Start, End and Duration of Maximum Drawdown in Pyt

Question

Given a time series, I want to calculate the maximum drawdown, and I also want to locate the beginning and end points of the maximum drawdown so I can calculate the duration. I want to mark the beginning and end of the drawdown on a plot of the timeseries like this:

a busy cat http://oi61.tinypic.com/r9h4er.jpg

So far I've got code to generate a random time series, and I've got code to calculate the max drawdown. If anyone knows how to identify the places where the drawdown begins and ends, I'd really appreciate it!

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

# create random walk which I want to calculate maximum drawdown for:

T = 50
mu = 0.05
sigma = 0.2
S0 = 20
dt = 0.01
N = round(T/dt)
t = np.linspace(0, T, N)
W = np.random.standard_normal(size = N) 
W = np.cumsum(W)*np.sqrt(dt) ### standard brownian motion ###
X = (mu-0.5*sigma**2)*t + sigma*W 

S = S0*np.exp(X) ### geometric brownian motion ###
plt.plot(S)

# Max drawdown function      

def max_drawdown(X):
    mdd = 0
    peak = X[0]
    for x in X:
        if x > peak: 
            peak = x
        dd = (peak - x) / peak
        if dd > mdd:
            mdd = dd
    return mdd    

drawSeries = max_drawdown(S)
MaxDD = abs(drawSeries.min()*100)
print MaxDD


plt.show()

Answer 1

on the back of this I added unerwater analysis if that helps anyone...

def drawdowns(equity_curve):
    i = np.argmax(np.maximum.accumulate(equity_curve.values) - equity_curve.values) # end of the period
    j = np.argmax(equity_curve.values[:i]) # start of period

    drawdown=abs(100.0*(equity_curve[i]-equity_curve[j]))

    DT=equity_curve.index.values

    start_dt=pd.to_datetime(str(DT[j]))
    MDD_start=start_dt.strftime ("%Y-%m-%d") 

    end_dt=pd.to_datetime(str(DT[i]))
    MDD_end=end_dt.strftime ("%Y-%m-%d") 

    NOW=pd.to_datetime(str(DT[-1]))
    NOW=NOW.strftime ("%Y-%m-%d")

    MDD_duration=np.busday_count(MDD_start, MDD_end)

    try:
        UW_dt=equity_curve[i:].loc[equity_curve[i:].values>=equity_curve[j]].index.values[0]
        UW_dt=pd.to_datetime(str(UW_dt))
        UW_dt=UW_dt.strftime ("%Y-%m-%d")
        UW_duration=np.busday_count(MDD_end, UW_dt)
    except:
        UW_dt="0000-00-00"
        UW_duration=np.busday_count(MDD_end, NOW)

    return MDD_start, MDD_end, MDD_duration, drawdown, UW_dt, UW_duration

Answer 2

Just find out where running maximum minus current value is largest:

n = 1000
xs = np.random.randn(n).cumsum()
i = np.argmax(np.maximum.accumulate(xs) - xs) # end of the period
j = np.argmax(xs[:i]) # start of period

plt.plot(xs)
plt.plot([i, j], [xs[i], xs[j]], 'o', color='Red', markersize=10)

Answer 3

Your max_drawdown already keeps track of the peak location. Modify the if to also store the end location mdd_end when it stores mdd, and return mdd, peak, mdd_end.