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Algorithm correctness and cross-comparison tests.
Proves every optimization objective (max_sharpe, min_variance, risk_parity,
target_return, hrp) produces mathematically valid, constraint-respecting
portfolios, and compares them against each other on the same data.
"""
import sys
from pathlib import Path
project_root = Path(__file__).resolve().parent.parent
if str(project_root) not in sys.path:
sys.path.insert(0, str(project_root))
import numpy as np
import pytest
from services.portfolio_optimizer import run_optimization, OptimizationResult
# --- Fixed synthetic data ---
SEED = 42
N_ASSETS = 10
OBJECTIVES = ['max_sharpe', 'min_variance', 'risk_parity', 'target_return', 'hrp']
def _fixed_data():
np.random.seed(SEED)
returns = np.array([0.12, 0.08, 0.15, 0.06, 0.10, 0.09, 0.14, 0.07, 0.11, 0.05])
A = np.random.randn(N_ASSETS, N_ASSETS)
cov = A.T @ A / N_ASSETS + np.eye(N_ASSETS) * 0.02
return returns, cov
def _equal_weight_metrics(returns, cov):
n = len(returns)
w = np.ones(n) / n
ret = float(w @ returns)
vol = float(np.sqrt(w @ cov @ w))
sharpe = ret / vol if vol > 0 else 0
return {'return': ret, 'volatility': vol, 'sharpe': sharpe}
# ============================================================================
# 3a. Mathematical invariants — every objective
# ============================================================================
class TestMathInvariants:
"""Every objective must satisfy basic portfolio invariants."""
@pytest.fixture(params=OBJECTIVES)
def result(self, request):
returns, cov = _fixed_data()
target = float(np.mean(returns)) if request.param == 'target_return' else None
return run_optimization(returns, cov, objective=request.param, target_return=target)
def test_weights_sum_to_one(self, result):
assert abs(np.sum(result.weights) - 1.0) < 1e-5
def test_weights_non_negative(self, result):
assert np.all(result.weights >= -1e-9)
def test_return_consistent(self, result):
returns, _ = _fixed_data()
expected = float(np.dot(result.weights, returns))
assert abs(result.expected_return - expected) < 1e-5
def test_volatility_consistent(self, result):
_, cov = _fixed_data()
expected = float(np.sqrt(result.weights @ cov @ result.weights))
assert abs(result.volatility - expected) < 1e-5
def test_sharpe_consistent(self, result):
if result.volatility > 1e-10:
expected = result.expected_return / result.volatility
assert abs(result.sharpe_ratio - expected) < 1e-5
def test_sharpe_non_negative(self, result):
# On positive-return data all objectives should produce non-negative Sharpe
assert result.sharpe_ratio >= -1e-5
class TestIdenticalAssets:
"""With identical assets all objectives should produce roughly equal weights."""
def test_equal_weights_for_identical_assets(self):
n = 5
returns = np.full(n, 0.10)
cov = np.eye(n) * 0.04
for obj in ['min_variance', 'risk_parity', 'hrp']:
result = run_optimization(returns, cov, objective=obj)
np.testing.assert_allclose(
result.weights, np.ones(n) / n, atol=0.05,
err_msg=f"objective={obj} should give equal weights for identical assets"
)
# ============================================================================
# 3b. Objective-specific correctness
# ============================================================================
class TestMinVariance:
def test_volatility_le_equal_weight(self):
returns, cov = _fixed_data()
ew = _equal_weight_metrics(returns, cov)
result = run_optimization(returns, cov, objective='min_variance')
assert result.volatility <= ew['volatility'] + 1e-6
class TestRiskParity:
def test_risk_contributions_more_equal_than_equal_weight(self):
"""Risk parity should produce more equal risk contributions than equal-weight."""
