Algorithms

[miron]

Algorithms used in Algorithmic Trading

• A* Search
• Simple Moving Average (SMA) Momentum Trading or Trend following: When moving average 50 falls below moving average of 200, sell (and short futures), otherwise, buy and go long.

  
  import pandas as pd  
  import numpy as np
  pd.DataFrame.rolling(window = 7, min_periods = 7).mean()
  pd.DataFrame.rolling(window = 25).mean()
  pd.DataFrame.rolling(window = 99).mean()

```python
# Common Movin Averages:
price.rolling(window = 50)
price.rolling(window = 200)

price.rolling(window = 5)
price.rolling(window = 10)
price.rolling(window = 20)
price.rolling(window = 100)

# Fibonacci:
price.rolling(window =  (5, 8, 13, 21 ...) )

month_ret = pd.DataFrame.resample('M', kind = 'period').last().pct_change().dropna()
for years in [1, 3, 5, 10, 20]:
      # Anualized Mean Returns For Last ... Years.
      pd.DataFrame['month_ret'].rolling(years * 12).mean() * 12 
      # Anualized Risk For Last ... Years.
      pd.DataFrame['month_ret'].rolling(years * 12).std() * np.sqrt(12) 

• Exponential Moving Average (EMA) reacts faster to recent price changes Typical short term are 12 and 26 days, long term 50 and 200 days

  price.ewm(span = 10, min_periods= 10).mean()

• Double Exponential Moving Average (DEMA) DEMA = 2*EMA - EMA(EMA)
• Expanding Windows Fixed lower bound Mean of price up to this point in time

  price.expanding().mean()

• Correlation

  returns.corr()

• Rolling Correlation

  returns['BTC'].rolling(36).corr(returns['ETH'])

  Logarithmic Returns

  mean_log_ret =  np.log(df / df.shift(1)).dropna().mean()

  I.e. price is 130, 110, 120, 90, 80:

returns are -15%, 9%, -25%, -11% mean: -12.13%

# Actual Price
investment * np.exp(periods * mean_log_ret) 

130 np.exp(4-0.1213) = 80

Geometric Average

[(1+R1)(1+R2 )(1+R3)…*(1+Rn)]**(1/n)-1 where: R=Return n=Count of the numbers in the series

I.e. returns are respectively 30%, 10%, 20%, -10%, and -80%

(1.3 *1.1 * 1.2 * 0.9 * 0.8)**(1/5)-1

The geometric average annual return == 4.3%

Other Statistic Measures

• Confidence Interval https://en.wikipedia.org/wiki/Confidence_interval