r"""
Amihud's illiquidity ratio
==========================

Yakov Amihud (2002) proposed a liquidity measure that needs only daily
returns and dollar volume: the average of :math:`|r_d| / \mathrm{DVol}_d`,
the price move per dollar traded. It approximates Kyle's lambda, which
needs signed order flow, and Amihud found that stocks with a higher
ratio earn higher expected returns, an illiquidity premium.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

from financialkit.market_microstructure import amihud_illiquidity, kyle_lambda

rng = np.random.default_rng(15)

# %%
# A cross-section of stocks
# -------------------------
#
# Each stock's daily return is its Kyle lambda times its signed dollar
# order flow plus public news. Lambdas span two orders of magnitude, and
# less liquid stocks trade less.

n_stocks, days = 80, 250
lam = 10 ** rng.uniform(-9, -7, n_stocks)  # return per dollar of net order flow
scale = 2e5 / np.sqrt(lam / 1e-9)  # typical net flow in dollars
amihud, kyle = [], []
for i in range(n_stocks):
    net = scale[i] * rng.standard_normal(days)
    dvol = np.abs(net) + scale[i] * rng.gamma(2.0, 1.0, days)
    r = lam[i] * net + 0.005 * rng.standard_normal(days)
    amihud.append(amihud_illiquidity(r, dvol))
    kyle.append(kyle_lambda(r, net).coef[1])

rho = stats.spearmanr(lam, amihud).statistic
print(f"rank correlation between Amihud's ratio and the true lambda: {rho:.2f}")

fig, ax = plt.subplots(figsize=(6, 4.5))
ax.loglog(lam, amihud, "o", color="C0", label="Amihud ratio (per $1M)")
ax.loglog(lam, 1e6 * np.abs(kyle), "x", color="C1", label="regression lambda (per $1M)")
ax.set_xlabel("true Kyle lambda")
ax.set_ylabel("estimate")
ax.legend()
fig.tight_layout()

plt.show()