#!/usr/bin/env python
# coding: utf-8

# # Drawdowns: Magnitudes and Frequencies
# 
# This will be an analysis of the market drawdowns from an empirical perspective, using daily data for the past 24 years.
# 
# I will be focusing on the daily returns of the S&P500 index from January 1993 onwards.
# 
# The focus on drawdowns is because its is a far more visceral measure of risk than the standard deviation, it's the negative outcome that the investor fundamentally cares about.
# 

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get_ipython().run_line_magic('matplotlib', 'inline')
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import math


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df = pd.read_csv("SP500.csv")


# Taking a peek, we find the following 

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df.head()


# Get log returns.

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df["log_returns"] = np.log(df["Adj Close"]).diff()
df["log_returns"][0] = 0


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df.head()


# Now we can define drawdown

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def drawdown(returns):
    out = []
    cum_returns = [0]
    for i in range(len(returns)):
        cum_returns.append(cum_returns[-1] + returns[i])
        out.append(max(cum_returns)-cum_returns[-1])
    return out


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def max_drawdown(drawdowns):
    out = []
    for i in range(len(drawdowns)+1):
        out.append(max(drawdowns[:i+1]))
    return out[:-1]


# Lets try it out with some fake data

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print(max_drawdown(drawdown([0.05, 0.001, -0.10, 0.002])))
print(drawdown([0.05, 0.001, -0.10, 0.002]))


# We can get now get drawdown magnitudes from our returns data

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df["drawdown"] = drawdown(df["log_returns"])
df["maxdrawdown"] = max_drawdown(df["drawdown"])


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df.head()


# Lets have a look at our data

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fig, ax = plt.subplots(3)
ax[0].hist(df["log_returns"], bins="auto", normed=True)
ax[0].set_title("Returns")
ax[1].hist(df["drawdown"], bins="auto", normed=True)
ax[1].set_title("Drawdown")
ax[2].hist(df["maxdrawdown"], bins="auto", normed=True)
ax[2].set_title("Maximum Drawdown")
plt.tight_layout(pad=0.4, w_pad=0.5, h_pad=1.0)
plt.show()


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def print_moments(data):
    print("Mean: {}".format(data.mean()))
    print("Variance: {}".format(data.var()))
    print("Skewness: {}".format(data.skew()))
    print("Kurtosis: {}".format(data.kurt()))
    


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print_moments(df["log_returns"])


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print_moments(df["drawdown"])


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print_moments(df["maxdrawdown"])


# Now plotting as timeseries, several variables of interest

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df.plot(x='Date', y='maxdrawdown')


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df.plot(x='Date', y='log_returns')


# Here we can see that large drawdown spikes happen in 2001 and 2008, corresponding to the tech and the housing bubble

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df.plot(x='Date', y='drawdown')


# Return multiple over the period

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math.pow(1 + df["log_returns"].mean(), len(df["log_returns"]))


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df["Adj Close"].iloc[-1]/df["Adj Close"].iloc[0]


# Omniscient Return over the period

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df["abs"] = df["log_returns"].map(math.fabs)
print(df["abs"].mean())
math.pow(1+ df["abs"].mean(), len(df["abs"]))


# A buy and hold position, yields a 9.5X multiple over the 25 year period.
# 
# While an omniscient market timer who is long before every up day
# and short before ever down day yields a 
# 9.7*10^20  multiple over the 25 year period.
# 
# 

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