MaximumDrawdown.py

import numpy
import numpy.random as nrand


"""
Note - for some of the metrics the absolute value is returns. This is because if the risk (loss) is higher we want to
discount the expected excess return from the portfolio by a higher amount. Therefore risk should be positive.
"""


def dd(returns, tau):
    # Returns the draw-down given time period tau
    values = prices(returns, 100)
    pos = len(values) - 1
    pre = pos - tau
    drawdown = float('+inf')
    # Find the maximum drawdown given tau
    while pre >= 0:
        dd_i = (values[pos] / values[pre]) - 1
        if dd_i < drawdown:
            drawdown = dd_i
        pos, pre = pos - 1, pre - 1
    # Drawdown should be positive
    return abs(drawdown)
 
 
def max_dd(returns):
    # Returns the maximum draw-down for any tau in (0, T) where T is the length of the return series
    max_drawdown = float('-inf')
    for i in range(0, len(returns)):
        drawdown_i = dd(returns, i)
        if drawdown_i > max_drawdown:
            max_drawdown = drawdown_i
    # Max draw-down should be positive
    return abs(max_drawdown)
    

def average_dd(returns, periods):
    # Returns the average maximum drawdown over n periods
    drawdowns = []
    for i in range(0, len(returns)):
        drawdown_i = dd(returns, i)
        drawdowns.append(drawdown_i)
    drawdowns = sorted(drawdowns)
    total_dd = abs(drawdowns[0])
    for i in range(1, periods):
        total_dd += abs(drawdowns[i])
    return total_dd / periods


def average_dd_squared(returns, periods):
    # Returns the average maximum drawdown squared over n periods
    drawdowns = []
    for i in range(0, len(returns)):
        drawdown_i = math.pow(dd(returns, i), 2.0)
        drawdowns.append(drawdown_i)
    drawdowns = sorted(drawdowns)
    total_dd = abs(drawdowns[0])
    for i in range(1, periods):
        total_dd += abs(drawdowns[i])
    return total_dd / periods


# Example Usage
r = nrand.uniform(-1, 1, 50)
print("Drawdown(5) =", dd(r, 5))
print("Max Drawdown =", max_dd(r))