Treasurer's Hedge Choice: Forward vs. Money-Market Hedge Under a Mismatched Basis
A US importer owes EUR 4,000,000 in 180 days. The treasurer obtains the following quotes from two banks. Bank A: spot EUR/USD 1.0850/1.0856; 180-day forward points 112/118 (quoted in pips, with the forward bid/ask constructed from spot bid/ask plus points). Bank B: USD 180-day borrowing rate 5.40% p.a. (actual/360), USD deposit rate 5.15%; EUR 180-day borrowing rate 3.10%, EUR deposit rate 2.85%. The treasurer notes the forward-implied EUR-USD differential appears wider than the money-market differential and wonders whether a covered money-market hedge (borrow USD, buy EUR spot, deposit EUR) creates an arbitrage. The company's policy requires hedging 90-100% of committed exposure and prohibits leaving residual unhedged. Day count 180/360. The treasurer must also document why the chosen hedge is consistent with the firm's risk objective.
1. Compute the outright 180-day forward EUR/USD bid and ask, and the all-in USD cost of hedging EUR 4,000,000 with an outright forward. Compare with the money-market hedge cost and explain whether an arbitrage exists.
Read the worked answer
Forward construction: spot bid 1.0850 + 112 pips (0.0112) = 1.0962 forward bid; spot ask 1.0856 + 118 pips (0.0118) = 1.0974 forward ask. The importer buys EUR forward, so it pays the ask: 4,000,000 × 1.0974 = USD 4,389,600.
Money-market hedge: borrow USD today for 180 days, convert to EUR at spot ask 1.0856 (buy EUR 4,000,000 costs USD 4,342,400), deposit EUR at 2.85% for 180 days. EUR deposit grows to 4,000,000 × (1 + 0.0285×180/360) = 4,057,000, which exceeds the payable, so the treasurer would only need to deposit 4,000,000 / 1.01425 = EUR 3,943,800. USD borrowed = 3,943,800 × 1.0856 = USD 4,281,389. Repay at 5.40%: 4,281,389 × (1 + 0.054×0.5) = 4,281,389 × 1.027 = USD 4,397,987.
The forward cost (4,389,600) is slightly cheaper than the money-market hedge (4,397,987) by about USD 8,387, reflecting bid-ask spreads and the bank's forward points. No arbitrage: the small difference is transaction cost, not riskless profit, because the treasurer cannot borrow at the interbank deposit rate or trade at mid. The forward-implied differential is consistent once spreads are included. Conclusion: use the outright forward, which locks the cost and satisfies the 90-100% hedge policy with no residual exposure.
2. The CFO asks whether the firm should instead leave 10% unhedged to capture favorable EUR moves. Draft the suitability rationale the treasurer should record, referencing policy and the firm's stated risk objective.
Read the worked answer
The treasurer should document: (1) the exposure is a committed payable of EUR 4,000,000 due in 180 days, so it is a genuine transaction exposure, not a speculative position; (2) board-approved policy mandates hedging 90-100% of committed exposure and prohibits deliberate residual open positions, so leaving 10% unhedged would breach policy and require an exception approved by the risk committee; (3) the firm's stated objective is budget certainty on import costs, not alpha generation from FX views, so an unhedged slice would introduce P&L volatility inconsistent with that objective; (4) the expected cost of the unhedged slice is zero in an efficient market, but the variance is material: a 3% adverse move on USD 438,960 (10% of the hedged cost) is roughly USD 13,000 of unbudgeted cost; (5) any recommendation to retain exposure must be recorded as a discretionary decision with rationale, approved by the appropriate authority, and disclosed to the client/CFO in writing. The record should state the hedge ratio chosen (e.g., 100%), the instrument (outright forward), the counterparty, the rate locked (1.0974), and the policy basis. This satisfies suitability and documentation standards and creates an auditable trail.