Momentum strategies are typically implemented by buying past winners and selling (shorting) past losers. The academic literature documents the efficacy of momentum strategies across multiple time periods, many markets, and in numerous asset classes (including currency). Simply buying assets with high recent returns and selling those assets that have experienced low recent returns usually results in a very profitable investment strategy. The returns from this strategy are difficult to explain by means of standard risk factors and present a challenge to standard financial theory.

However, the strong positive average returns and Sharpe ratios of momentum strategies are punctuated with occasional crashes. Like the returns to the carry trade in currencies (Brunnermeier, Nagel, and Pedersen 2008), momentum returns are negatively skewed, and the negative returns can be pronounced and persistent. These negative returns tend to occur in times of market stress, when the market has fallen and ex-ante measures of volatility are high.

When considering the use of momentum strategies in the currency markets, Menkhoff et al. (2012) suggest that the excess returns are as large as 10% per annum if one is able to ride out the periods of large negative returns. Of course it would be the case that everyone would not necessarily be able to ride out these periods and as such the limits on arbitrage trading may be one reason for abnormally large profits that have been observed.

The other possible rationale for the relatively large profits that have been realised from this strategy is that the market participants have been subject to periods of systematic under-reaction and over-reaction. In what follows we consider the properties of this trading strategy.

1 The success of momentum strategies

The execution of momentum strategies in foreign exchange markets are conducted by professional investors in a market that is very liquid, has no short-selling constraints, and seeks to exploit the trending behaviour of exchange rates. The obvious strategy is to go long in currencies with high past excess returns (i.e. past winners) and short in currencies that have experienced low or negative excess returns (i.e. past losers). It is worth noting that an investor could make use of different formation and holding periods when implementing these strategies; where a formation period refers to the sample period that is used to determine whether a particular currency is a winner or loser, and the holding period refers to the length of time that the position is held before the trader closes out.

While the literature on momentum returns in stock markets is relatively extensive, it is still unclear as to whether-or-not momentum returns are exploitable in these market, due in part to the existence of transaction costs and limits to arbitrage. In addition, there would appear to be two strands of the literature that have sough to explain the apparent excess returns from exposure to risk (i.e. Chordia and Shivakumar (2002), Johnson (2002), Pastor and Stambaugh (2003), while another strand seeks to explain these results to investor irrationality (i.e. Chui, Titman, and Wei (2010)). In essence, these authors are looking to explain the behaviour that is evident in Figure 1, where those equities that have performed well in the recent past continue to do so in the future. This graph is contained in Daniel and Moskowitz (2013), which makes use of monthly data from 1947m1 to 2006m12.

Figure 1: Momentum investment strategies (1947-2006)

More detailed results that relate to this finding are displayed in Table 1. The biggest winners and losers are split into deciles, where decile 1 represents the biggest losers and decile 10 the biggest winners, with WML representing the zero-cost winners minus losers portfolio. The mean excess return, standard deviation, and alpha are in annualized percentages. The $$\alpha$$, $$t(\alpha)$$, and $$\beta$$ are estimated from a full-period regression of each decile portfolio’s excess return on the excess CRSP-value weighted index, while the Sharpe ratio is also annualized. For all portfolios except WML, $$sk(m)$$ denotes the full-period realized skewness of the monthly log returns (not excess) to the portfolios and $$sk(d)$$ denotes the full-period realized skewness of the daily log returns. For WML, $$sk$$ is the realized skewness of $$\log(1+r_{\text{WML}}+rf)$$.

