quiz_kit.py

import pandas as pd
import numpy as np
from scipy.optimize import minimize
from scipy.stats import norm

def get_hfi_returns():
    """
    Load and format 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 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)/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 annualize_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 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


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 a Series or DataFrame")



def var_gaussian(r, level=5, modified=False):
    """
    Returns the Parametric Gauusian 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(level/100)
    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 portfolio_return(weights, returns):
    """
    Computes the return on a portfolio from constituent returns and weights
    weights are a numpy array or Nx1 matrix and returns are a numpy array or Nx1 matrix
    """
    return weights.T @ returns


def portfolio_vol(weights, covmat):
    """
    Computes the vol of a portfolio from a covariance matrix and constituent weights
    weights are a numpy array or N x 1 maxtrix and covmat is an N x N matrix
    """
    return (weights.T @ covmat @ weights)**0.5


def msr(riskfree_rate, er, cov):
    """
    Returns the weights of the portfolio that gives you the maximum sharpe ratio
    given the riskfree rate and expected returns and a covariance matrix
    """
    n = er.shape[0]
    init_guess = np.repeat(1 / n, n)
    bounds = ((0.0, 1.0),) * n  # an N-tuple of 2-tuples!
    # construct the constraints
    weights_sum_to_1 = {'type': 'eq',
                        'fun': lambda weights: np.sum(weights) - 1
                        }

    def neg_sharpe(weights, riskfree_rate, er, cov):
        """
        Returns the negative of the sharpe ratio
        of the given portfolio
        """
        r = portfolio_return(weights, er)
        vol = portfolio_vol(weights, cov)
        return -(r - riskfree_rate) / vol

    weights = minimize(neg_sharpe, init_guess,
                       args=(riskfree_rate, er, cov), method='SLSQP',
                       options={'disp': False},
                       constraints=(weights_sum_to_1,),
                       bounds=bounds)
    return weights.x

def gmv(cov):
    """
    Returns the weights of the Global Minimum Volatility portfolio
    given a covariance matrix
    """
    n = cov.shape[0]
    return msr(0, np.repeat(1, n), cov)