Table 2,

which consists of only closed positions. The reason for the difference is that only paid subscribers have access to

open positions. Age of Account in Years measures the life of the account measured in years. Monthly Subscription

Cost reflects the cost that Developers charge for access to their system. Average Holding Time for Trades (in Hours)

represents the average time each trade is held. Opening Equity Value represents the amount of capital that each

account started with on the date of inception. Number of Trades reflects the total number of trades that are closed

and currently open at the time the data were extracted on April 2005. Some Winning Trades, Number of Losing

Trades, Percent of Losing Trades, Percent of Winning Trades, Trades per Month and Trade per Year are compiled

from the aggregate data provided by the Trade System Host and are based on all open and closed positions. Total

Dollar Gain and Total Dollar Loss represent the pre-transaction gross gains realized by each account and are

measured in U.S. dollars. Total Gain/Loss represents the net of the Total Dollar Loss/Gain.

Variable Mean Std. Dev Minimum Maximum

Age of Account in Years 0.59 0.47 0.16 3.55

Monthly Subscription Cost 130.14 181.20 0.00 2000.00

Holding Time for Trades (in Hours) 195.67 587.98 0.72 8140.00

Opening Equity Value 91,413.53 25,696.99 1000.00 10,0000.00

Number of Trades 153.53 286.30 11.00 4002.00

Number of Winning Trades 87.34 160.15 2.00 1,936.00

Percent of Winning Trades 56.29% 17.50% 16.36% 96.50%

Number of Losing Trades 66.20 137.84 1.00 2066.00

Percent of Losing Trades 43.71% 17.50% 3.50% 83.64%

Total Dollar Gain 132,676.07 211,741.89 317.38 182,4780.00

Total Dollar Loss -131,751.97 -173,591.07 149.13 1,557,940.00

Total Dollar Net Gain/Loss 924.11 86,550.70 -99,964.10 937,220.00

Trades per Year 305.84 439.31 - -

Trades per Month 25.49 36.61 - -

26

Table 6. Individual FX investor annual alpha and ranking based on information ratio.

Table 6 uses the following specification to capture alpha for individual FX investors

𝑟𝑗,𝑡 = 𝛼𝑗,𝑡 + ∑ 𝛽𝑖,𝑗

4

𝑖=1

𝐹𝑖,𝑡 + 𝜀𝑡

The four factors include the (1) Carry factor measured as the Citibank Beta3 G10 Carry Index, (2) Trend-following

factor measured by the AFX Currency Management Index, (3) Value factor measured by the Citibank Beta3 G10

Purchasing Power Index and (4) Volatility factor proxied by the Deutsche Bank FX Volatility Index. Table 6

includes 1,883 account-month observations and encompasses the time period from April 2005 to March 2008. The

Information Ratio was calculated using the following two equations: We omitted other individual’s data for space

consideration


𝜎(𝑅𝑗,𝑡) ; 𝐼𝑅𝑗,𝑡

∗ =𝛼𝑗,𝑡

𝜎(𝛼𝑗,𝑡).

Individual Id Excess Annual Return S.D. IR RANK Annual Alpha Tracking Error IR* RANK

