Free lesson · Optimization

Exposure constraints before optimization

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A target portfolio is useful only if it fits the mandate and the available capital.

Net exposure adds signed positions; gross exposure adds their magnitudes. A long/short book can have little net exposure while still requiring substantial financing and collateral. A position cap, gross cap and dollar-neutral constraint are different restrictions.

Check final rounded positions after any adjustment. Clipping each position independently can break neutrality. Build an explicit feasibility report before comparing expected utility.

Apply it in a strategy

• Freeze inputs at the stated decision time and record their units.
• Use this report at pre-trade checks and after rounding or partial fills.
• Recompute the example, then change the material assumption and explain the difference.

Research deliverable

Exposure constraints before optimization: produce the worked calculation, a timestamped input record and a written decision addressing this limitation: A low net exposure does not bound factor, liquidity or funding risk.

These are synthetic mechanics examples, not historical performance or paper replications. Module evidence and research boundaries record the 12 September 2026 review.

Research sources, review dates and limitations

# Python 3.10+; standard library and NumPy only.
# Synthetic teaching inputs; conventions and units are defined in the notation above.
import numpy as np

def exposures(weights):
    w=np.asarray(weights,dtype=float)
    if w.ndim!=1 or not np.isfinite(w).all(): raise ValueError('Finite weight vector required')
    return float(w.sum()),float(np.abs(w).sum())

assert np.allclose(exposures([.6,-.4,.2]),[.4,1.2])
print(exposures([.6,-.4,.2]))