How to calculate MaximumDrawdown using Returns in Python

Question

I have DataFrame final with returns of my portfolio. I am trying to calculate the MaxDrawdown using the returns. I have tried the below code and did see many stackexchange questions. But not able to solve this. Is there any way possible to calculate the maximum draw down using returns of the portfolio.

              Returns
1/2/2009     0.030483579
1/5/2009     0.002872092
1/6/2009     0.01461333
1/7/2009    -0.032431836
1/8/2009     0.0055774
1/9/2009    -0.019844336
1/12/2009   -0.019705618
1/13/2009    0.001093185
1/14/2009   -0.032726765
1/15/2009    0.013635182
1/16/2009    0.009807648
1/20/2009   -0.044440252
1/21/2009    0.035156229
1/22/2009   -0.01460641
1/23/2009    0.007399468
1/26/2009    0.007910521
1/27/2009    0.007848472
1/28/2009    0.028944903
1/29/2009   -0.023816962
1/30/2009   -0.02550717
2/2/2009    -0.000292223
2/3/2009     0.020191091
2/4/2009    -7.93651E-06
2/5/2009     0.020070065
2/6/2009     0.026235957
2/9/2009    -0.001606124
2/10/2009   -0.03629415
2/11/2009    0.00248416
2/12/2009    0.001925152
2/13/2009   -0.00441840

Code:

cum_returns = (1 + final).cumprod()
drawdown =  1 - final.div(final.cummax())

Can anyone help me in solving this. Thanks!

BENY · Accepted Answer · 2018-09-27 15:00:25Z

6

IIUC after cumprod adding diff and min is the max-draw-down

(df.Returns+1).cumprod().diff().min()
Out[316]: -0.043177386133390616

Base on the MDD definition

s=(df.Returns+1).cumprod()
np.ptp(s)/s.max()
Out[319]: 0.11457761692384323

edited Sep 27, 2018 at 15:00

answered Sep 27, 2018 at 14:30

BENY

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3 Comments

Alex_MN Over a year ago

Thanks for the answer! How can a drawdown be negative?? Can you explain more in detail what the code is doing.

Alex_MN Over a year ago

THe calculation I think is drawdown rather than Maximum Drawdown . Correct me if I am wrong

Alex_MN Over a year ago

Thanks! SOlved my problem

Mabel Villalba · Accepted Answer · 2018-09-27 15:29:04Z

5

You can get a dataframe with the maximum drawdown up to the date using pandas.expanding()(doc) and then applying max to the window.

pandas.expanding will apply a function in the manner pandas.rolling does, but with a window that starts at the beginning of the dataframe and expands up to the current row (more info about the Window Functions here and pandas.expanding):

>> cum_returns = (1 + final).cumprod()
>> drawdown =  1 - final.div(final.cummax())
>> drawdown.expanding().max()

            Returns
1/2/2009   0.000000
1/5/2009   0.000000
1/6/2009   0.000000
1/7/2009   0.032432
1/8/2009   0.032432
1/9/2009   0.046343
1/12/2009  0.065136
1/13/2009  0.065136
1/14/2009  0.094742
1/15/2009  0.094742
1/16/2009  0.094742
1/20/2009  0.114578
1/21/2009  0.114578
1/22/2009  0.114578
1/23/2009  0.114578
1/26/2009  0.114578
1/27/2009  0.114578
1/28/2009  0.114578
1/29/2009  0.114578
1/30/2009  0.114578
2/2/2009   0.114578
2/3/2009   0.114578
2/4/2009   0.114578
2/5/2009   0.114578
2/6/2009   0.114578
2/9/2009   0.114578
2/10/2009  0.114578
2/11/2009  0.114578
2/12/2009  0.114578
2/13/2009  0.114578

Putting drawdowns and the Maximum Drawdown (MDD) together in a dataframe so you can compare the result:

>> df_dd =  pd.concat([drawdown, drawdown.expanding().max()], axis=1)

>> df_dd.columns = ['drawdown', 'MDD'] 

>> df_dd
           drawdown       MDD
1/2/2009   0.000000  0.000000
1/5/2009   0.000000  0.000000
1/6/2009   0.000000  0.000000
1/7/2009   0.032432  0.032432
1/8/2009   0.027035  0.032432
1/9/2009   0.046343  0.046343
1/12/2009  0.065136  0.065136
1/13/2009  0.064114  0.065136
1/14/2009  0.094742  0.094742
1/15/2009  0.082399  0.094742
1/16/2009  0.073399  0.094742
1/20/2009  0.114578  0.114578
1/21/2009  0.083450  0.114578
1/22/2009  0.096837  0.114578
1/23/2009  0.090154  0.114578
1/26/2009  0.082957  0.114578
1/27/2009  0.075759  0.114578
1/28/2009  0.049007  0.114578
1/29/2009  0.071657  0.114578
1/30/2009  0.095336  0.114578
2/2/2009   0.095601  0.114578
2/3/2009   0.077340  0.114578
2/4/2009   0.077347  0.114578
2/5/2009   0.058830  0.114578
2/6/2009   0.034137  0.114578
2/9/2009   0.035688  0.114578
2/10/2009  0.070687  0.114578
2/11/2009  0.068379  0.114578
2/12/2009  0.066585  0.114578
2/13/2009  0.070709  0.114578

edited Sep 27, 2018 at 15:29

answered Sep 27, 2018 at 14:56

Mabel Villalba

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3 Comments

Alex_MN Over a year ago

Can you explain more about the code. It is a bit unclear

Mabel Villalba Over a year ago

Added more comments. You have more info in the links.

Alex_MN Over a year ago

Thanks a lot @Alex_MN

Caio Castro · Accepted Answer · 2020-11-24 20:59:31Z

Assuming you already have a column with the cumulative return, it is pretty straight forward: you want to get the max value at any given point and compare it with the actual cumulative return of the rows occurring only after such point.

Then, if you take the the lowest value, you get the maximum drawdown of the array.

import pandas as import pd
import numpy as np

def max_drawdown(arr: pd.Series) -> int:
    return np.min(arr / arr.expanding().max()) - 1

In case you need to calculate the cumulative return first, using log makes it pretty straight forward:

import numpy as np

final['log_return'] = np.log(1 + final['Returns'])
final['log_cum_return'] = np.cumsum(final['log_return'])
final['cumulative_returns'] = np.expm1(final['log_cum_return'])

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