modulus.py

import pandas as pd
import numpy as np


def get_drdown(data):
    '''
    

    Parameters
    ----------
    data : TYPE series
        DESCRIPTION.

    Returns dataframe
    -------
    df : TYPE
        DESCRIPTION.

    '''
    import pandas as pd
    wealth_index=1000*(1+data).cumprod()
    previous_peak=wealth_index.cummax()
    drawdown=(wealth_index-previous_peak)/previous_peak
    dict={"wealth":wealth_index, "previous_high":previous_peak, "Drawdown":drawdown}
    df=pd.DataFrame(dict)
    return df
    
def get_hfi_returns():
    import pandas as pd 
    X=pd.read_csv("E:/pfconstdata/data/edhec-hedgefundindices.csv", header=0, index_col=0, parse_dates=True,
                 na_values=-99.99)
    X=X/100
    X.index=X.index.to_period("M")
    return X

def skewness(r):
    demeaned_r=r-r.mean()
    sigma=r.std(ddof=0)
    exp=(demeaned_r**3).mean()
    return exp/sigma**3

def kurtosis(r):
    demeaned_r=r-r.mean()
    sigma=r.std(ddof=0)
    exp=(demeaned_r**4).mean()
    return exp/sigma**4

def is_normal(r, level=0.01):
    import scipy.stats
    stats,pvalue=scipy.stats.jarque_bera(r)
    return pvalue>level

def semideviation(r):
    """
    Returns the semideviation aka negative semideviation of r
    r must be a Series or a DataFrame, else raises a TypeError
    """
    if isinstance(r, pd.Series):
        is_negative = r < 0
        return r[is_negative].std(ddof=0)
    elif isinstance(r, pd.DataFrame):
        return r.aggregate(semideviation)
    else:
        raise TypeError("Expected r to be a Series or DataFrame")

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")


from scipy.stats import norm
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 cvar_historic(r, level=5):
    """
    Computes the Conditional VaR of Series or DataFrame
    """
    if isinstance(r, pd.Series):
        is_beyond = r <= -var_historic(r, level=level)
        return -r[is_beyond].mean()
    elif isinstance(r, pd.DataFrame):
        return r.aggregate(cvar_historic, level=level)
    else:
        raise TypeError("Expected r to be a Series or DataFrame")


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 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 = annualize_vol(r, periods_per_year)
    return ann_ex_ret/ann_vol

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 plot_ef2(n_points, er, cov):
    """
    Plots the 2-asset efficient frontier
    """
    if er.shape[0] != 2 or er.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=".-")

from scipy.optimize import minimize

def minimize_vol(target_return, er, cov):
    """
    Returns the optimal weights that achieve the target return
    given a set of 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
    }
    return_is_target = {'type': 'eq',
                        'args': (er,),
                        'fun': lambda weights, er: target_return - portfolio_return(weights,er)
    }
    weights = minimize(portfolio_vol, init_guess,
                       args=(cov,), method='SLSQP',
                       options={'disp': False},
                       constraints=(weights_sum_to_1,return_is_target),
                       bounds=bounds)
    return weights.x

def optimal_weights(n_points, er, cov):
    """
    Returns a list of weights that represent a grid of n_points on the efficient frontier
    """
    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):
    """
    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 plot_ef(n_points, er, cov, style='.-', legend=False, show_cml=False, riskfree_rate=0, show_ew=False, show_gmv=False):
    """
    Plots the multi-asset efficient frontier
    """
    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, legend=legend)
    if show_cml:
        ax.set_xlim(left = 0)
        # get MSR
        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', linewidth=2, markersize=10)
    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)
        # add EW
        ax.plot([vol_ew], [r_ew], color='goldenrod', marker='o', markersize=10)
    if show_gmv:
        w_gmv = gmv(cov)
        r_gmv = portfolio_return(w_gmv, er)
        vol_gmv = portfolio_vol(w_gmv, cov)
        # add EW
        ax.plot([vol_gmv], [r_gmv], color='midnightblue', marker='o', markersize=10)
        
        return ax
    
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)