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edhec_risk_kit.py
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edhec_risk_kit.py
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import pandas as pd
def drawdown(return_series: pd.Series):
"""
Takes a times series of asset returns
Computes and returns a DataFrame that contains:
the wealth index
the previous peak
percent drawdowns
"""
wealth_index = 1000 * (1 + return_series).cumprod()
previous_peaks = wealth_index.cummax()
drawdowns = (wealth_index - previous_peaks) / previous_peaks
return pd.DataFrame({
"Wealth": wealth_index,
"Peaks": previous_peaks,
"Drawdown": drawdowns
})
def get_ffme_returns():
"""
Load the Famma-French Dataset for the returns of the Top and Bottom Deciles by MarketCap
"""
me_me = pd.read_csv("data/Portfolios_Formed_on_ME_monthly_EW.csv", header=0, index_col=0, na_values=-99.99)
rets = me_m[['Lo 10', 'Hi 10']]
rets.columns = ['SmallCap', 'LargeCap']
rets = rets / 100
rets.index = pd.to_datetime(rets.index, format='%Y%m').to_period('M')
return rets
def get_hfi_returns():
"""
Load the EDHEC Hedge Fund Index Returns
"""
hfi = pd.read_csv("data/edhec-hedgefundindices.csv", header=0, index_col=0, parse_dates=True)
hfi = hfi / 100
hfi.index = hfi.index.to_period('M')
return hfi
def skewness(r):
"""
Alternative to scipy.stats.skew()
Computes the skewness of the supplied Series or DataFrame
Returns a float or a Series
"""
demeaned_r = r - r.mean()
# use the population standard deviation, so set dof=0
sigma_r = r.std(ddof=0)
exp = (demeaned_r ** 3).mean()
return exp / sigma_r ** 3
def kurtosis(r):
"""
Alternative to scipy.stats.kurtosis()
Computes the kurtosis of the supplied Series or DataFrame
Returns a float or a Series
"""
demeaned_r = r - r.mean()
# use the population standard deviation, so set dof=0
sigma_r = r.std(ddof=0)
exp = (demeaned_r ** 4).mean()
return exp / sigma_r ** 4
import scipy as sp
def is_normal(r, level=0.01):
"""
Applies the Jarque-Bera test to determine if a Series is normal or not
Test is applied at the 1% level by default
Returns True if the hypothesis of normality is accepted, False otherwise
"""
statistic, p_value = sp.stats.jarque_bera(r)
return p_value > level
def semideviation(r):
"""
Returns the semideviation aka negative semideviation of r
r must be a Series or a DataFrame
"""
is_negative = r < 0
return r[is_negative].std(ddof=0)
import pandas as pd
import numpy as np
def var_historic(r, level=5):
"""
Returns the historic Value at Risk at a specified level
i.e. returns the number such that "level" percent of the returns
fall below that number, and the (100 - level) percent are above
"""
if isinstance(r, pd.DataFrame):
return r.aggregate(var_historic, level=level)
elif isinstance(r, pd.Series):
return -np.percentile(r, level)
else:
raise TypeError("Expected r to be Series or DataFrame")
from scipy.stats import norm
def var_gaussian(r, level=5, modified=False):
"""
Returns the Parametric Gaussion VaR of a Series or DataFrame
If "modified" is True, then the modified VaR is returned,
using the Cornish-Fisher modification
"""
# compute the Z score assuming it was Gaussian
z = norm.ppf(.05)
if modified:
# modify the Z score based on observed skewness and kurtosis
s = skewness(r)
k = kurtosis(r)
z = (z +
(z**2 - 1) * s / 6 +
(z**3 - 3 * z) * (k - 3) / 24 -
(2 * z**3 - 5 * z) * (s**2) / 36
)
return -(r.mean() + z*r.std(ddof=0))
def cvar_historic(r, level=5):
"""
Compute the Conditional VaR of Series or DataFrame
"""
if isinstance(r, pd.DataFrame):
return r.aggregate(cvar_historic, level=level)
elif isinstance(r, pd.Series):
is_beyond = r <= -var_historic(r, level=level)
return -r[is_beyond].mean()
else:
raise TypeError("Expected r to be a Series or DataFrame")
def semideviation3(r):
"""
Returns the semideviation aka negative semideviation of r
r must be a Series or a DataFrame, else raises a TypeError
"""
excess= r-r.mean() # We demean the returns
excess_negative = excess[excess<0] # We take only the returns below the mean
excess_negative_square = excess_negative**2 # We square the demeaned returns below the mean
n_negative = (excess<0).sum() # number of returns under the mean
return (excess_negative_square.sum()/n_negative)**0.5 # semideviation
def get_annualized_volatility(r):
"""
Calculate annualized volatility for the given returns
"""
annualized_vol = r.std() * np.sqrt(12)
return annualized_vol
def get_annualized_return(r):
"""
Calculate annualized return for the given returns
"""
n_months = r.shape[0]
return_per_month = (r + 1).prod() ** (1 / n_months) - 1
annualized_return = (return_per_month + 1) ** 12 - 1
return annualized_return
def get_ind_returns():
"""
