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Problem · Database

Hedge Inventory with Return Covariance

● Hard

MillenniumNEW GRADINTERNOA

Problem statement

A desk holds inventory in three assets and may add hedge quantities only in assets marked as liquid. Estimate return risk from the time-sorted price history, solve the ridge-regularized hedge, and report the remaining portfolio variance.

Risk model

Sort prices by period. Convert the price columns to IEEE-754 float64, then compute consecutive simple returns current_price / previous_price - 1.
Build the sample covariance matrix Sigma of those return rows, using denominator return_count - 1.
Sort portfolio by asset_order; rows must align with asset_1, asset_2, and asset_3. Convert the quantities to float64.
Let q be the inventory vector and L the indices marked is_liquid. Solve (Sigma_LL + ridge * I) * h_L = -Sigma_LA * q in float64. Set hedge quantities outside L to 0.
Let r = q + h. Compute residual variance as r^T * Sigma * r.

Return exactly one row containing the three hedge quantities in price-column order and the residual variance.

Table schema

Pandas

Use the same input data with any supported language. Open the Schema tab in the editor to see the generated SQL setup or Pandas DataFrames.

prices

Column	Type	Nullable	Description
periodPK	Integer	No	—
asset_1	Decimal	No	—
asset_2	Decimal	No	—
asset_3	Decimal	No	—

portfolio

Column	Type	Nullable	Description
asset_orderPK	Integer	No	—
asset	Text	No	—
quantity	Decimal	No	—
is_liquid	Boolean	No	—

parameters

Column	Type	Nullable	Description
config_idPK	Integer	No	—
ridge	Decimal	No	—

Expected result

Your query or function must return these columns.

Column	Type	Nullable	Description
asset_1_hedge	Decimal	No	—
asset_2_hedge	Decimal	No	—
asset_3_hedge	Decimal	No	—
residual_variance	Decimal	No	—

Row order: must match exactly. Numeric tolerance: 0.000001.

Constraints

3 <= prices.row_count <= 2000, and periods are unique.
Every price is an exact decimal in [1, 1000000] with at most 6 fractional digits. After sorting by period, every consecutive price ratio for the same asset lies in [0.9, 1.1].
portfolio contains exactly three rows with unique orders 1, 2, and 3 and matching asset names asset_1, asset_2, and asset_3.
Every portfolio quantity is in [-1000, 1000] with at most 6 fractional digits, and at least one portfolio row has is_liquid = true.
parameters contains exactly one row with 0.0001 <= ridge <= 1.
The ratio and ridge bounds keep each return in [-0.1, 0.1] and the ridge-regularized liquid system symmetric positive definite with 2-norm condition number at most 601.
The return covariance and every reported value are finite.
Numeric results are compared with absolute tolerance 0.000001.