Sep 12 2023

Table of Contents

- Difficulty: ★☆☆☆☆
- Bollinger band consists mainly of the stock price moving average and its positive, and negative standard deviation. With the above three lines, we can draw the upper, lower, and middle bounds for determining when to long or short stocks.
- This article is revised from Bollinger Band Trading Strategy via TQuant Lab.

Bollinger Band is a technical indicator that John Bollinger invented in the 1980s. Bollinger Band consists of the concepts of statistics and moving averages. The moving Average(MA) is the average closing price of a past period. Usually, the period of MA in Bollinger Band is 20 days, and Standard Deviation(SD) is usually represented by σ in mathematical sign, which is used to evaluate the data’s degree of discrete*.*

Bollinger Band is composed of three tracks:

● The upper track：20 MA＋double standard deviation

● The middle track：20 MA

● The lower track：20 MA＋double standard deviation

The investment target price distribution during the long-term observation period will be Normal Distribution. According to statistics, there is a 95% probability that the price will present between μ − 2σ and μ + 2σ, which is also called a 95% Confidence Interval(CI). Bollinger Band is the technical indicator based on the theories above.

- When today`s close price touches the upper bound and currently holds the position, sell the asset tomorrow.
- When today`s close price touches the lower bound and the cash position is positive, buy the asset tomorrow.
- When today`s close price touches the lower bound, the cash position is positive, and the current close price is lower than the last buy price, buy the asset tomorrow.

This article uses Windows 11 as a system and jupyter notebook as an editor.

The backtesting time period is between 2021/04/01 to 2022/12/31, and we take AUO(2409) as an example.

```
import pandas as pd
import numpy as np
import tejapi
import os
import matplotlib.pyplot as plt
os.environ['TEJAPI_BASE'] = 'https://api.tej.com.tw'
os.environ['TEJAPI_KEY'] = 'Your Key'
os.environ['mdate'] = '20210401 20221231'
os.environ['ticker'] = '2409'
# 使用 ingest 將股價資料導入暫存，並且命名該股票組合 (bundle) 為 tquant
!zipline ingest -b tquant
from zipline.api import set_slippage, set_commission, set_benchmark, attach_pipeline, order, order_target, symbol, pipeline_output, record
from zipline.finance import commission, slippage
from zipline.data import bundles
from zipline import run_algorithm
from zipline.pipeline import Pipeline
from zipline.pipeline.filters import StaticAssets
from zipline.pipeline.factors import BollingerBands
from zipline.pipeline.data import EquityPricing
```

`Pipeline()`

enables users to quickly process multiple assets’ trading-related data. In today`s article, we use it to process:

- Upper bound for Bollinger Bands in 20 days duration.
- Middle bound for Bollinger Bands in 20 days duration.
- Lower bound for Bollinger Bands in 20 days duration.
- Current close price.

```
def make_pipeline():
perf = BollingerBands(inputs=[EquityPricing.close], window_length=20, k=2)
upper,middle,lower = perf.upper,perf.middle, perf.lower
curr_price = EquityPricing.close.latest
return Pipeline(
columns = {
'upper': upper,
'middle': middle,
'lower': lower,
'curr_price':curr_price
}
)
```

`Initialize()`

enables users to set up the trading environment at the beginning of the backtest period. In this article, we set up :

- Slippage
- Commission
- Set the return of buying and holding AUO as the benchmark
- Attach
`Pipline()`

function into backtesting. - Set
`context.last_signal_price`

to record the last buy price

```
def initialize(context):
context.last_buy_price = 0
set_slippage(slippage.VolumeShareSlippage())
set_commission(commission.PerShare(cost=0.00285))
set_benchmark(symbol('2409'))
attach_pipeline(make_pipeline(), 'mystrategy')
context.last_signal_price = 0
```

`handle_data()`

is used to process data and make orders daily.

```
def handle_data(context, data):
out_dir = pipeline_output('mystrategy') # 取得每天 pipeline 的布林通道上中下軌
for i in out_dir.index:
upper = out_dir.loc[i, 'upper']
middle = out_dir.loc[i, 'middle']
lower = out_dir.loc[i, 'lower']
curr_price = out_dir.loc[i, 'curr_price']
cash_position = context.portfolio.cash
stock_position = context.portfolio.positions[i].amount
buy, sell = False, False
record(price = curr_price, upper = upper, lower = lower, buy = buy, sell = sell)
if stock_position == 0:
if (curr_price <= lower) and (cash_position >= curr_price * 1000):
order(i, 1000)
context.last_signal_price = curr_price
buy = True
record(buy = buy)
elif stock_position > 0:
if (curr_price <= lower) and (curr_price <= context.last_signal_price) and (cash_position >= curr_price * 1000):
order(i, 1000)
context.last_signal_price = curr_price
buy = True
record(buy = buy)
elif (curr_price >= upper):
order_target(i, 0)
context.last_signal_price = 0
sell = True
record(sell = sell)
else:
pass
else:
pass
```