Load and format the Ken French 30 Industry Portfolios Value Weighted Monthly Returns
"""
ind = pd.read_csv("data/ind30_m_vw_rets.csv", header=0, index_col=0, parse_dates=True) / 100
ind.index = pd.to_datetime(ind.index, format='%Y%m').to_period('M')
ind.columns = ind.columns.str.strip()
return ind
def annualize_rets(r, periods_per_year):
"""
Annualizes a set of returns
We should infer the periods per year
but that is currently left as an exercise
to the reader :-)
"""
compounded_growth = (1 + r).prod()
n_periods = r.shape[0]
return compounded_growth ** (periods_per_year / n_periods) - 1
def annualized_vol(r, periods_per_year):
"""
Annualizes the vol of a set of returns
We should infer the periods per year
but that is currently left as an exercise
to the reader :-)
"""
return r.std() * (periods_per_year ** 0.5)
def sharpe_ratio(r, riskfree_rate, periods_per_year):
"""
Computes the annualized sharpe ratio of a set of returns
"""
# convert the annual riskfree rate to per period
rf_per_period = (1 + riskfree_rate) ** (1 / periods_per_year) - 1
excess_ret = r - rf_per_period
ann_ex_ret = annualize_rets(excess_ret, periods_per_year)
ann_vol = annualized_vol(r, periods_per_year)
return ann_ex_ret / ann_vol
def portfolio_return(weights, returns):
"""
Weights -> Returns
"""
return weights.T @ returns
def portfolio_vol(weights, covmat):
"""
Weights -> Vol
"""
return (weights.T @ covmat @ weights) ** 0.5
def plot_ef2(n_points, er, cov, style=".-"):
"""
Plots the 2-asset efficient frontier
"""
if er.shape[0] != 2 or cov.shape[0] != 2:
raise ValueError("plot_ef2 can only plot 2-asset frontiers")
weights = [np.array([w, 1 - w]) for w in np.linspace(0, 1, n_points)]
rets = [portfolio_return(w, er) for w in weights]
vols = [portfolio_vol(w, cov) for w in weights]
ef = pd.DataFrame({
"Returns": rets,
"Volatility": vols
})
return ef.plot.line(x="Volatility", y="Returns", style=style)
def minimize_vol(target_return, er, cov):
"""
target return -> W
"""
n = er.shape[0]
init_guess = np.repeat(1/n, n)
bounds = ((0.0, 1.0),) * n
return_is_target = {
'type': 'eq',
'args': (er,),
'fun': lambda w, er: target_return - portfolio_return(w, er)
}
weights_sum_to_1 = {
'type': 'eq',
'fun': lambda w: np.sum(w) - 1
}
results = sp.optimize.minimize(portfolio_vol,
init_guess,
args=(cov,),
method="SLSQP",
options={'disp': False},
constraints=(return_is_target, weights_sum_to_1),
bounds=bounds
)
return results.x
def optimal_weights(n_points, er, cov):
"""
-> list of weights to run the optimizer on to minimize the vol
"""
target_rs = np.linspace(er.min(), er.max(), n_points)
weights = [minimize_vol(target_return, er, cov) for target_return in target_rs]
return weights
def msr(riskfree_rate, er, cov):
"""
RiskFree rate + ER + COV -> W
"""
n = er.shape[0]
init_guess = np.repeat(1/n, n)
bounds = ((0.0, 1.0),) * n
weights_sum_to_1 = {
'type': 'eq',
'fun': lambda w: np.sum(w) - 1
}
def neg_sharpe_ratio(weights, riskfree_rate, er, cov):
"""
Returns the negative of the sharpe ratio, given weights
"""
r = portfolio_return(weights, er)
vol = portfolio_vol(weights, cov)
return -(r - riskfree_rate) / vol
results = sp.optimize.minimize(neg_sharpe_ratio,
init_guess,
args=(riskfree_rate, er, cov,),
method="SLSQP",
options={'disp': False},
constraints=(weights_sum_to_1),
bounds=bounds
)
return results.x
def gmv(cov):
"""
Return the weight of the Global Minimum Vol (Variance) portfolio
give the covariance matrix
"""
n = cov.shape[0]
return msr(0, np.repeat(1, n), cov)
def plot_ef(n_points, er, cov, show_cml=False, style='.-', riskfree_rate=0, show_ew=False, show_gmv=False):
"""
Plots the N-asset efficient frontier
show_cml - show capital-market line
show_ew - show equally-weighted portfolio
show_gmv - show global minimum variance portfolio
"""
weights = optimal_weights(n_points, er, cov)
rets = [portfolio_return(w, er) for w in weights]
vols = [portfolio_vol(w, cov) for w in weights]
ef = pd.DataFrame({
"Returns": rets,
"Volatility": vols
})
ax = ef.plot.line(x="Volatility", y="Returns", style=style)
if show_ew:
n = er.shape[0]
w_ew = np.repeat(1/n, n)
r_ew = portfolio_return(w_ew, er)
vol_ew = portfolio_vol(w_ew, cov)
# display EW
ax.plot([vol_ew], [r_ew], color="goldenrod", marker='o', markersize=12)
if show_ew:
w_gmv = gmv(cov)
r_gmv = portfolio_return(w_gmv, er)
vol_gmv = portfolio_vol(w_gmv, cov)
# display GMV
ax.plot([vol_gmv], [r_gmv], color="midnightblue", marker='o', markersize=10)
if show_cml:
ax.set_xlim(left = 0)
w_msr = msr(riskfree_rate, er, cov)
r_msr = portfolio_return(w_msr, er)
vol_msr = portfolio_vol(w_msr, cov)
# Add CML
cml_x = [0, vol_msr]
cml_y = [riskfree_rate, r_msr]
ax.plot(cml_x, cml_y, color="green", marker='o', linestyle='dashed', markersize=12, linewidth=2)
return ax