M4 0.008 0.204 0.038 23 -0.034 0.163 -0.21 41

M13 0 0.122 0.003 27 -0.007 0.112 -0.059 33

M17 -0.027 0.246 -0.111 37 0 0.218 -0.001 29

M21 0.097 0.271 0.359 3 0.097 0.226 0.431 6

M47 0.013 0.074 0.177 9 0.015 0.066 0.231 9

M48 -0.002 0.063 -0.035 33 -0.003 0.045 -0.077 35

M52 0.001 0.305 0.003 28 0.014 0.283 0.051 21

M57 0.038 0.446 0.086 19 0.023 0.389 0.059 20

M60 0.093 0.167 0.555 1 0.102 0.164 0.622 3

M91 0.015 0.082 0.185 8 0.009 0.077 0.12 15

M92 -0.108 0.23 -0.468 49 -0.071 0.215 -0.33 43

M101 -0.044 0.232 -0.189 38 -0.061 0.17 -0.36 44

M102 0.002 0.094 0.023 25 0.002 0.09 0.018 26

M105 -0.087 0.278 -0.313 44 -0.017 0.194 -0.089 36

M123 0.014 0.086 0.167 11 0.023 0.078 0.29 8

M125 0.016 0.14 0.114 17 0.015 0.136 0.107 17

M133 0.034 0.392 0.087 18 0.051 0.292 0.174 11

M144 0.03 0.216 0.138 14 0.043 0.204 0.213 10

M159 0.016 0.212 0.077 21 0.021 0.2 0.104 18

M162 0.051 0.128 0.401 2 0.075 0.097 0.776 1

27

Table 7. Beta regressions.

To investigate if individual FX investors produced pure alpha and not only exposure to the four-factor Betas, we ran

cross-sectional regressions on each of the four-factors and we used the following equation:

𝛽𝑘𝑗,𝑡

= 𝛾0 + 𝛾𝑡−1𝛽𝑘𝑗,𝑡

+ 𝜕𝑗,𝑡

Panel A to Panel D indicate that Beta coefficients for all four factors are not significant with t-stat from 0.011 to

1.478. Therefore, we conclude that individual FX investors produce pure alpha and not just exposure to factor Betas.

Panel A Number of Individual FX investors Intercept t-stat Coefficient, Beta Vol year t-1 t-stat R-Square

April 11-March 12 13 -0.705 -0.752 0.220 1.478 0.166

April 12-March 13 27 0.032 0.009 0.302 0.568 0.013

April 13-March 14 37 1.794 1.154 0.555 1.182 0.038

Panel B

Number of Individual FX

investors

Intercept t-stat Coefficient, Beta-Vol year t-1 t-stat R-Square

April 11-March 12 13 4.290 0.901 0.799 1.787 0.225

April 12-March 13 27 -0.868 -0.581 0.255 1.214 0.040

April 13-March 14 37 0.949 0.673 0.024 0.465 0.009

Panel C


investors

Intercept t-stat Coefficient, Beta Trend year t-1 t-stat R-Square

April 11-March 12 13 1.447 0.828 0.032 0.218 0.004

April 12-March 13 27 -5.693 -0.377 -0.194 -0.429 0.007

April 13-March 14 37 2.035 0.734 -0.105 -0.718 0.015

Panel D


investors

Intercept t-stat

Coefficient, Beta

Carry year t-1

t-stat R-Square

April 11-March 12 13 3.016 0.560 -1.360 -1.783 0.224

April 12-March 13 27 1.726 0.868 0.001 0.011 0.000

April 13-March 14 37 -0.094 -0.084 0.111 0.604 0.010

28

Table 8. Percentage of individual FX investors with significant Betas.

Table 8 provides the percentage of individual FX investors with significant exposure to every single factor during

multiple year periods. Table 8 reveals that only 3.85% of the individual FX investors had significant exposure to the

Trend factor during the year 2011–2012 and approximately 4%-6% of the individual FX investors had significant

exposure to all four factors during the year 2012–2013. In addition, 11.7% of individual FX investors had significant

exposure to the Carry factor, 8.51% had significant exposure to the volatility factor and 9.57% had significant

exposure to both the Value and Trend factors during the year 2013–2014.

Volatility Value Trend Carry

April 11-March 12 0.00% 0.00% 3.85% 0.00%

April 12-March 13 5.56% 4.17% 5.56% 5.56%

April 13-March 14 8.51% 9.57% 9.57% 11.70%

Table 9. Individual FX investors that produced alpha by their timing ability.

