Arbitrager

The derivatives market has three kinds of participant. A hedger has a risk and wants rid of it. A speculator has no risk and takes one on purpose. An arbitrager has neither.

What he has is a price difference. The same instrument, or the same economic position, is available at two prices in two markets. He buys the cheap one and sells the dear one simultaneously, and the profit is fixed the moment both legs are done — regardless of what prices do afterwards.

The workbook is precise about the distinction from a trader: "arbitragers generally lock in their profits unlike traders who trade naked contracts". A naked contract has one leg and an open outcome. An arbitrage has two legs and a determined one.

And the activity is self-extinguishing. As more participants notice the gap and put on the same trade, the prices converge and the opportunity disappears — which is the mechanism by which the derivatives market keeps the cash market honest.

In interest rate derivatives the gap can appear in three places: between the cash bond and the futures, between the OTC and exchange markets, and between futures and options.

Regular arbitrage is buying the bond in the cash market and selling futures on it, available when the futures price is above its theoretical value. Reverse arbitrage is the opposite — selling the bond, lending the money in the repo market against it, and buying futures — available when futures trade below theoretical value. The workbook notes that reverse arbitrage is not open to everyone, because short selling government securities is restricted.

The theoretical price the arbitrager measures against is the cash-and-carry price:

Futures price = Cash price + financing cost − income on cash position

Bond futures usually trade at a discount to the cash price, because the coupon accruing on the bond exceeds the cost of financing it — which is also why the basis on bond futures is usually positive under the NISM convention of basis = spot − futures.

The risks that remain. The workbook lists them and they are operational rather than directional. Both legs must execute together; even on electronic systems there can be a gap. If either leg is illiquid, one may fill and the other may not, leaving the arbitrager naked — the very position he exists to avoid. And where a leg is not cash settled, unwinding requires a reversal trade in that market with its own execution risk. The worked example also ignores transaction costs, impact cost and carry cost, which the workbook says must all be considered in real life.

Theoretical futures price = Cash (dirty) price + Financing cost − Income on cash position

Regular arbitrage : futures RICH  →  buy the bond, sell futures
Reverse arbitrage : futures CHEAP →  sell the bond, lend in repo, buy futures

Locked profit = | Futures price − Cash price |  × lot size × lots
                independent of the price at expiry

NISM convention:  Basis = Spot price − Futures price
                  futures above spot → NEGATIVE basis

The workbook's demonstration that the outcome does not depend on the outcome. On 1 January the underlying trades at Rs 100 and the March futures at Rs 110, with a lot size of 50. The arbitrager buys cash at 100 and sells futures at 110, locking Rs 10 a unit.

Profit = Rs 10 × 50 = Rs 500, either way

The two columns are the whole idea. The arbitrager does not care where the price goes, because he is on both sides of it.

A bond futures version. A 6.10% GOI 2031 trades at a dirty price of Rs 103.02. Carrying it for 23 days costs Rs 0.26 in financing and earns Rs 0.37 in accrued interest, so the theoretical futures price is:

103.02 + 0.26 − 0.37 = Rs 102.91  (dirty)

The futures are quoted at Rs 103.40, forty-nine paise rich. A dealer buys Rs 5 crore of the bond and sells 250 lots:

Locked profit = Rs 0.49 × 2,000 × 250 = Rs 2,45,000

Rs 2.45 lakh on Rs 5 crore — about 49 basis points of face value, annualising to something substantial over 23 days, and available only until enough dealers see it.

Where it goes wrong. The bond leg fills at 103.02 but the futures leg — thin at that hour — fills only half. The dealer is now long Rs 2.5 crore of an unhedged bond on a position that was supposed to carry no risk at all. A 25 bp move against him with a modified duration of 7.35 costs Rs 4.6 lakh, wiping out nearly twice the arbitrage he was chasing.

Chapter 2, section 2.4, introduces the arbitrager as the third market participant and defines arbitrage as exploiting a price difference in two markets. Chapter 5, section 5.1, returns to it with the Rs 100 / Rs 110 worked example, the two expiry scenarios, and the risks — execution gaps, illiquid legs, naked exposure and the costs the example ignores. Chapter 3, section 3.7.2, supplies the theoretical futures price the arbitrager measures against, and section 3.7.1.4 defines basis as spot minus futures.

Questions are classification questions — hedger, speculator or arbitrager from a description — plus the distinguishing points: the arbitrager locks in profit, takes no view and holds no naked contract.

• An arbitrager takes no view and no exposure. If the position has an opinion about where prices go, it is speculation.
• Both legs must be simultaneous. A sequential trade is not an arbitrage; it is a directional bet with extra steps.
• The profit is the same in every scenario. If a worked answer gives different profits at different expiry prices, a leg has been mis-signed.
• Illiquidity is the real risk. One leg failing leaves a naked contract, which the workbook singles out as the arbitrager's characteristic danger.
• The textbook profit ignores costs. Transaction cost, impact cost and carry cost all have to come out of it, and the workbook says so.
• Under the NISM convention, basis is spot minus futures. Futures above spot gives a negative basis — the opposite of the sign many candidates assume.