## 01 Jul Learning From AQR's "Which Trend is Your Friend?"

###### Most trend measurement methods are similar at a higher level and would produce similar results.

*In this article, Absolute Momentum will be used interchangeably with trend following or time series momentum. Relative Momentum will be used interchangeably with cross-sectional momentum or relative strength.*

The paper shows that the two most common and important statistical measures of price trends, namely time series momentum and moving average crossovers, are closely connected. They also capture many other types of trend signals such as HP filter, Kalman filter and all other linear filters.

Absolute Momentum is based on the idea that price trends are more likely to continue than not. The basic strategy is to buy when prices are rising and sell when prices are falling. However finding a price trend among noisy random price moves presents a similar challenge to that of “filtering” information from the noise in many other applications such as astronomy, audio, ballistics, image processing and macroeconomics.

One of the simplest measures of trend is the return over some recent time period, such as returns over the past 12 months. Another simple measure is the moving average crossover method where a shorter term moving average crosses a longer term moving average. The paper shows that the most general form of moving average crossover can be viewed as a special case of the most general time-series momentum using past returns described earlier. Hence using either measure to detect trends would yield similar results. “Table 1” of the paper (reproduced below) shows the similar Sharpe ratio of both Time series momentum and moving average crossover signals using various parameters.

*Source: Ari Levine and Lasse Heje Pedersen (AQR Capital Management)*

Furthermore the paper shows that other seemingly unique trend filtering techniques such as HP filter and Kalman filter are similar at a higher level. Many generalized forms of trend following strategies would produce similar results.

It is therefore important to focus on the robustness and quality of implementation such as optimally managing transaction costs, dynamic trading, diversification, position sizing, portfolio construction and risk management.

Research Paper: Which Trend is Your Friend?

Authors: Ari Levine, Lasse Heje Pedersen

Company: AQR Capital Management

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