var vs cvar - coherence of risk measures

var_cvar_example.py

import numpy as np
import pandas as pd

A = np.array([1.0] * 18 + [-100.0, 0.0, -30.0])
B = np.array([1.0] * 18 + [0.0, -100.0, -30.0])
P = 0.5 * A + 0.5 * B


def var(r, alpha=0.90):
    return np.percentile(r, 100 * (1 - alpha))


def cvar(r, alpha=0.90):
    v = var(r, alpha)
    return r[r <= v].mean()


tgt_threshold = 0.9
out = pd.DataFrame({
    "A": [var(A, tgt_threshold), cvar(A, tgt_threshold)],
    "B": [var(B, tgt_threshold), cvar(B, tgt_threshold)],
    "Portfolio": [var(P, tgt_threshold), cvar(P, tgt_threshold)]
}, index=["VaR", "CVaR"])

corr_AB = np.corrcoef(A, B)[0, 1]

out = out.astype(float).map(lambda x: f"{x:,.2f}")
print(out)
print(f"\nCorrelation between A and B: {corr_AB:.2f}")

### OUTPUT ###
#           A       B     Portfolio
# VaR    -0.00   -0.00    -30.00
# CVaR  -65.00  -65.00    -50.00
#
# Correlation between A and B: 0.03