Value at Risk Gist

ValueAtRisk.py

import numpy
import numpy.random as nrand


"""
Note - for some of the metrics the absolute value is returns. This is because if the risk (loss) is higher we want to
discount the expected excess return from the portfolio by a higher amount. Therefore risk should be positive.
"""


def var(returns, alpha):
    # This method calculates the historical simulation var of the returns
    sorted_returns = numpy.sort(returns)
    # Calculate the index associated with alpha
    index = int(alpha * len(sorted_returns))
    # VaR should be positive
    return abs(sorted_returns[index])
 
 
def cvar(returns, alpha):
    # This method calculates the condition VaR of the returns
    sorted_returns = numpy.sort(returns)
    # Calculate the index associated with alpha
    index = int(alpha * len(sorted_returns))
    # Calculate the total VaR beyond alpha
    sum_var = sorted_returns[0]
    for i in range(1, index):
        sum_var += sorted_returns[i]
    # Return the average VaR
    # CVaR should be positive
    return abs(sum_var / index)


# Example usage
r = nrand.uniform(-1, 1, 50)
print("VaR(0.05) =", var(r, 0.05))
print("CVaR(0.05) =", cvar(r, 0.05))