This table includes monthly data regarding individual FX returns on Carry, Purchasing Power Parity (PPP) or Value,

Momentum or Trend and Volatility. Each factor was separated into observations of positive and negative returns and

separate coefficients are estimated on each as a test of whether individual FX investors possessed the skill in loading

positively (negatively) on factors when factor returns are positive (negative).


4

𝑖=1

[𝐹𝑖,𝑡|𝐹𝑖,𝑡 > 0] + ∑ 𝛾𝑖,𝑗

4

𝑖=1

[𝐹𝑖,𝑡|𝐹𝑖,𝑡 < 0]

Then, we calculated the Information Ratio using the following two equations:



∗ =𝑅𝑗,𝑡

𝜎(𝑅𝑗,𝑡)

This table provides the annual alpha, IR, IR* and ranking for individual FX trader. We omitted the remainder of the

information regarding all the individual FX investors from the table due to space considerations.

Individual Id Excess Annual Return S.D. IR Rank Annual Alpha Tracking Error IR* Rank

M48 -0.002 0.063 -0.035 33 0.006 0.084 0.074 30

M52 0.001 0.305 0.003 28 0.041 0.424 0.096 27

M57 0.038 0.446 0.086 19 -0.001 0.53 -0.001 33

M60 0.093 0.167 0.555 1 0.188 0.202 0.932 1

M135 0.026 0.211 0.121 16 -0.117 0.449 -0.26 42

M139 -0.087 0.25 -0.35 47 0.092 0.288 0.319 12

M144 0.03 0.216 0.138 14 0.081 0.257 0.318 13

M159 0.016 0.212 0.077 21 0.312 0.603 0.518 9

M162 0.051 0.128 0.401 2 0.206 0.269 0.766 4

M168 0.006 0.039 0.141 13 0.069 0.089 0.775 3

M183 -0.119 0.421 -0.283 42 0.135 0.267 0.505 10

M191 -0.015 0.301 -0.051 35 -0.146 0.443 -0.331 44

M316 0.595 2.908 0.205 7 -2.26 2.942 -0.768 50

M325 -0.139 0.439 -0.318 45 0.2 0.245 0.816 2

M338 0.013 0.051 0.263 5 0.046 0.067 0.68 6

M339 0.004 0.072 0.061 22 0.022 0.088 0.249 16

Table 10. Individual FX investor’s timing ability.

This table includes monthly data regarding individual FX returns on Carry, PPP or Value, Momentum or Trend and Volatility. Each factor was separated into

observations of positive and negative returns and separate coefficients are estimated as a test to determine if individual FX investors possessed the skill in loading

positively (negatively) on factors when factor returns are positive (negative). Statistically, significant t-statistics are reported in bold.


4

𝑖=1

[𝐹𝑖,𝑡|𝐹𝑖,𝑡 > 0] + ∑ 𝛾𝑖,𝑗

4

𝑖=1


Individual ID Constant Tstat Carrypos Tstat Carryneg Tstat PPPpos Tstat PPPneg Tstat VOLpos Tstat VOLneg Tstat TRENDpos Tstat TRENDneg Tstat Rsquare Nobs

M4 -0.023 -0.26 -3.022 -1.17 0.704 0.29 3.554 1.23 3.762 0.79 1.585 1.36 -0.655 -0.81 -0.056 -1.28 0.048 0.67 0.58 23

M17 0.3 2.53* -8.926 -1.17 5.217 0.57 3.022 0.48 -6.522 -0.82 -9.449 -3.14** 6.046 1.28 -14.471 -1.4 12.034 1.08 0.584 23

M21 0.174 1.31 -8.922 -1.3 10.987 1.1 6.35 1.1 -14.558 -1.52 2.372 0.67 11.774 2.24* -0.386 -0.03 7.167 0.53 0.433 26

M48 0.004 0.1 -0.507 -0.51 0.66 0.66 0.495 0.39 -0.7 -0.32 -0.078 -0.16 0.262 0.84 -0.033 -2.1 -0.044 -1.64 0.537 18

M52 0.214 1.55 -2.485 -0.39 18.399 2.85* 4.689 0.62 -24.329 -2.66* -2.539 -0.91 14.094 2.59* -17.429 -1.37 14.079 0.79 0.56 25

