An on-balance-sheet hedge involves matching the currency of assets with the currency of liabilities (e.g., funding EUR-denominated assets with EUR-denominated liabilities). This eliminates currency mismatch risk entirely.

• Option A is correct: By matching currencies, the bank locks in a predetermined net return (the difference between the asset yield and the liability cost in the same currency), regardless of future FX movements.
• Option B is incorrect: The on-balance-sheet hedge removes volatility entirely; it does not allow for positive but volatile returns.
• Option C is incorrect: The hedge can ensure a positive net return if the asset yield exceeds the liability cost in the matched currency.
• Option D is incorrect: A forward foreign currency contract is an off-balance-sheet hedge, not an on-balance-sheet hedge. The question specifically asks about on-balance-sheet hedging.

The answer is A.