## Momentum Rule and Its Anatomy

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Interactive illustrations to Chapters 4 and 5 of the book Market Timing with Moving Averages: The Anatomy and Performance of Trading Rules by Valeriy Zakamulin

Chapter 4 reviews the most common trend-following rules.

Chapter 5 uncovers the anatomy of trend-following rules and demonstrates that the computation of a technical trading indicator for any rule can alternatively be given by the following simple formula $\text{Indicator}_t^{TR(n)} = \sum_{i=1}^{n-1} \pi_i \Delta P_{t-i}.$ In words, any trading indicator is computed as a weighted average of price changes over the averaging window. The price-change weighting function $$\pi_i$$ of a trading rule reveals the anatomy of this rule.

These interactive illustrations demonstrate the trading with the Momentum rule and the anatomy of this rule.

The Momentum rule represents the simplest and most basic market timing rule. In this rule, the last closing price $$P_t$$ is compared with the closing price $$n-1$$ periods ago, $$P_{t-n+1}$$. A Buy signal is generated when the last closing price is greater than the closing price $$n-1$$ periods ago.

Formally, the technical trading indicator for the Momentum rule is computed as: $\text{Indicator}_t^{\text{MOM}(n)} = P_t - P_{t-n+1}.$

In the Application to S&P 500 panel, the top figure plots the monthly values of the S&P 500 index. The shaded areas in this plot indicate the periods where this rule generates a Sell signal. The bottom figure plots the values of the technical trading indictor of the $$MOM(n)$$ rule.

The Anatomy of the rule panel plots the price-change weighting function of the $$MOM(n)$$ rule.

One can change the data range and the size of the window, $$n$$, to compute the trading signal.