Momentum trading, *ie* buying past winners and selling past losers, is a very popular trading strategy in many assets. In foreign exchange high returns to momentum trading have been documented since the 1970s and have fuelled concerns about destabilising speculation. However, such concerns may be a bit one-sided because it is not really obvious whether there is too much momentum trading or possibly even not enough.

Given how simple it is to set up a momentum strategy a natural question is why arbitrage activity does not erase momentum returns (Vayanos and Woolley 2012)? This seems especially puzzling since the foreign exchange market is the most liquid of all asset markets; it is also populated by highly professional traders and asset managers who have strong incentives to exploit momentum returns. In recent research (Menkhoff *et al* 2012), we argue that there are severe limits to arbitrage in the case of currency momentum trading preventing the full exploitation of potential returns.

The use of momentum trading in foreign exchange markets is well known among practitioners and well documented (*eg* Pojarliev and Levich 2010). Still, momentum returns persist until today and earlier doubts about the profitability of momentum trading have not proven to be justified by recent data.

# Momentum in action

Momentum strategies basically come in two forms:

- Time-series momentum” in returns,
*ie*the legs of a certain currency pair are purchased or sold, depending on momentum signals received by the trading strategy (Moskowitz*et al*forthcoming).

Strategies on single exchange rates can be combined into a portfolio.

- “Cross-sectional momentum”,
*ie*one takes a universe of currencies and goes long (short) in a basket of selected currencies which experienced the highest (lowest) returns over a recent time period (Menkhoff*et al*2012).

We examine these trading strategies on a universe of up to 48 currencies during the period 1976 to 2010. Excess returns on this kind of momentum can reach up to 10% per year (see Figure 1) without being exposed to conventional measures of systematic risk. We focus on these cross-sectional momentum strategies as returns are even higher than on time-series currency momentum.

**Figure 1.** Cumulative excess returns to three different momentum strategies

# High trading costs

Momentum strategies require frequent portfolio rebalancing so the consideration of transaction costs is crucial. This is also important here because of two reasons:

- Shorter-term strategies are more profitable but also require more portfolio turnover; and
- The profitability of momentum trading relies on the inclusion of emerging market currencies with higher transaction costs.

In sum, transaction costs account for about 30%-50% of momentum returns. Despite these high costs, the main finding of momentum profitability survives and, hence, needs a different explanation. There are three limits to arbitrage which contribute to such an explanation.

# Limits to arbitrage

First, in contrast to the overwhelming long-run profitability of momentum trading there is significant short-run variation in profitability. This is demonstrated in Figure 2, where returns to a standard momentum strategy are plotted over time without considering transaction costs.

In order to make the case more realistic we show the average profitability over three-year moving windows. It is clear from Figure 2 that gross returns can be disappointing over years and that additionally considering transaction costs will produce extended periods of negative returns to momentum trading. As a three-year window is often seen as the maximum period an unsuccessful asset manager can survive, the application of currency momentum trading is clearly risky from this point of view.

**Figure 2. **Rolling momentum profits

A second limit to arbitrage results from high idiosyncratic volatility of those currencies that are preferably involved in momentum trading. Highly idiosyncratic movements of a currency make it harder for potential speculators to hedge their positions which might hinder the exploitation of momentum profits. Considering idiosyncratic volatility yields a clear result: the returns to momentum trading in currencies that have high idiosyncratic volatility are about twice as high than in currencies with low idiosyncratic volatility. This provides a limit at least to those investors who may wish to hedge their position so that the momentum trading becomes a pure bet on return continuation.

As another manifestation of this impact of unsystematic risk on the profitability of momentum strategies, there is a third limit to arbitrage resulting from country risk. Interestingly, the currencies being involved in momentum trading are tentatively characterised by higher country risk (and higher exchange-rate stability risk). Splitting the sample and then running momentum strategies separately in low risk and high risk sub-samples shows that the high risk sub-sample allows about twice as high excess returns. This effect applies to both sides of momentum trading, to investment currencies, and to funding currencies. The country risk involved here means that investment and funding currencies are subject to political instability, involving higher probability of sudden capital account restrictions or other problems of convertibility.

# Conclusion

We document high and robust excess returns to momentum trading which cannot be explained by conventional risk factors. Practitioners are attracted by these strategies but obviously do not execute momentum strategies to a degree that excess returns would be wiped out. This may be explained to some degree by considerably high transaction costs and even more by several limits to arbitrage: returns to momentum trading are subject to very high time-variation, involved currencies are characterised by high idiosyncratic volatility, and involved countries are classified as highly risky.

# References

Menkhoff, Lukas, Lucio Sarno, Maik Schmeling and Andreas Schrimpf (2012), “Currency momentum strategies”, CEPR Discussion Paper 8747, *Journal of Financial Economics*, forthcoming.

Moskowitz, Tobias J, Yao Hua Ooi, and Lasse Heje Pedersen (forthcoming), “Time series momentum”, *Journal of Financial Economics*.

Pojarliev, Momtchil and Richard M Levich (2010), “Trades of the living dead: Style differences, style persistence and performance of currency fund managers”, *Journal of International Money and Finance*, 29:1752–75.

Vayanos, Dimitri and Paul Woolley (2012), “New light on choice of investment strategy”, VoxEU.org, 18 January.