#### Abstract

Significant cross-sectional spread gives excess returns of 10% pa, not explained by traditional risk factors but explained by under and over reactions of investors. Different from carry trade.

#### Introduction

Momentum in stocks poses challenge to standard finance theory. Apart from conventional risk-factors, factors like credit risk/bankruptcy risk, limits to arbitrage, under reaction, or high transaction costs have been proposed.

FX time series momentum strategies like moving average cross-overs, filter rules, channel breakouts deteriorate over time. FX cross-sectional strategies are less examined. We study 1976 - 2010 with 48 currencies. We decompose these momentum returns into systematic and unsystematic risk components, compare momentum strategies to carry and trading rules, qualify the importance of transaction cost and investigating non-standard sources of momentum returns like under- and over- reaction and limits to arbitrage.

We find evidence of return continuation and subsequent reversal over 36 months. These are different from carry returns and technical trading rules. Momentum profits are skewed towards currencies with high transaction costs. But these returns are not systematically related to standard proxies for business cycle risk, liquidity risk, carry trade risk factor, volatility risk, three Fama-French factors, Carhart four factor. These profits vary significantly over time suggesting limit to arbitrage. Momentum in countries with higher risk rating tend to yield significantly positive excess returns. Similar effect is found for a measure of exchange rate stability risk.

#### Related Literature

*Stock market momentum*- We established empirically, explained by

- risk-based and characteristic-based explanations: not linked to macroeconomic risk, but firm-specific risks, e.g. stronger in smaller firms, firms with lower credit rating, firms with higher revenue growth volatility, firms with higher likelihood to go bankrupt.
- behavioral biases: investor's under reaction to news, weak analyst coverage causes stronger momentum.
- Transaction costs or limit to arbitrage: reasonably high transaction costs may wipe out momentum profits.

*Bonds and commodities momentum*- Momentum strategies don't work for investment grade bonds or bonds at the country level, but yield positive returns for non-investment grade corporate bonds. Momentum returns are not related to liquidity but seem to reflect default risk in the winner and loser portfolios. Commodities high momentum returns are related to low levels of inventories.

*Currency momentum*- Mostly time series momentum has been analyzed.

- Technical trading in FX markets: highly correlated to trend following. Filter rules (like go long if moving returns are >1%) and moving average cross-over rules seem to work. This has slowed down recently.
- Contribution of this paper: cross-sectional momentum of FX and its analysis.

#### Data and currency portfolio

spot and 1 month forward rate from 1976-2010, end of month data. 48 countries. Interest rate differential (forward discount) contribute a significant share of the excess return of currency investments. We track pure spot returns as well to identify source of momentum. The long short portfolio is dollar neutral.

#### Characterizing Currency Momentum Returns

- Returns to Momentum strategies in currency markets - Returns driven by spot rates momentum and not mostly driven by interest rate changes (like for carry trades), especially for 1 year momentum with 1 month holding period. (1,1) is the best of the all. Though the cross-section of currencies is small relative to equities, the performance is still good because of much lower correlations in the currencies vs equities.
- Out of sample perspective - do specific momentum strategies identified to be attractive in-sample continue to do well? Out of the universe of 144 strategies, we look for momentum in the lagged momentum returns! We find that 1 month lagged best portfolio is equally good (0.94) and hence can be seen as an out of sample test. These strategies have been stable over time.
- Comparing momentum and technical trading rules - moving average cross overs of 1-20, 1-50 and 1-200 is used as a proxy for technical trading strategies (IR from 0.88 to 0.77). These are correlated to momentum but there is significant economic alpha. Similarly the cross-sectional momentum strategy has alpha over time series momentum strategies as well.
- Comparing Currency momentum and the carry trade - Interest rate differentials are strongly auto-correlated and spot rate changes do not seem to adjust to compensate for this interest rate differential (forward rate puzzle). Hence, it may be the case that lagged high returns simply proxy for lagged high interest rate differentials and that cross-sectional momentum is simply carry. We show that that is not the case. Carry trade has negative skewness while momentum has slightly positive skewness. The high-low momentum strategies are uncorrelated with high-low carry strategies. Double sorting ( divide currencies into two portfolios based on median lagged forward discount and then divided each into three portfolios based on lagged returns) shows no material difference in long-short momentum returns among high vs low interest rate currencies. Cross-sectional Fama-Macbeth regression of currency excess returns on lagged excess returns over the last $l$-months, lagged forward discounts and lagged spot rate changes for each month show that lagged spot returns explain the regressions.
- Post-formation momentum returns - Initial under-reaction is accompanied by over-reaction which gets corrected over the long run. This causes reversal over longer periods. There is a clear pattern of increasing returns which peaks after 8-12 months across strategies and a subsequent period of declining excess returns, more pronounced for momentum strategies with longer formation periods, suggesting equity and currency momentum have similar origins.

