Momentum Strategies

Researchers sometimes classify momentum in asset prices into two types:

• Time Series Momentum. Past returns are correlated with future returns
• Cross Sectional Momentum. Relative performance of a price series in relation to another price series. ie prices with returns that outperformed other price series will likely keep doing so in the future.

Tests for Time Series Momentum

I computing correlations of pairs of returns from different look back and holding periods, we must not use overlapping data.

If look back is greater than the holding period, we must shift forward by the holding period.

If the holding period is greater than the lookback period, we must shift forward by the lookback.

Whichever period is shorter, we use that to shift forward

Time Series Strategy

For a certain future, if we find that the correlation coefficient between a past return of a lookback period and a future return of a holding period is high and the p value is small, we can proceed to see if a profitable momentum strategy can be found using this set of optimal time periods.

We can simply buy the future if it has a positive 12 month return, and hold the position for 1 month.

Concepts

Hurst Exponent

Measure of long term memory of a time series. Used to assess the persistence or trend following characteristics of the time series.

Ranges from 0 to 1

• H is close to 0.5 (between 0.4 and 0.6) it suggests a random walk or a series with no long-term autocorrelation. In this case, past values have little influence on future values, indicating lack of momentum