5 Performance Metrics for Trading Algorithms and Investment Portfolios

metrics.py

from blankly import Alpaca, CoinbasePro # supports stocks, crypto, and forex
import numpy as np
from math import sqrt


def cagr(start_value: float, end_value: float, years: int):
    return (end_value / start_value) ** (1.0 / years) - 1

def sharpe(account_values: np.array, risk_free_rate, annualize_coefficient):
    diff = np.diff(account_values, 1) / account_values[1:] # this gets our pct_return in the array
    # we'll get the mean and calculate everything
    # we multiply the mean of returns by the annualized coefficient and divide by annualized std
    annualized_std = diff.std() * sqrt(annualize_coefficient) 
    return (diff.mean() * annualize_coefficient - risk_free_rate) / annualized_std

def sortino(account_values: np.array, risk_free_rate, annualize_coefficient):
    diff = np.diff(account_values, 1) / account_values[1:]
    # we'll get the mean and calculate everything
    # remember, we're only using the negative returns 
    neg_returns = diff[diff < 0] 
    annualized_std = neg_returns.std() * sqrt(annualize_coefficient)
    return (diff.mean() * annualize_coefficient - risk_free_rate) / annualized_std

def value_at_risk(account_values, alpha: float):
    initial_value = account_values[0]
    returns = np.diff(account_values, 1) / account_values[1:]
    returns_sorted = np.sort(returns) # sort our returns (should be estimated normal)
    index = int(alpha * len(returns_sorted))
    return initial_value * abs(returns_sorted[index])

def max_drawdown(account_values):
    returns = account_values.diff(1) / account_values[1:]
    cumulative = (returns + 1).cumprod()
    peak = cumulative.expanding(min_periods=1).max()
    dd = (cumulative / peak) - 1
    return dd.min()

  
a = Alpaca() # initialize the Alpaca Exchange
def beta(returns, baseline='SPY', return_resolution='1m'):
    market_base_returns = a.interface.history(baseline, len(returns), resolution=return_resolution) # get the last X month bars of the baseline asset
    m = np.matrix([returns, market_base_returns])
    return np.cov(m)[0][1] / np.std(market_base_returns)