returns, cov = _fixed_data()
result = run_optimization(returns, cov, objective='risk_parity')
w_rp = result.weights
w_ew = np.ones(N_ASSETS) / N_ASSETS
def rc_std(w):
vol = np.sqrt(w @ cov @ w)
if vol < 1e-10:
return 0.0
mcr = (cov @ w) / vol
rc = w * mcr
return float(np.std(rc))
assert rc_std(w_rp) <= rc_std(w_ew) + 1e-4, (
f"Risk parity rc_std ({rc_std(w_rp):.4f}) > equal-weight rc_std ({rc_std(w_ew):.4f})"
)
class TestTargetReturn:
def test_return_near_target(self):
returns, cov = _fixed_data()
target = float(np.mean(returns))
result = run_optimization(returns, cov, objective='target_return', target_return=target)
# Allow fallback to min_variance if target is infeasible
if result.objective == 'target_return':
assert abs(result.expected_return - target) < 0.02
class TestHRPCorrectness:
def test_lower_variance_asset_gets_higher_weight(self):
"""On 2-asset data, HRP raw weights give higher weight to lower-variance asset."""
from core.optimizers.hrp import hrp_weights
cov = np.array([[0.04, 0.01], [0.01, 0.16]])
w = hrp_weights(cov)
assert w[0] > w[1], "Lower-variance asset should have higher HRP weight"
def test_deterministic(self):
returns, cov = _fixed_data()
r1 = run_optimization(returns, cov, objective='hrp')
r2 = run_optimization(returns, cov, objective='hrp')
np.testing.assert_array_equal(r1.weights, r2.weights)
class TestMaxSharpe:
def test_sharpe_ge_equal_weight(self):
"""QSW max_sharpe should beat or match equal-weight Sharpe."""
returns, cov = _fixed_data()
ew = _equal_weight_metrics(returns, cov)
result = run_optimization(returns, cov, objective='max_sharpe')
# Allow small tolerance — QSW is heuristic
assert result.sharpe_ratio >= ew['sharpe'] - 0.1
# ============================================================================
# 3c. Cross-algorithm comparison
# ============================================================================
class TestCrossComparison:
"""Run all objectives on the same data and compare."""
@pytest.fixture(scope='class')
def all_results(self):
returns, cov = _fixed_data()
results = {}
for obj in OBJECTIVES:
target = float(np.mean(returns)) if obj == 'target_return' else None
results[obj] = run_optimization(returns, cov, objective=obj, target_return=target)
return results
def test_all_valid_portfolios(self, all_results):
for obj, r in all_results.items():
assert isinstance(r, OptimizationResult), f"{obj} didn't return OptimizationResult"
assert abs(np.sum(r.weights) - 1.0) < 1e-5, f"{obj} weights don't sum to 1"
assert np.all(r.weights >= -1e-9), f"{obj} has negative weights"
def test_min_variance_le_equal_weight_vol(self, all_results):
"""min_variance volatility should be <= equal-weight volatility."""
_, cov = _fixed_data()
ew = _equal_weight_metrics(_fixed_data()[0], cov)
mv_vol = all_results['min_variance'].volatility
assert mv_vol <= ew['volatility'] + 1e-4
def test_hrp_competitive_vol(self, all_results):
"""HRP should achieve competitive (often lower) volatility vs classical objectives."""
hrp_vol = all_results['hrp'].volatility
mv_vol = all_results['min_variance'].volatility
# HRP vol should be finite and reasonable (within 50% of min_variance either way)
assert hrp_vol < mv_vol * 1.5
def test_no_negative_sharpe(self, all_results):
for obj, r in all_results.items():
assert r.sharpe_ratio >= -1e-5, f"{obj} has negative Sharpe: {r.sharpe_ratio}"
def test_summary_table(self, all_results, capsys):
"""Print comparison table for human review."""
print("\n\n=== Cross-algorithm comparison (seed=42, N=10) ===")
print(f"{'Objective':<20} {'Sharpe':>8} {'Return':>8} {'Vol':>8} {'Active':>7}")
print("-" * 55)
for obj in OBJECTIVES:
r = all_results[obj]
print(f"{obj:<20} {r.sharpe_ratio:8.4f} {r.expected_return:8.4f} {r.volatility:8.4f} {r.n_active:7d}")
print("=" * 55)
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