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import math
import os
import pandas as pd
import feather
from index_data import index_returns, get_index_quotes
from arch import arch_model
from math import log, exp, sqrt
import numpy as np
from scipy.optimize import minimize_scalar
from statsmodels.tsa.ar_model import AR
import matplotlib.pyplot as plt
def calc_returns():
returns = index_returns(index=['IG', 'HY'], tenor='5yr')
returns_hy = (returns.
xs('HY', level=1).
dropna().
reset_index(level='series').
groupby(level=['date']).
nth(-1))
returns_hy = returns_hy.set_index('series', append=True)
returns_ig = returns.xs('IG', level=1).reset_index('tenor', drop=True)
# hy starts trading later than ig, so we line it up based on hy series
df = pd.merge(returns_hy, returns_ig, left_index=True, right_index=True,
suffixes=('_hy','_ig'))
returns = df[['price_return_hy', 'price_return_ig']]
returns.columns = ['hy', 'ig']
#feather.write_dataframe(returns.reset_index(),
# os.path.join(os.environ["DATA_DIR"], "index_returns.fth"))
return returns.reset_index('series', drop=True)
def calc_betas(returns=None, spans=[5, 20]):
if returns is None:
returns = calc_returns()
return [(returns.
ewm(span=span).
cov().
groupby(level='date').
apply(lambda df: df.values[0,1]/df.values[1,1])) for span in spans]
def plot_betas(betas=None):
spans = [5, 20]
if betas is None:
betas = calc_betas(spans)
for beta, span in zip(betas, spans):
plt.plot(beta, label = 'EWMA'+str(span))
plt.xlabel('date')
plt.ylabel('beta')
plt.legend()
def calc_realized_vol(returns=None):
# three ways of computing the volatility
# 1) 20 days simple moving average
# 2) exponentially weighted moving average
# 3) GARCH(1,1), we scale returns by 10 to help with the fitting
if returns is None:
returns = calc_returns()
vol_sma = returns.rolling(20).std() * math.sqrt(252)
vol_ewma = returns.ewm(span=20).std() * math.sqrt(252)
scale = 10
vol_garch = pd.DataFrame()
for index in returns:
am = arch_model(scale * returns[index].dropna())
res = am.fit()
vol_garch[index] = res.conditional_volatility * math.sqrt(252)/scale
vol = pd.concat([vol_sma, vol_ewma, vol_garch], axis=1, keys=['sma', 'ewma', 'garch'])
return vol
#feather.write_dataframe(beta_ewma.to_frame('beta'),
# os.path.join(os.environ['DATA_DIR'], "beta.fth"))
def spreads_ratio(series=list(range(22, 29)), index=['IG', 'HY'], tenor='5yr'):
df = get_index_quotes(series=series, index=index, tenor=tenor)
df = df['modelspread'].groupby(['date', 'index']).last().unstack()
df['ratio'] = df.HY / df.IG
return df
def loglik(beta, returns):
x = (returns.hy - beta*returns.ig)
model = AR(x, missing='drop')
fit = model.fit(maxlag=1)
return - fit.llf
if __name__ == "__main__":
returns = calc_returns()
betas = calc_betas(returns)
plot_betas(betas)
vol = calc_realized_vol(returns)
ratios = spreads_ratio()
prog = minimize_scalar(loglik, bracket=(3, 5), args=(returns,))
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