M92 0.143 1.11 0.805 0.14 -0.472 -0.08 1.495 0.2 -17.335 -2 -0.08 -0.03 8.696 1.89 -35.154 -2.51* 48.276 2.85* 0.602 20

M101 -0.067 -0.58 4.96 0.91 10.918 2.24* 7.419 1.2 -15.639 -2.06 1.161 0.49 2.601 0.63 -15.679 -1.19 15.784 1.04 0.629 21

M125 0.098 1.55 -3.477 -1.45 1.013 0.45 0.116 0.04 1.29 0.35 1.642 1.25 -3.861 -1.84 -7.349 -1.67 10.697 2.41* 0.333 30

M135 -0.111 -1.68 5.527 1.92 -22.587 -6.06*** -1.902 -0.46 26.996 2.06 1.793 1.19 -5.861 -2.08 13.642 0.68 2.736 0.35 0.9 18

M139 -0.045 -0.32 -1.547 -0.25 -4.387 -0.55 17.085 1.92 -4.345 -0.15 -4.697 -1.45 -3.04 -0.5 -38.673 -0.9 5.698 0.34 0.671 18

M168 0.006 0.3 -0.318 -0.5 -1.553 -2.13 2.497 2.07 -2.552 -1.81 -1.348 -3.58** 0.529 0.83 -2.393 -1.29 -0.828 -0.57 0.671 20

M183 0.043 0.84 4.862 2.56* -4.129 -3.01** -10.046 -4.39*** -5.444 -1.88 -2.017 -1.83 0.056 0.03 -9.966 -3.22** 8.028 2.42* 0.96 26

M191 0.239 2.08 -3.455 -0.83 7.649 1.88 -13.391 -2.14* 8.598 1.34 -0.248 -0.1 2.1 0.49 15.89 1.94 2.12 0.28 0.637 25

M217 -0.046 -0.56 5.388 1.83 0.458 0.21 -0.156 -0.04 -7.725 -1.64 1.298 0.74 0 0 -3.721 -0.73 7.002 1.33 0.489 23

M222 0.056 1.09 4.141 2.2* -5.117 -3.62** -7.463 -3.16** -6.275 -2.09 -1.791 -1.6 0.584 0.31 -13.902 -4.29** 8.623 2.56* 0.971 23

M228 0.066 1 0.994 0.46 1.762 0.68 -2.828 -0.62 5.214 1.22 0.777 0.6 -0.046 -0.02 -4.195 -0.69 1.483 0.38 0.544 19

M240 0.018 0.5 4.918 3.56** 0.07 0.07 -6.758 -3.73** -2.112 -0.97 -0.842 -1.06 -0.734 -0.55 -4.723 -2 1.327 0.54 0.96 22

M253 0.004 0.96 -0.055 -0.3 0 0 -0.148 -0.84 0.282 0.94 -0.01 -0.12 0.058 1.35 0.114 0.54 -0.009 -0.93 0.24 17

M287 -0.178 -0.4 -3.234 -0.22 58.532 5.17** 45.639 2.34* -5.632 -0.24 24.772 2.44* 15.646 0.97 29.273 1 -11.672 -0.44 0.962 18

M316 -0.254 -0.47 -6.721 -0.36 55.5 4.25** 57.116 2.55* -11.103 -0.42 20.622 1.81 23.71 1.31 34.385 1.02 -24.821 -0.7 0.965 16

M325 0.086 1.18 -0.401 -0.16 -4.772 -2.7* -9.458 -3.13* -0.591 -0.17 -1.322 -0.86 0.9 0.37 -8.794 -1.92 3.798 0.8 0.972 16

