Section 1.1: The Concept of Volatility

To grasp the Average True Range (ATR), it’s essential to first understand volatility, a fundamental concept in finance. Mastery of volatility can provide a significant advantage in trading. Unfortunately, accurately measuring and predicting volatility can be challenging. While it holds greater importance in options trading, it is critical across all trading contexts. Traders rely on volatility for effective position management and risk assessment, and quantitative analysts need it for their analyses.

To illustrate this concept visually, consider the following graph:

You can implement the following code in Python to visualize high and low volatility:

# Importing the necessary libraries

import numpy as np

import matplotlib.pyplot as plt

# Creating high volatility noise

hv_noise = np.random.normal(0, 1, 250)

# Creating low volatility noise

lv_noise = np.random.normal(0, 0.1, 250)

# Plotting

plt.plot(hv_noise, color='red', linewidth=1.5, label='High Volatility')

plt.plot(lv_noise, color='green', linewidth=1.5, label='Low Volatility')

plt.axhline(y=0, color='black', linewidth=1)

plt.grid()

plt.legend()

The various types of volatility can be summarized as follows:

• Historical Volatility: This is the actual volatility observed over a specific timeframe. Although it looks backward, traders often use it to predict future volatility. The standard deviation is a common historical measure.
• Implied Volatility: This is the expected future volatility inferred from market prices of options.
• Forward Volatility: This refers to volatility anticipated over a specific future period.
• Actual Volatility: Also known as local volatility, this represents the volatility at a specific moment, which is often difficult to calculate.

Volatility reflects the average deviation from the mean when analyzing time series data.

Section 1.2: Introducing the Average True Range

In technical analysis, the Average True Range (ATR) serves as an indicator of historical volatility. While it is considered a lagging indicator, it provides insights into current and past volatility levels.

To understand how the True Range is calculated, consider an OHLC dataset (Open, High, Low, Close). For each time period, the True Range is identified as the maximum of three price differences:

1. High – Low
2. High – Previous Close
3. Previous Close – Low

The ATR is the smoothed average of these True Range calculations over a specified number of periods. Notably, during periods of heightened market activity or panic, the ATR tends to increase, while it often decreases in stable market conditions.

The ATR was developed by Welles Wilder Jr., who also created the Relative Strength Index. It employs Wilder's smoothed moving average, which can be derived from an exponential moving average.

The following function calculates the ATR:

def atr(data, lookback, high, low, close, where):

# Adding columns

data = adder(data, 2)

# True range calculation

for i in range(len(data)):

try:

data[i, where] = max(data[i, high] - data[i, low],

abs(data[i, high] - data[i - 1, close]),

abs(data[i, low] - data[i - 1, close]))

except ValueError:

pass

data[0, where] = 0

# Average True Range calculation

data = ema(data, 2, (lookback * 2) - 1, where, where + 1)

# Cleaning

data = deleter(data, where, 1)

data = jump(data, lookback)

return data

Now, let’s explore the Trailing Stop Indicator.

Summary and Best Practices

In summary, my aim is to contribute to the realm of objective technical analysis, promoting transparent techniques that require back-testing before implementation. This approach can help dispel the negative perception surrounding technical analysis.

When assessing any trading technique or strategy, consider the following steps:

1. Maintain a critical mindset, free from emotional biases.
2. Perform back-testing under realistic conditions.
3. If promising, optimize and conduct forward testing.
4. Incorporate transaction costs and slippage into your simulations.
5. Always integrate risk management and position sizing into your evaluations.

Even with thorough preparation, remain vigilant as market dynamics can change, potentially affecting the effectiveness of your strategy.