Momentum Decile Portfolios
1 2 3 4 5 6 7 8 9 10 WML Mkt
$$r-rf$$ -2.5 2.9 2.9 6.4 7.1 7.1 9.2 10.4 11.3 15.3 17.9 7.7
$$\sigma$$ 36.5 30.5 25.9 23.2 21.3 20.2 19.5 19 20.3 23.7 30 18.8
$$\alpha$$ -14.7 -7.8 -6.4 -2.1 -0.9 -0.6 1.8 3.2 3.8 7.5 22.2 0
$$t(\alpha)$$ (-6.7) (-4.7) (-5.3) (-2.1) (-1.1) (-1.0) -2.8 -4.5 -4.3 -5.1 -7.3 0
$$\beta$$ 1.61 1.41 1.23 1.13 1.05 1.02 0.98 0.95 0.99 1.03 -0.58 1
$$SR$$ -0.07 0.09 0.11 0.28 0.33 0.35 0.47 0.54 0.56 0.65 0.6 0.41
$$sk(m)$$ 0.09 -0.05 -0.19 0.21 -0.13 -0.3 -0.55 -0.54 -0.76 -0.82 -4.7 -0.57
$$sk(d)$$ 0.12 0.29 0.22 0.27 0.1 -0.1 -0.44 -0.66 -0.67 -0.61 -1.18 -0.44

Table 1: Momentum Portfolio Characteristics (1927m1-2013m3)

What is particularly interesting in this table is that the Sharpe ratios increase by a relatively large amount, as we move from decile 1 (losers) to decile 10 (winners).

1.1 Momentum strategies in foreign exchange market

When we turn our attention to the performance of momentum strategies in the foreign exchange market, we note that most of the research suggests that these strategies would have derived positive returns. For example, Okunev and White (2003) study eight currencies from 1980 to 2000 and find positive momentum returns, while Asness, Moskowitz, and Pedersen (2009) report similar findings. In addition, Burnside, Eichenbaum, and Rebelo (2011) show, among other things, that standard risk factors cannot account for currency momentum. In addition, Menkhoff et al. (2012) perform a comprehensive study of momentum in currency excess returns (and spot rate changes). They make use of a broad cross-section of 48 countries (developed and emerging markets) and data over the period 1976 to 2010.1 They are also able to control for transaction costs for the full sample period and all currencies.

Figure 2: Momentum Returns in Foreign Exchange Market

They find that momentum returns in foreign exchange markets show very similar characteristics to the momentum in stock markets. Figure 2 displays the cumulative excess returns of momentum strategies on currency markets. This shows cumulative log excess returns (not adjusted for transaction costs) accruing to three different momentum returns. The momentum strategies are for a formation period of 1, 6, and 12 months, respectively, and the holding period is one month. The bold line shows returns to the momentum strategy with a one-month formation period (MOM (1,1) in the diagram), the dashed line shows returns to a strategy with a six-month formation period (MOM (6,1)), whereas the thin, black line shows returns to a momentum strategy with a 12-month formation period (MOM (12,1)). Shaded areas correspond to NBER recessions.

In addition, Menkhoff et al. (2012) note that the returns from currency momentum are more or less unrelated to the carry trade, which supports the finding of Burnside, Eichenbaum, and Rebelo (2012) who suggest that the Sharpe ratios of both carry trade and momentum currency strategies are substantially higher than that of the stock market. In addition, they note that as the pay-offs to the carry and momentum strategies are relatively uncorrelated, there are obvious gains to using both currency-trading strategies simultaneously. Furthermore, the pay-offs to both currency strategies were found to be uncorrelated with stock market returns. Hence, currency-trading strategies would provide a natural source of diversification when combined with a broad portfolio of U.S. stocks. Evidence of this is shown in Figure 3.

Figure 3: Currency Strategies in Foreign Exchange Market

2 Explanations for high momentum returns

2.1 Macroeconomic risk factors

The returns from currency momentum strategies are not correlated with any of the established macroeconomic risk factors. To show this feature of the data Menkhoff et al. (2012) make use of a number of simple bivariate linear regression models, where the explanatory variable pertains to measures of macroeconomic activity. The macroeconomic variables include those for real growth in consumption expenditures, employment growth, manufacturing index, growth in real industrial production, consumer inflation, growth in real money balances, growth in real disposable personal income, difference between 3-month interbank rate, Libor and 3-month T-bill rate, term spread (20-year maturity less 3-month T-bill rate), return to the carry trade long-short portfolio, proxy for global foreign exchange volatility.