M338 0.01 0.52 -0.387 -0.65 -0.037 -0.07 -0.483 -0.81 -2.171 -2.25* -0.092 -0.38 -0.296 -1.56 0.001 0.12 0.03 1.79 0.619 23

M411 -0.062 -1.37 0.824 0.59 -1.727 -1.27 1.745 1.07 -1.132 -0.44 0.57 0.9 -0.459 -0.76 -0.159 -7.21*** 0.067 1.53 0.87 19

M426 0.389 1.1 -17.271 -1.17 -12.138 -1.3 -27.506 -1.98 7.81 0.33 -29.568 -4.32** 9.79 2.92* 92.581 5.54** 1.695 2.14 0.911 16

M439 0.039 0.4 0.338 0.12 -1.219 -0.44 -3.029 -0.92 3.28 0.57 0.702 0.55 0.627 0.72 -0.182 -3.99** 0.076 0.96 0.732 19

M443 0.169 1.83 1.173 0.21 -4.736 -0.63 -4.867 -0.83 4.023 0.58 -2.457 -1.09 8.553 2.24* -1.679 -0.21 -5.858 -0.54 0.672 19

31

Table 11. Style persistence and alpha regressions.

To perform the analysis, we first ran a regression on alpha where 𝛼𝑗 is the excess return for each individual FX

trader j that is not explained by the four factors.

𝛼𝑗,�̂� = 𝑅𝑗,𝑡 − ∑ 𝛽𝑖,𝑗

4

𝑖=1

𝐹𝑖,𝑡

Then, we ran a second regression to investigate to determine if individual FX investors who performed well in

the past continued to perform well in the future. The reason we investigated the investors’ performance was to

determine if the present alpha was related to the future alpha because if the alphas are not linked, this investigation

provides additional evidence of the individual FX investor’s market timing ability. Therefore, we used the model

developed by Aggarwal and Jorion (2010) and the following regression equation:

𝛼𝑗,𝑡 = 𝜑0 + 𝜑1𝛼𝑗,𝑡−1 + 𝜇𝑗,𝑡 .

Table 11 indicates that the regression did not yield a significant coefficient on the prior year’s alpha and implies that

the past performance measured by the alpha was not related to future performance. This result supports the concept

that individual FX investors vary their exposure from year to year, which is additional evidence of their timing

ability.


investors

Intercept t-stat Coefficient, Alpha Year t-1 t-stat R-Square

April 11-March 12 13 0.038 2.407* 0.067 0.516 0.024

April 12-March 13 27 -0.022 -0.716 -0.064 -0.343 0.005

April 13-March 14 37 0.009 0.252 0.059 0.175 0.001

32

Table 12 Robustness check for market timing model using different specification:

The following equation was used for Table 12

𝑟𝑗,𝑡 = 𝛼𝑗 + ∑ 𝛽𝑖,𝑗

4

𝑖=1

𝐹𝑖,𝑡 + ∑ 𝛾𝑖,𝑗

4

𝑖=1

𝐹𝑖,𝑡2 + 𝜇𝑗,𝑡

IndId Intercept t-stat b-Vol t-stat b-PPP t-stat b-Trend t-stat b-Carry t-stat Y-Vol t-stat Y-PPP t-stat Y-Trend t-stat Y-Carry t-stat Rsquare Nobs

M4 0.001 0.02 0.679 0.99 4.645 2.29* -0.006 -0.12 -1.31 -1.1 4.793 0.94 -22.927 -0.36 -0.011 -0.91 -5.927 -1.14 0.591 23

M13 0.074 1.47 0.55 0.47 1.971 0.86 1.617 0.73 -3.381 -1.05 17.438 0.57 -13.368 -0.16 -8.589 -0.86 -6.476 -1.14 0.42 24

M17 0.179 1.99 -1.951 -0.79 -2.91 -0.64 -1.989 -0.5 -0.619 -0.09 -13.962 -2.43* 4.275 0.64 -4.474 -1.06 -4.614 -0.93 0.556 23

