Reverse cash and carry arbitrage

When a futures contract is too cheap relative to the cash market, do the opposite of cash and carry: sell the asset in the cash market, buy the futures.

The workbook's definition: reverse cash and carry arbitrage refers to long position in futures market and short position in the underlying or cash market.

Selling in the cash market brings in money today, which can earn interest until expiry. At expiry the futures price converges to spot, the arbitrageur takes back the asset through the futures leg, and the original underpricing plus the interest earned is the profit.

There is a practical catch the workbook spells out: you need the stock to sell. Either the arbitrageur already holds it, or he must borrow it — and the cost of borrowing the stock must then be counted when judging profitability. Where nobody will lend the asset, reverse arbitrage simply cannot happen.

1. Compute the fair futures price. A traded futures price below it signals reverse cash and carry.
2. Sell the underlying in the cash market (from holdings or borrowed stock) and buy futures.
3. Invest the sale proceeds for the period.
4. At expiry or earlier, buy the stock back and square off the futures.

The arbitrage selling pushes the spot price down and the buying pushes the futures price up until they align.

The workbook flags a case in the commodities world where this breaks down: when convenience yield dominates the cost of carry, futures can trade at a discount and reverse arbitrage is not possible, because no one lends traders the asset to sell short.

The position need not be held to expiry. If prices move favourably earlier, both legs can be reversed and the profit booked.

Triggered when Traded futures price < Fair futures price
Locked gain = (Cash price − Futures price) × Lot + Interest on sale proceeds

The workbook's stock B (Chapter 5, section 5.1). Cash price Rs 100, one-month futures Rs 90, contract multiplier 200 — a negative cost of carry.

Sell 200 shares at 100 (proceeds Rs 20,000), buy 1 futures contract at 90.

Locked gain = (100 − 90) × 200 = Rs 2,000

Interest on Rs 20,000 at 9% p.a. for one month, continuous compounding:

20,000 × e^(0.09 × 1/12) − 20,000 = Rs 150.56

Case I — stock ends at Rs 110: loss on shares (110 − 100) × 200 = −2,000; profit on futures (110 − 90) × 200 = +4,000; net Rs 2,000, plus interest = Rs 2,150.56.

Case II — stock ends at Rs 85: profit on shares (100 − 85) × 200 = +3,000; loss on futures (90 − 85) × 200 = −1,000; net Rs 2,000, plus interest = Rs 2,150.56.

Early exit. On the 15th, spot is Rs 130 and futures Rs 135. Reverse both legs:

Loss on shares     = (130 − 100) × 200 = −6,000
Profit on futures  = (135 − 90) × 200  = +9,000
Net                = Rs 3,000
Interest, 15 days  = 20,000 × e^(0.09 × 15/365) − 20,000 = Rs 74.11
Total              = Rs 3,074.11

Exiting early earned more than holding to expiry, because the futures had swung to a premium.

Chapter 3, section 3.7, introduces reverse cash and carry arbitrage using gold, and section 3.9 lists it among the arbitrage types. Chapter 5, section 5.1, works the stock B example above, including the early exit on the 15th. The convenience yield discussion in section 3.7 explains when it cannot be done.

• Futures underpriced → sell cash, buy futures. The mirror image of cash and carry.
• Interest is earned, not paid, because the cash leg is a sale.
• Borrowed stock has a cost that must be deducted.
• Convenience yield can block it — no one lends the asset.
• You do not have to wait for expiry. The workbook's early exit on the 15th earned Rs 3,074.11, more than the Rs 2,150.56 at expiry.
• The workbook computes the one-month interest with /12 and the 15-day interest with /365. Follow whichever convention the question gives.