MOM(1,1)
MOM(6,1)
MOM(12,1)
$$\alpha$$ $$\beta$$ $$R^2$$ $$\alpha$$ $$\beta$$ $$R^2$$ $$\alpha$$ $$\beta$$ $$R^2$$
Consumption 9.65 -0.05 0 8.95 -0.12 0 6.03 0.07 0.00
Employment 10.57 -0.72 0 7.74 0.62 0 5.86 0.23 0.00
ISM 9.46 0.04 0 8.6 0.03 0 6.14 0.04 0.00
IP 9.72 0.11 0 8.72 0.04 0 6.26 0.03 0.00
CPI 11.73 -0.55 0 9.11 -0.12 0 6.6 -0.1 0.00
M2 9.97 0.34 0 8.68 0.02 0 6.18 -0.01 0.00
DispInc 9.33 0.07 0 8.42 0.1 0 5.95 0.1 0.00
TED 13.64 -0.38 0.01 11.95 -0.3 0.01 9.73 -0.32 0.01
Term 4.48 0.22 0.01 7.54 0.05 0 5.05 0.05 0.00
HMLFX 9.5 0.04 0 8.65 0.02 0 6.21 0.08 0.00
VOLFX 11.7 -0.44 0 18.75 -2.04 0.01 27.59 -4.29 0.04

Table 2: Regression Analysis for Macroeconomic Factors

Table 2 shows the results of this analysis, where we note that the coefficient of determination in each regression is almost zero. Hence, it would not appear as if macroeconomic (or business cycle) risk factors are able to explain the positive returns from currency momentum strategies.

2.2 Transaction costs

While several papers that consider possible returns from stock market momentum strategies do not adjust for transaction costs, there are a few that do. These suggest that transaction costs matter and that by adjusting for these costs, the historic profits would reduce significantly. When considering the results for momentum strategies in the foreign exchange market, Menkhoff et al. (2012) find that while adjusting for transaction costs reduces the profits of momentum strategies, one is still able to derive a relatively large return from these strategies. Hence, transaction costs are not the sole reason for the results that were reported earlier.

2.3 Limits to arbitrage

However, currency momentum returns do not come as a free lunch for investors trying to exploit these strategies. Menkhoff et al. (2012)} find that momentum portfolios in the foreign exchange market are significantly skewed towards minor currencies that have relatively high transaction costs, accounting for roughly 50% of momentum returns. Also, the concentration of minor currencies in momentum portfolios raises the need to setup trading positions in currencies with higher idiosyncratic volatility, higher country risk, and higher expected risk of exchange rate instabilities, which clearly imposes risks to investors that are not captured by standard risk factors in a covariance risk framework. Hence, there seem to be effective limits to arbitrage that prevent a straight forward exploitation of momentum returns. Furthermore, momentum profits are highly time-varying, which can also pose an obstacle to arbitrage activity for some of the key foreign exchange market participants (e.g., proprietary traders and hedge funds) who typically have fairly short-term investment horizons.

2.4 Slow information processing

Jegadeesh and Titman (1995) suggest that momentum profits could be due to an initial under-reaction to news, which is normally followed by a subsequent overreaction to changes in observed market activity (i.e. the realised high (low) returns). Under this explanation, one would expect to see a clear pattern in post-information returns of momentum returns. In addition, Chui, Titman, and Wei (2010) recently showed for international stock markets that under-reaction seems to be important, which would suggest that the market may be relatively slow at processing this information.

To test this behaviour Jegadeesh and Titman (1995) returns tend to increase for several months up to one-year after portfolio formation but then peak and start to decrease significantly. To test for similar behaviour in the foreign exchange market, Menkhoff et al. (2012) plot cumulative post-formation excess returns over periods of $$1, 2, \ldots, 60$$ months for the zero-cost long-short momentum portfolios with a one, six, and twelve month formation period.