M21 0.184 2.06 8.365 3.52** -8.393 -1.67 5.804 1.12 4.696 0.8 -10.89 -1.68 4.807 2.31* -4.814 -0.83 -9.497 -2.54* 0.513 26

M47 0.015 0.38 0.48 0.79 0.093 0.05 -0.072 -0.35 -0.16 -0.14 0.34 0.09 -10.294 -0.18 -0.039 -0.36 4.216 0.17 0.217 16

M48 0.007 0.26 0.182 0.59 0.208 0.23 -0.047 -2.56* -0.048 -0.1 -0.976 -0.5 -0.992 -0.03 0.003 0.67 -7.695 -0.65 0.541 18

M52 0.117 1.08 4.452 1.5 -5.596 -1.03 -0.74 -0.09 3.984 1.03 -97.947 -1.97 2.79 1.26 -7.825 -0.86 -1.065 -0.97 0.461 25

M57 -0.031 -0.37 -2.627 -2.17* 0.414 0.14 0.193 1.61 4.846 1.91 12.277 1.19 -28.417 -0.31 -0.027 -0.94 3.886 0.95 0.275 47

M60 0.246 2.89* 0.02 0.01 -2.411 -0.42 3.028 0.53 -4.184 -0.7 14.26 0.26 5.752 0.37 -9.893 -1.72 -4.552 -0.5 0.34 19

M91 0.034 1.03 0.587 0.83 -2.308 -1.54 2.732 1.5 -0.505 -0.52 6.43 0.42 3.303 1.25 -7.268 -1.94 -6.034 -0.13 0.335 25

M92 0.102 1.39 5.159 2.57* -9.898 -2.12 13.667 2.86* -0.803 -0.29 -4.214 -1.5 363.408 2.96* -3.399 -4.37** -3.66 -0.35 0.741 20

M101 -0.122 -1.42 0.879 0.39 0.375 0.08 1.454 0.25 7.401 2.97* 1.931 0.05 203.93 1.38 -3.289 -0.25 -19.521 -0.17 0.591 21

M102 0.016 0.81 -0.093 -0.36 1.112 1.65 -0.001 -0.04 -0.693 -1.26 -5.253 -2.34* 5.067 0.26 0.007 1.11 -2.283 -0.16 0.272 42

M105 -0.044 -0.41 -3.143 -1.09 11.369 1.7 -17.201 -2.37* -4.764 -1.25 -4.166 -1.04 -195.329 -1.02 8.99 1.06 9.398 0.75 0.58 20

M123 0.014 0.74 0.064 0.24 -1.503 -2.01 0.02 0.79 0.048 0.09 0.068 0.03 13.661 0.6 0.003 0.46 -1.091 -0.08 0.198 41

M125 0.061 1.46 -1.528 -1.46 2.155 1.33 2.138 0.78 -1.328 -1.04 3.859 1.72 -2.193 -0.28 -3.595 -2.12* -6.531 -1.02 0.275 30

M133 0.081 0.7 -1.268 -0.43 -5.404 -0.9 -1.28 -0.13 5.877 1.61 -8.842 -1.55 -1.313 -0.38 7.725 1.44 2.097 0.19 0.545 25

M135 -0.056 -1.41 -0.178 -0.12 15.483 2.63* 20.123 1.93 -5.709 -3.9** 2.419 1.07 -4.634 -2.24 1.107 1.45 3.19 4.74** 0.917 18

M139 0.006 0.06 -4.705 -1.31 5.673 0.41 -16.03 -0.65 -3.533 -1.02 18.889 0.31 5.945 0.57 -2.469 -0.79 -6.536 -0.34 0.667 18

