Subject:

How well do time series (intrinsic) and cross-sectional (relative) momentum work for different types of currency exchange rates? In their April 2017 paper entitled “Momentum in Traditional and Cryptocurrencies Made Simple”, Janick Rohrbach, Silvan Suremann and Joerg Osterrieder compare the effectiveness of time series and cross-sectional momentum as applied to three groups of currency exchange rates: G10 currencies; non-G10 conventional currencies; and, cryptocurrencies.

To measure momentum they employ three pairs (one fast and one slow) of exponential moving averages (EMA) spanning short, intermediate and long horizons.

## AHL Explains - Momentum

When the fast EMA of a pair is above (below) the slow EMA, the trend is positive (negative). They extract a momentum signal for each exchange rate from these three EMA pairs by:

- For each EMA pair, taking the difference between the fast and slow EMA.
- For each EMA pair, dividing the output of step 1 by the standard deviation of the exchange rate over the last three months to scale currency fluctuations to the same magnitude.
- For each EMA pair, dividing the output of step 2 by its own standard deviation over the last year to suppress series volatility.
- For each EMA pair, mapping all outputs of step 3 to signals between -1 and 1.
- Averaging the signals across the three EMA pairs to produce an overall momentum signal.

The time series portfolio holds all currencies weighted each day according to their respective prior-day overall momentum signals.

The cross-sectional portfolio is each day long (short) the three currencies with the highest (lowest) overall momentum signals.

Key performance metrics are annualized average gross return, annualized standard deviation of returns, annualized gross Sharpe ratio (assuming risk-free rate 0%) and maximum drawdown. Using daily foreign currency exchange rates for 23 conventional currencies and seven cryptocurrencies versus the U.S.

dollar as available through late March 2017, *they find that:*

- For G10 currencies (data start July 1974):
- The time series (cross-sectional) portfolio generates annualized average gross return 22% (7%), with annualized standard deviation 41% (24%) and annualized gross Sharpe ratio 0.53 (0.27).
- Maximum drawdown of the time series (cross-sectional) portfolio is about -17% (-35%).
This drawdown for the cross-sectional portfolio commences in 2001 and has not yet recovered its high water mark.

- For 13 non-G10 conventional currencies (data start January 1995):
- The time series (cross-sectional) portfolio generates annualized average gross return 31% (21%), with annualized standard deviation 38% (28%) and annualized gross Sharpe ratio 0.82 (0.78).
- Maximum drawdown of the time series (cross-sectional) portfolio is about -25% (-35%).

- For seven cryptocurrencies (data start March 2015):
- The time series (cross-sectional) portfolio generates annualized average gross return 299% (359%), with annualized standard deviation 185% (242%) and annualized gross Sharpe ratio 1.62 (1.48).
- Maximum drawdown of the time series (cross-sectional) portfolio is about -40% (-70%).

- Across the samples:
- Time series portfolios offer higher risk-adjusted performances returns than corresponding cross-sectional portfolios.
- Strategies work well during calm markets but suffer crashes during unusual events.

In summary, *evidence indicates that time series momentum generally works better than cross-sectional momentum across different groups of currency exchange rates on a gross risk-adjusted basis.*

Cautions regarding findings include:

- As noted in the paper, return calculations are gross, not net.
Accounting for trading frictions (likely substantial due to daily portfolio reformation) would reduce all returns. Since turnovers may vary by currency and by strategy (time series or cross-sectional), net findings may differ from gross findings.

- There may be an issue of performing all required calculations and executing portfolio reformation in a timely manner on a daily basis.
- Assuming a risk-free rate of 0% in calculating Sharpe ratio seems unreasonable, especially for the sample of G10 currencies that commences in the mid-1970s.
- Signal generation rules are elaborate, suggesting potential for snooping bias in rule construction and/or parameter settings and therefore overstatement of expected returns.
- As noted in the paper, the sample period for cryptocurrencies is extremely short in terms of variety of currency market and economic conditions.

See also “When Carry, Momentum and Value Work”.