Regular arbitrage

An arbitrager, in the workbook's description, looks for mispricing, executes a simultaneous buy and sell to capture it, and takes no view on market direction.

Regular arbitrage is the version used when a bond future is too expensive. The arbitrager buys the bond in the underlying market and sells futures on the same bond. The workbook says this strategy is generally possible when the futures price is more than the theoretical futures price.

Having bought the bond and sold it forward at a fixed price, the arbitrager no longer cares where the bond goes. If it falls, the futures gain offsets the bond's loss; if it rises, the bond's gain offsets the futures loss. What remains is the bond's accrued interest, minus the cost of borrowing to buy it, plus the gap between the two prices at entry.

The positions.

When it works. Futures above the theoretical price given by the cash and carry model: cash price + financing cost − income on cash position. The excess is the arbitrage profit, before frictions.

What can go wrong. The workbook lists the risks arbitragers carry:

• Execution gap — even on seamless electronic systems, there may be a gap between the two orders.
• Illiquid legs — if one leg is illiquid, only one leg may get executed, leaving a naked exposure.
• Unwinding — depending on cash or physical settlement, trades may need reversing, adding risk.
• Frictions — brokerage, taxes, stamp duty, margin cost, impact cost and funding costs are ignored in the example and must be provided for.

The mirror trade, used when futures are too cheap, is reverse arbitrage.

The workbook's example. On 3 August, 7.59% GOI trades at Rs 102.60 and the August futures at Rs 102.62. Face value Rs 10 crore — 500 lots. Cost of borrowing in repo: 5%.

Trade: buy Rs 10 crore of the bond at 102.60; sell 500 lots of futures at 102.62.

At August expiry, two outcomes:

Check one line of each: 0.32 × 10,00,000 bonds = Rs 3,20,000; 0.18 × 10,00,000 = Rs 1,80,000.

The figures correspond to 21 days: accrued interest 7.59% × Rs 10 crore × 21/360 = Rs 4,42,750, and borrowing 5% × Rs 10.26 crore × 21/365 ≈ Rs 2,95,151.

Rs 1,67,599 either way. The bond moved 30 paise down in one case and 20 paise up in the other; the result did not move at all. That is what a locked-in pay-off means — and it is before brokerage, taxes, stamp duty and impact cost.

Chapter 5 (Strategies using Interest Rate Derivatives), section 5.5.1, works regular arbitrage with single bond interest rate futures using the 7.59% GOI example and both price cases, then discusses the risks arbitragers carry. Chapter 3 supplies the theoretical futures price that defines when futures are "too expensive". Expect a question that describes buy-bond-sell-futures and asks for the name, one that asks when the strategy is possible, and one on why the pay-off is identical in both cases.

• Regular arbitrage = buy the bond, sell the futures. Reverse arbitrage = sell the bond, lend in repo, buy the futures.
• It is possible when futures trade above the theoretical price.
• The pay-off is the same whether prices rise or fall — the workbook shows Rs 1,67,599 in both cases.
• Accrued interest is income; cost of borrowing is an outflow. Both appear in every case.
• Arbitragers take no directional view. A trader with a view is a speculator.
• An unfilled leg leaves naked exposure. Execution risk and illiquid legs are the arbitrager's real danger.
• The example ignores frictions — brokerage, taxes, stamp duty, margin and impact cost.