M144 0.115 2.14* 0.434 0.52 2.137 1 3.921 1.1 -1.879 -1.06 -3.553 -0.47 -8.388 -0.54 -3.001 -0.9 -3.508 -0.78 0.319 31

M191 0.153 2.51* 0.367 0.23 -2.378 -1.01 6.261 1.56 -0.134 -0.07 -19.69 -0.6 -3.009 -2.54* 212.014 1.3 -5.547 -1.07 0.756 25

M195 -0.479 -1.15 -23.914 -2.32* 45.688 2.25 -3.465 -0.1 3.767 0.34 10.311 1.6 -10.743 -0.91 -4.265 -0.09 1.48 0.44 0.671 17

M216 -0.122 -1.53 -0.889 -0.45 5.527 1.11 -5.021 -0.66 -0.228 -0.09 -23.72 -0.42 4.233 0.63 -2.956 -0.36 1.567 1.22 0.627 16

M217 -0.006 -0.12 1.05 0.81 -3.272 -1.53 4.087 1.29 3.61 2.46* 5.663 0.21 1.329 1.13 -1.628 -1.25 22.321 0.49 0.523 23

M253 0.002 0.98 0.064 1.65 0.146 1.24 -0.023 -0.67 -0.072 -0.87 0.028 0.11 -4.496 -1.22 -0.014 -0.37 -1.625 -0.88 0.4 17

M263 0.027 0.44 -0.927 -0.66 -5.07 -1.89 0.457 0.13 1.216 0.74 4.158 1.58 -3.508 -1.21 -3.093 -0.15 -1.631 -1.07 0.677 19

M394 -0.01 -0.08 1.842 0.61 -4.623 -0.79 0.016 0 -6.693 -1.63 -4.492 -0.62 -2.466 -1.43 1.114 0.41 1.301 0.13 0.869 16

M411 -0.016 -0.51 0.05 0.12 0.543 0.46 -0.014 -0.39 -0.758 -1.09 2.284 0.61 11.722 0.32 -0.03 -3.9** 10.762 0.54 0.862 19

M426 0.204 0.91 -8.944 -2.64* -2.718 -0.27 18.134 6.02*** -0.063 -0.01 -3.894 -1.86 7.794 1.37 15.668 4.92** -2.295 -0.63 0.917 16

M471 0.021 1.13 -0.09 -0.44 -0.47 -0.77 0.009 0.64 0.831 2.35* -0.642 -0.44 14.328 0.75 -0.003 -1.01 -9.158 -1.03 0.441 19

M473 0.007 0.13 0.866 0.54 -6.75 -3.11** 1.325 0.36 2.843 1.39 0.119 0 -5.743 -0.06 -53.447 -0.31 4.398 0.37 0.424 38

M499 0.075 0.31 -0.063 -0.02 5.018 0.64 -0.054 -0.36 -2.82 -0.66 -4.371 -0.27 31.12 0.12 -0.019 -0.54 -1.844 -0.18 0.32 16

33

Table 13 Robustness check for market timing model using different specification


4

𝑖=1


4

𝑖=1


Then, we calculated the Information Ratio using the following two equations:



∗ =𝑅𝑗,𝑡

𝜎(𝑅𝑗,𝑡)

This table provides the annual alpha, IR, IR* and ranking for individual FX trader. We omitted the remainder of the

information regarding all the individual FX investors from the table due to space considerations.

