Asymmetric risk exposure

Put a futures contract and an option side by side and move the underlying price up and down. The futures position gains and loses in step, rupee for rupee, whichever way the price goes. The option does not.

The workbook states it directly at the end of its pay-off tables: options are products with asymmetric risk exposure, i.e., the gains when the underlying asset moves in one direction is significantly different from the losses when the underlying asset moves in the opposite direction. Under a call, if the price falls, the buyer's loss is limited to the purchase price of the option; if the price rises, the buyer gains in proportion to the rise. In contrast, futures have symmetric risk exposures (symmetric pay off).

The reason is the contract itself. In futures both parties have a right as well as an obligation, so they face similar risk. In options the buyer has only rights and no obligation, so he risks only the premium, while the seller is under obligation and faces the large loss. The seller's upside is capped at the premium received.

The four basic positions, from the workbook's tables on 6.10% GOI 2031.

Reading the long call table. At 98.00, 98.10, 98.20 and every price up to 98.50 the pay-off is the same: −0.20. Above the strike each 0.10 rise in the bond adds 0.10: 98.70 gives 0, 98.90 gives +0.20. One side of the chart is flat; the other slopes. That picture is asymmetry.

Break-even is instrument-specific. The workbook points out that the BEP of a put is X − P for both the long and the short, because BEP depends on the instrument, not on which side you hold.

Cash settlement. On exercise of a cash settled option the buyer receives only the profit amount, for example Rs 0.40 when the bond closes at 98.90 against a 98.50 strike.

Ten lots, two instruments (lot size from the workbook; positions illustrative). One lot of an exchange-traded interest rate option is 2,000 bonds of face value ₹2 lakh. Ten lots = 20,000 bonds.

Long 10 lots of the 98.50 call at 0.20. Premium paid = 0.20 × 20,000 = ₹4,000.

Check the last row: 1.30 × 20,000 = ₹26,000 and 1.50 × 20,000 = ₹30,000.

The futures column is a mirror image: a one-rupee fall costs ₹20,000, a one-rupee rise earns ₹20,000. The option column is not: the downside stops at ₹4,000 however far the bond falls, while the upside keeps growing. Whoever wrote those calls has the reverse: at most ₹4,000 of gain and an open-ended loss.

Chapter 4 (Exchange Traded Interest Rate Options) builds the long and short call and put pay-off tables in section 4.8 and closes them with the asymmetric risk exposure statement; section 4.2 explains why buyer and seller face different risks. Sample question 2 in the chapter asks exactly this: the option buyer faces limited risk and the option seller faces unlimited risk. Expect a statement-type question contrasting options with futures, and break-even and maximum-loss calculations.

• Options are asymmetric; futures are symmetric. A question that calls futures asymmetric is wrong.
• Buyer: loss limited to the premium. Seller: gain limited to the premium.
• A short put's loss is large but bounded — the workbook says it runs until the underlying price becomes zero.
• BEP does not change with position. Long and short calls share X + P; long and short puts share X − P.
• Asymmetric does not mean the buyer usually wins. Below the strike, every outcome for a call buyer is the same loss.
• In a cash settled option the buyer receives only the profit amount, not the bond.