Currency momentum seem similar to equity momentum. But the highly liquid FX markets are dominated by professional traders, where irrationality should be quickly arbitraged away. Hence examining possible limits to arbitrage activity which could explain the persistence of momentum profits in FX markets.

#### Understanding the results

- Transaction cost - full bid-ask spread used. The 1,1 momentum returns from 10 to 4 percent. FX momentum strategies are much more profitable in the later part of the sample, but they do not always deliver high returns. There is much variation in profitability. Transaction costs can be decomposed into turnover across portfolios and bid-ask spreads across portfolio. Turnover can be extremely high for 1,1 momentum strategy, up to 70% per month. Winner and loser currencies do have higher transaction costs than the average exchange rate and the markup ranges from about 2.5 to 7 basis points per month. Transaction costs have declined over time due to more efficient trading technologies. This could imply (i) higher momentum returns due to lower trading costs (ii) lower momentum returns since lower cost facilitates more capital being deployed for arbitrage activity. Looking at 1,1 strategy for 1992 to 2010, we find profitability. Thus, lower bid-ask spreads do not necessarily lead to lower excess returns, which further indicate that trading costs are not the sole driving force behind momentum returns. Also suggesting that momentum returns are a phenomenon which is still exploitable.
- Momentum returns and Business cycle risk - Various univariate regressions on business cycle state variables - real growth in non-durables and service consuption expenditures, nonfarm employment growth, ISM manufacturing index, real industrial production, inflation rate, real money balances, growth in real disposable personal income, TED spread (3m libor - t-bill rate), term spread (20y - 3m tbill rate), carry trade long-short portfolio, global FX volatility - yield no explanation power. Regression on Fama-French three factors is also not explanatory.
- Limit to Arbitrage: Time-variation in momentum profitability - 36 months moving window returns plot shows that there is time variation in performance. Hence, investor seeking to profit from momentum returns has to have a long enough investment horizon. Since the bulk of currency speculation is accounted for by professional market participants with rather short horizon.
- Limit to Arbitrage: Idiosyncratic volatility - We investigate whether momentum returns are different between currencies with high or low idiosyncratic volatility (relative to an FX asset pricing model). When we double sort with respect to lagged idiosyncratic volatility and returns we find high idiosyncratic volatility explain higher returns.
- Limit to Arbitrage: Country risk - we sort on a measure of country risk and a measure of exchange rate stability risk. Data based on International Country Risk Guide (ICRG) database from the Political Risk Services group. We employ relative to US values. Momentum returns are significantly positive and always larger in high-risk countries than in low-risk countries. Hence country risk should be an important limit to arbitrage activity in FX markets. These risk ratings are not simple proxies for interest rate differentials, because the country risk and exchange rate risk are high both for winner and loser momentum currencies. Sorting based on forward discount show that country risk highest for carry trade target countries and lowest for carry trade funding currency. For top 15 developed countries, the momentum returns are non-existent after transaction cost.

#### Robustness and additional tests

- Capital account restrictions and readability -

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