Figure 4: Momentum Returns Information Processing

There is a clear pattern of increasing returns that peaks after 8-12 months, across strategies, and a subsequent period of declining excess returns. The decline is more pronounced for momentum strategies with longer formation periods. Thus, on the face of it, this evidence looks very similar to the pattern identified in equity markets as in Jegadeesh and Titman (1995). This result is interesting since it suggests that the prices of foreign exchange instruments are similar to those of other financial assets.

3 Conclusion

There is currently no clear, unified explanation for the excess returns that have been generated by currency momentum strategies. Menkhoff et al. (2012) suggest that the momentum strategies deliver high excess returns in the foreign exchange markets, comparable in magnitude to the excess returns documented in stock markets. This occurs despite the characteristics of currency markets, such as huge trading volumes, a large contingent of professional traders, no short-selling constraints, and a considerable degree of central bank interference.

They also find evidence for initial under-reaction and subsequent over-reaction in long-horizon momentum returns, which suggests that the market may be somewhat slow to process various types of information. In addition, they also show that after adjusting profits for transaction costs the profitability is reduced, but not negated. A large part of the excess returns could possibly be attributed to *frictions} such as the time variation in momentum profitability, high volatility and exposure to country risks (particularly where it is hard to hedge against such a currency). However, it is difficult to quantify many of these factors correctly.

As a final point, it is important to note that the use of carry trades and the momentum trades are important strategies in the foreign exchange market and the use of these strategies has the potential to influence the behaviour of most exchange rates.

4 References

Asness, C., T. Moskowitz, and L. Pedersen. 2009. “Value and Momentum Everywhere.” AQR Capital Management, University of Chicago, Copenhagen Business School.

Brunnermeier, M.K., S. Nagel, and L.H. Pedersen. 2008. “NBER Macroeconomics Annual 2008.” In. Cambridge, MA: National Bureau of Economic Research.

Burnside, Craig, Martin Eichenbaum, and Sergio Rebelo. 2011. “Carry Trade and Momentum in Currency Markets.” Annual Review of Financial Economics 3: 511–35.

———. 2012. “Understanding the Profitability of Currency-Trading Strategies.” Research Summary 3. NBER Reporter 2012. Vol. Number 3. National Bureau of Economic Research.

Chordia, T., and L. Shivakumar. 2002. “Momentum, Business Cycle, and Time-Varying Expected Returns.” Journal of Finance 62: 985–1019.

Chui, A., S. Titman, and K. Wei. 2010. “Individualism and Momentum Around the World.” Journal of Finance 65: 361–92.

Daniel, K. D., and T. J. Moskowitz. 2013. “Momentum Crashes.” 13-61. Swiss Finance Institute Research Paper.

Jegadeesh, N., and S. Titman. 1995. “Overreaction, Delayed Reaction, and Contrarian Profits.” Review of Financial Studies 8 (4). Soc Financial Studies: 973.

Johnson, T. 2002. “Rational Momentum Effects.” Journal of Finance 57: 585–608.

Menkhoff, Lukas, Lucio Sarno, Maik Schmeling, and Andreas Schrimpf. 2012. “Currency Momentum Strategies.” Journal of Finacial Economics 106: 660–84.

Okunev, J., and D. White. 2003. “Do Momentum-Based Strategies Still Work in Foreign Currency Markets?” Journal of Financial and Quantitative Analysis 38: 425–47.

Pastor, L., and R. Stambaugh. 2003. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy 111: 642–85.

1. The sample of countries includes: Australia, Austria, Belgium, Brazil, Bulgaria, Canada, Croatia, Cyprus, Czech Rep., Denmark, Egypt, Euro area, Finland, France, Germany, Greece, Hong, Kong, Hungary, India, Indonesia, Ireland, Israel, Italy, Iceland, Japan, Kuwait, Malaysia, Mexico, Netherlands, New Zealand, Norway, Philippines, Poland, Portugal, Russia, Saudi Arabia, Singapore, Slovakia, Slovenia, South Africa, South, Korea, Spain, Sweden, Switzerland, Taiwan, Thailand, Ukraine, and United Kingdom.