# Intelligent Dynamic Backlash Agent: A Trading Strategy Based on the Directional Change Framework
## 2 Directional Changes: An Introduction
### DC Notations  
In this section, we introduce some basic notations related to the DC concept. These notations were initially introduced in [PERSON] et al. [8] and reshaped to fit with the context of this paper. -\(P_{c}\): This denotes the current price. -Extreme point: This is the point at which the current DC event starts. -\(P_{EXT}\) : It is the price at the extreme point of the current DC event. In the case of a downward DC event, \(P_{EXT}\) refers to the highest price in this trend. In the case of an upward DC event, \(P_{EXT}\) refers to the lowest price in this trend. -\(P_{EXT}^{next}\): If the market is in a downtrend (uptrend), then \(P_{EXT}^{next}\) would refer to the lowest (highest) price in this downtrend (uptrend). Figure 3: An example of a DC-based summary of the price series shown in Figure 1. Threshold \(theta=0.2\%\). The black line indicates GBP/CHF mid-prices. Solid green lines represent DC events. Dashed green lines represent OS events. Each of the points A, B, E is an extreme point. Each of the points A\({}^{0.2}\), B\({}^{0.2}\), E\({}^{0.2}\) is a DC confirmation point. \(P_{DCC\downarrow}\) and \(P_{DCC\uparrow}\) : The interpretations of these two variables depend on whether the market is in uptrend or downtrend: \(\odot\) If the market is in uptrend, then \(P_{DCC\uparrow}\) would denote the minimum price required to confirm the current uptrend (see Equation (3)). If the market is in downtrend, then \(P_{DCC\uparrow}\) would denote the minimum price required to confirm the next downtrend. \(\odot\) If the market is in downtrend, then \(P_{DCC\downarrow}\) would denote the highest price required to confirm  
\[Profit\ factor=\frac{\text{sum of all profits}}{\text{sum of all losses}} \tag{7}\]
* Max drawdown (%) [20]: The drawdown (Equation (8)) is defined as the difference, in percentage, between the highest profit (or capital), previous to the current time point, and the current profit (or capital) value. The Maximum Drawdown (_MDD_) is the largest drawdown observed during a specific trading period. _MDD_ measures the risk as the \"worst case scenario\" for a trading period. This metric can help measure the amount of risk incurred by a system and determine if a system is practical. In Equations (8) and (9), \(t_{i}\) denotes the time-index (i.e., time-stamp). _capital_(\(t_{i}\)) denotes the value of capital at time \(t_{i}\). The _maximum capital_(\(t_{i}\)) refers to the peak capital's value that has been reached since the beginning of trading up to time \(t_{i}\). Thus, _drawdown_ (\(t_{i}\)) (Equation (8)) is interpreted as the peak-to-trough decline from the start of the trading period up to time \(t_{i}\). The _MDD_ (Equation (9)) is the maximum value among all computed _drawdown_ (\(t_{i}\)). Many studies (e.g., [11; 21; 22]) have used _MDD_ to measure the risk of a trading strategy. If the largest amount of money that a trader is willing to risk is greater than the maximum drawdown, the trading system is not suitable for the trader. \[drawdown\ (t_{i})=\left|\frac{capital\ (t_{i})-\ maximum\ capital(t_{i})}{ maximum\ capital(t_{i})}\right|\] (8) \[MDD=Max\ (drawdown\ (t_{i})),\ \ \forall\ time\ t_{i}\in trading\ period\] (9)
* Win ratio [17]: The win ratio is calculated by dividing the number of winning trades by the total number of trades for a specified trading period. It expresses the probability that a trade will have a positive return. \[Win\ ratio=\frac{number\ of\ winning\ trades}{total\ number\ of\ all\ trades}\] (10)
* Sharpe ratio [22]: The Sharpe ratio (Equation (11)) is a measure for calculating risk-adjusted return. The basic purpose of the Sharpe ratio is to allow an investor to analyze how much greater a return he or she is obtaining in relation to the level of additional risk taken to generate that return. The Sharpe ratio can be seen as the average return earned in excess of the risk-free rate per unit of volatility or total risk. To date, it remains one of the most popular risk-adjusted performance measures due to its practical use.