Apparent Futures-Forward Arbitrage on a Bank Proprietary Desk
The proprietary desk of an AD bank sees a three-month interbank USD/INR forward quoted 84.15/84.18 and the exchange-traded three-month USD/INR futures contract trading at 84.55. Spot is 83.90, three-month INR money market is 6.80% and three-month USD is 5.30% (both Actual/365, 90 days). The desk's funding cost is 7.00%. Exchange margin is SPAN plus exposure, approximately 4% of notional, settled daily in cash, and the desk is told its position will be within the exchange limits applicable to a trading member. The desk head wants to sell USD 10,000,000 of futures against a bought interbank forward and book a locked profit. The interbank quote is indicative and firm for USD 2,000,000.
1. Compute the covered-interest-parity fair forward and state whether the futures price is rich or cheap. Quantify the apparent locked gain per USD and on USD 10,000,000.
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Fair forward = 83.90 x (1 + 0.068 x 90/365) / (1 + 0.053 x 90/365).
- INR factor: 1 + 0.016767 = 1.016767
- USD factor: 1 + 0.013068 = 1.013068
- Ratio: 1.003651; fair forward = 83.90 x 1.003651 = 84.21.
The interbank forward at 84.18 sits 3 paise below fair, inside a normal bid-offer. The futures at 84.55 are 34 paise above fair - rich.
Locked gain = 84.55 (sold futures) - 84.18 (bought forward) = 0.37 per USD, or 0.37 x 10,000,000 = Rs 37,00,000. Both legs settle off the same RBI reference rate, so basis risk is small and the gain looks almost riskless. That is the trap: a 34 paise gap against a fair value that the desk itself computed to the paise should prompt a check of the inputs, not an immediate trade.
2. Identify why this is probably not a riskless arbitrage, and quantify at least one cost that erodes the Rs 37 lakh.
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Four practical leaks:
- Quote size and firmness. The 84.18 is indicative and firm for only USD 2,000,000. At USD 10,000,000 the executable interbank level will be worse, plausibly 84.25-84.30, cutting the gain to roughly Rs 25-30 lakh or less.
- Margin funding. Notional = 84.55 x 10,000,000 = Rs 84.55 crore; 4% = Rs 3.38 crore of margin, funded at 7% for 90 days = 3.38 crore x 0.07 x 90/365 = about Rs 5.83 lakh, plus daily MTM funding on any adverse move.
- Maturity and fixing mismatch. The futures final settlement price is the RBI reference rate on the last trading day, which is typically two business days before month end; the forward value date is the month-end spot date. The two legs do not settle on the same day or against the same print, so the 'locked' amount carries a small residual.
- Position limits and brokerage/exchange fees on both legs, plus the risk that the futures price reflects a stale or thin order book.
A Rs 37 lakh headline with Rs 6 lakh of funding cost and a size-dependent slippage of Rs 7-12 lakh is a much thinner trade than it first appears.
3. What should the desk head do before the trade is booked?
Read the worked answer
First, request a firm, executable interbank quote for the full USD 10,000,000 at the intended value date and re-run the parity calculation - if the executable forward moves to the fair level, the opportunity disappears and the desk has lost nothing. Second, confirm the exchange contract's last trading day and final settlement price definition, and match the forward value date to it as closely as possible. Third, recompute the locked gain net of margin funding, brokerage, exchange fees and the expected MTM funding on a 1-sigma move in the futures price; only a net figure should go to the risk committee. Fourth, confirm the futures position falls within the desk's approved limits and that the bank's own OTC position is permitted on a proprietary basis.
If all four pass and the net gain is still material, the trade is legitimate - but the candidate should recognise that the real test is whether the price gap survives executable size and cost of carry, not whether a mid-quote comparison shows a spread.