IndId Excess Annual Return S.D. IR Rank Annual Alpha Tracking Error IR* Rank

M4 0.008 0.204 0.038 23 -0.075 0.252 -0.298 38

M13 0 0.122 0.003 27 -0.07 0.174 -0.401 44

M17 -0.027 0.246 -0.111 37 -0.182 0.372 -0.489 47

M21 0.097 0.271 0.359 3 -0.08 0.456 -0.174 26

M47 0.013 0.074 0.177 9 -0.021 0.111 -0.186 29

M48 -0.002 0.063 -0.035 33 -0.023 0.059 -0.396 43

M52 0.001 0.305 0.003 28 -0.233 0.522 -0.447 46

M57 0.038 0.446 0.086 19 0.101 0.459 0.221 9

M60 0.093 0.167 0.555 1 0.051 0.128 0.401 2

M91 0.015 0.082 0.185 8 -0.021 0.118 -0.177 28

M92 -0.108 0.23 -0.468 49 -0.447 0.725 -0.617 49

M101 -0.044 0.232 -0.189 38 -0.017 0.254 -0.065 19

M102 0.002 0.094 0.023 25 -0.022 0.128 -0.172 25

M105 -0.087 0.278 -0.313 44 0.035 0.255 0.138 12

M123 0.014 0.086 0.167 11 0.036 0.086 0.412 4

M125 0.016 0.14 0.114 17 -0.016 0.234 -0.07 21

M133 0.034 0.392 0.087 18 -0.029 0.433 -0.067 20

M135 0.026 0.211 0.121 16 0.17 0.54 0.315 7

M139 -0.087 0.25 -0.35 47 -0.064 0.317 -0.203 32

M144 0.03 0.216 0.138 14 -0.124 0.473 -0.263 36

M159 0.016 0.212 0.077 21 0.127 0.248 0.513 3

M162 0.049 0.118 0.350 2 0.152 0.227 0.669 1

M168 0.006 0.039 0.141 13 0.023 0.061 0.374 5

M183 -0.119 0.421 -0.283 42 -0.218 0.768 -0.284 37

M191 -0.015 0.301 -0.051 35 -0.191 0.516 -0.371 41

M195 -0.299 0.981 -0.304 43 0.384 1.79 0.214 10

M216 -0.098 0.203 -0.484 50 -0.001 0.197 -0.003 17

M217 0.015 0.173 0.086 20 0.016 0.287 0.055 15

M264 0.005 0.311 0.017 26 0.009 0.358 0.026 16

M282 -0.224 0.368 -0.61 51 -0.257 0.397 -0.647 51

M287 0.458 2.685 0.17 10 0.939 4.68 0.201 11

M316 0.595 2.908 0.205 7 1.231 5.051 0.244 8

M325 -0.139 0.439 -0.318 45 -0.329 0.778 -0.423 45

M338 0.013 0.051 0.263 5 0.029 0.049 0.596 2

M339 0.004 0.072 0.061 22 -0.012 0.096 -0.128 22

M394 -0.194 0.574 -0.338 46 -0.58 1.047 -0.553 48

M411 -0.015 0.173 -0.085 36 -0.037 0.289 -0.129 23

M426 -0.056 1.359 -0.041 34 3.081 8.966 0.344 6

M443 0.048 0.181 0.265 4 0.018 0.231 0.077 14

M471 0.006 0.045 0.13 15 0.005 0.059 0.086 13

M473 -0.01 0.288 -0.034 32 -0.009 0.267 -0.034 18

M499 0.101 0.396 0.254 6 -0.079 0.401 -0.196 30

34

Figure 1: Relationship between individual investor’s Alpha and R2

We regress the intercept (alpha) for each individual investor against R2 from the time series to check

the robustness of individual FX investor timing ability. Figure 1 shows an inverse relationship

between FX investor Alpha and R2 which supports our analysis that individual FX investors have

timing ability. FX


4

𝑖=1

[𝐹𝑖,𝑡|𝐹𝑖,𝑡 > 0] + ∑ 𝛾𝑖,𝑗

4

𝑖=1


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

R2

Constant

35





timing ability. FX

𝑟 = 𝛼 + ∑ 𝛽𝑖

4

𝑖=1

𝐹𝑖,𝑡 + 𝜀𝑡

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

R2

36





timing ability. FX


4

𝑖=1


4

𝑖=1


-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1 1.2

R2

forex markets and abnormal returns...

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