Here, we apply `matplotlib.pyplot`

for the trading signals and the portfolio value visualization.

```
def analyze(context, perf):
fig = plt.figure()
ax1 = fig.add_subplot(211)
perf.portfolio_value.plot(ax=ax1)
ax1.set_ylabel("Portfolio value (NTD)")
ax2 = fig.add_subplot(212)
ax2.set_ylabel("Price (NTD)")
perf.price.plot(ax=ax2)
perf.upper.plot(ax=ax2)
perf.lower.plot(ax=ax2)
ax2.plot( # 繪製買入訊號
perf.index[perf.buy],
perf.loc[perf.buy, 'price'],
'^',
markersize=5,
color='red'
)
ax2.plot( # 繪製賣出訊號
perf.index[perf.sell],
perf.loc[perf.sell, 'price'],
'v',
markersize=5,
color='green'
)
plt.legend(loc=0)
plt.gcf().set_size_inches(18,8)
plt.show()
```

Via `run_algorithm()`

, we can execute the strategy we just built. The backtesting time period is set between 2021-06-01 to 2022-12-31. The data bundle we use is *tquant*. We assume the initial capital base is 500,000. The output of `run_algorithm()`

, which is *result*s, contains information on daily performance and trading receipts.

By observing the following graph, one can discover that there is an upper trend between 2021/11 to 2021/12. Since the close prices were not able to hit the lower bound, there was no buying transaction in this time period. And that made us fail to earn a profit.

The same issue has happened in the continuously lower trend. A sharp lower trend occurred in 2022-04, which led to consistently touching the lower bound. That means we have bought a bunch of stocks in this time zone. However, after the price recovered shortly, the close price touched the upper bound immediately. As a result, we sell the holding positions and earn a net loss during this time period.

As a matter of fact, due to the latency of 20 days Bollinger band, the band has difficulty reflecting the short-term high volatility price movement. If your target asset is more volatile, we suggested shortening the duration of the Bollinger band or adding trend-related indicators to fine-tune your strategy.

```
results = run_algorithm(
start = pd.Timestamp('2021-06-01', tz='UTC'),
end = pd.Timestamp('2022-12-31', tz ='UTC'),
initialize=initialize,
bundle='tquant',
analyze=analyze,
capital_base=5e5,
handle_data = handle_data
)
results
```

Then, we used `Pyfolio `

module which came with TQuant Lab to analyze strategy`s performance and risk. First, we use `extract_rets_pos_txn_from_zipline()`

to calculate returns, positions, and trading records.

```
import pyfolio as pf
returns, positions, transactions = pf.utils.extract_rets_pos_txn_from_zipline(results)
```

Calculating daily portfolio return.

- Equity(0 [2406]): AUO
- Cash

- sid: index
- symbol: ticker symbol
- price: buy/sell price
- order_id: order number
- amount: trading amount
- commission: commission cost
- dt: trading date
- txn_dollar: trading dollar volume

```
benchmark_rets = results['benchmark_return']
pf.plotting.plot_rolling_returns(returns, factor_returns=benchmark_rets)
```

With `show_perf_stats()`

, one can easily showcase the performance and risk analysis table.

```
pf.plotting.show_perf_stats(
returns,
benchmark_rets,
positions=positions,
transactions=transactions)
```

From late 2021 to 2022, the stock price of AUO is clearly in a downward spiral. if choosing buy and hold strategy, the accumulated return would turn out to be a horrible -40% to -50%. On the contrary, with Bollinger band strategy, the performance is way better than the buy and hold strategy.

However, the pure Bollinger Bands strategy tends to have the disadvantage of exiting prematurely during the rebound phase after a significant downward trend and the predicament of entering very rarely during the upward phase. Therefore, for stocks with significant price fluctuations, it is recommended to use other indicators to assess trend strength and optimize their strategy.

Please note that this strategy and the underlying assets are for reference only and do not constitute any recommendations for commodities or investments. In the future, we will also introduce the use of TEJ database to construct various indicators and backtest indicator performance. So, readers interested in various trading backtesting can choose relevant solutions from TEJ E-Shop to build their own trading strategies with high-quality databases.

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