# Volatility Momentum in Python

### Coding and Trading a Volatility-Adjusted RSI in Python

Structured indicators are the result of fusing two or more together to form a weighted or adjusted indicator that takes into account more variables. For example, we know that there is a Stochastic-RSI indicator which combines the two formulas together in an attempt to improve the signals, this article discusses the creation of an RSI-ATR indicator which adjusts the RSI for the average true range, a measure of volatility.

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### The Relative Strength Index

First introduced by J. Welles Wilder Jr., the RSI is one of the most popular and versatile technical indicators. Mainly used as a contrarian indicator where extreme values signal a reaction that can be exploited. Typically, we use the following steps to calculate the default RSI:

Calculate the change in the closing prices from the previous ones.

Separate the positive net changes from the negative net changes.

Calculate a smoothed moving average on the positive net changes and on the absolute values of the negative net changes.

Divide the smoothed positive changes by the smoothed negative changes. We will refer to this calculation as the Relative Strength — RS.

Apply the normalization formula shown below for every time step to get the RSI.

The above chart shows the hourly values of the GBPUSD in black with the 13-period RSI. We can generally note that the RSI tends to bounce close to 25 while it tends to pause around 75. To code the RSI in Python, we need an OHLC array composed of four columns that cover open, high, low, and close prices.

```
def add_column(data, times):
for i in range(1, times + 1):
new = np.zeros((len(data), 1), dtype = float)
data = np.append(data, new, axis = 1)
```

`return data`

```
def delete_column(data, index, times):
for i in range(1, times + 1):
data = np.delete(data, index, axis = 1)
```

`return data`

```
def delete_row(data, number):
data = data[number:, ]
return data
```

```
def ma(data, lookback, close, position):
data = add_column(data, 1)
for i in range(len(data)):
try:
data[i, position] = (data[i - lookback + 1:i + 1, close].mean())
except IndexError:
pass
data = delete_row(data, lookback)
return data
```

```
def smoothed_ma(data, alpha, lookback, close, position):
lookback = (2 * lookback) - 1
alpha = alpha / (lookback + 1.0)
beta = 1 - alpha
data = ma(data, lookback, close, position)
```

`data[lookback + 1, position] = (data[lookback + 1, close] * alpha) + (data[lookback, position] * beta)`

```
for i in range(lookback + 2, len(data)):
try:
data[i, position] = (data[i, close] * alpha) + (data[i - 1, position] * beta)
except IndexError:
pass
return data
```

```
def rsi(data, lookback, close, position):
data = add_column(data, 5)
for i in range(len(data)):
data[i, position] = data[i, close] - data[i - 1, close]
for i in range(len(data)):
if data[i, position] > 0:
data[i, position + 1] = data[i, position]
elif data[i, position] < 0:
data[i, position + 2] = abs(data[i, position])
data = smoothed_ma(data, 2, lookback, position + 1, position + 3)
data = smoothed_ma(data, 2, lookback, position + 2, position + 4)
```

```
data[:, position + 5] = data[:, position + 3] / data[:, position + 4]
data[:, position + 6] = (100 - (100 / (1 + data[:, position + 5])))
```

```
data = delete_column(data, position, 6)
data = delete_row(data, lookback)
```

`return data`

Make sure to focus on the concepts and not the code. You can find the codes of most of my strategies in my books. The most important thing is to comprehend the techniques and strategies.

### The Average True Range Indicator

We sometimes measure volatility using the Average True Range. Although the ATR is considered a lagging indicator, it gives some insights as to where volatility is right now and where has it been last period (day, week, month, etc.). But before that, we should understand how the **True Range** is calculated (the ATR is just the average of that calculation).

The true range is simply the greatest of the three price differences:

**High — Low****| High — Previous close |****| Previous close — Low |**

Once we have gotten the maximum out of the above three, we simply take an average of n periods of the true ranges to get the Average True Range. Generally, since in periods of panic and price depreciation we see volatility go up, the ATR will most likely trend higher during these periods, similarly in times of steady uptrends or downtrends, the ATR will tend to go lower.

One should always remember that this indicator is lagging and therefore has to be used with extreme caution. Below is the function code that calculates the ATR. Make sure you have an OHLC array of historical data.

```
def atr(Data, lookback, high, low, close, where, genre = 'Smoothed'):
# Adding the required columns
Data = adder(Data, 1)
# 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
if genre == 'Smoothed':
# Average True Range Calculation
Data = ema(Data, 2, lookback, where, where + 1)
if genre == 'Simple':
# Average True Range Calculation
Data = ma(Data, lookback, where, where + 1)
# Cleaning
Data = deleter(Data, where, 1)
Data = jump(Data, lookback)
```

`return Data`

### The RSI/ATR Indicator

The idea is to divide the values of the RSI by the ATR so that we find a measure adjusted by the recent volatility. However, by doing so, we will find unbounded values, which is why we will apply the RSI formula on the values we find. Therefore, to calculate the RSI/ATR indicator, we follow these steps:

**Calculate a 14-period RSI on the market price.****Calculate a 14-period ATR on the market price.****Divide the RSI by the ATR values.****Calculate a 14-period RSI on the results from the last step.**

```
lookback = 14
upper_barrier = 70
lower_barrier = 30
```

```
# Calculating a 14-period RSI
my_data = rsi(my_data, lookback, 3, 4)
```

```
# Calculating a 14-period ATR
my_data = atr(my_data, lookback, 1, 2, 3, 5)
```

```
# Adding a few empty columns
my_data = adder(my_data, 10)
```

```
# Dividing the RSI by the ATR
my_data[:, 6] = my_data[:, 4] / my_data[:, 5]
```

```
# Calculating the RSI on the values from the last step
my_data = rsi(my_data, lookback, 6, 7)
```

```
# Cleaning
my_data = deleter(my_data, 4, 3)
```

The RSI/ATR resembles the regular RSI but takes into account some volatility measures. It is of course not a perfect indicator nor is it proven that it is better than the RSI but it is very optimizable as it has more variables and is an uncharted territory.

```
def signal(Data, rsi_col, buy, sell):
Data = adder(Data, 10)
for i in range(len(Data)):
if Data[i, rsi_col] <= lower_barrier and Data[i - 1, buy] == 0 and Data[i - 2, buy] == 0 and Data[i - 3, buy] == 0:
Data[i, buy] = 1
elif Data[i, rsi_col] >= upper_barrier and Data[i - 1, sell] == 0 and Data[i - 2, sell] == 0 and Data[i - 3, sell] == 0:
Data[i, sell] = -1
return Data
```

`my_data = signal(my_data, 4, 6, 7)`

The signal charts show the trades taken whenever the 14-period RSI/ATR reaches 30 (For a long position) and 70 (For a short position).

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### Summary

To sum up, what I am trying to do is to simply contribute to the world of objective technical analysis which is promoting more transparent techniques and strategies that need to be back-tested before being implemented. This way, technical analysis will get rid of the bad reputation of being subjective and scientifically unfounded.

I recommend you always follow the the below steps whenever you come across a trading technique or strategy:

*Have a critical mindset and get rid of any emotions.**Back-test it using real life simulation and conditions.**If you find potential, try optimizing it and running a forward test.**Always include transaction costs and any slippage simulation in your tests.**Always include risk management and position sizing in your tests.*

Finally, even after making sure of the above, stay careful and monitor the strategy because market dynamics may shift and make the strategy unprofitable.