Imperfect hedge

An OTC contract is negotiated. It can be for any amount, on any date, on any underlying — which is why the workbook says a customised product "can provide perfect hedge".

An exchange-traded contract is not negotiated. The exchange fixes the size, the expiry and the settlement method, and the hedger takes them as they come. That standardisation is what delivers the price transparency, the liquidity and the elimination of counterparty credit risk through the clearing corporation — and it is also what guarantees a residue.

The workbook lists the limitation in the same form three separate times: exchange-traded derivatives "may lead to imperfect hedge as amount and settlement dates cannot be customized", and "cash settlement in ETD may not be helpful to actual hedgers".

The hedger is choosing which imperfection to live with, not whether to have one.

Four mismatches account for almost all of it.

Amount. The lot is Rs 2 lakh of face value. An exposure that is not a whole multiple of it cannot be covered exactly, and the hedger rounds up or rounds down.

Date. Bond futures expire on the last Thursday of the month. An exposure running to the 15th of the following month must either be left uncovered for two weeks or over-hedged by rolling into the next contract.

Underlying. Futures exist on a handful of GOI securities. A corporate borrower hedging an NCD issue with G-Sec futures is hedging a different instrument — the workbook works exactly this case in section 5.2.3 and notes that "this will not provide perfect hedge to market participants as the underlying instruments are different and hence there will be a basis risk".

Settlement. A cash-settled contract pays the profit or loss but does not deliver the bond. A hedger who actually needed the security still has to buy it in the cash market at whatever price prevails, and the Chapter 5 scenario table lists "matching of expiry price with trade price on expiry (as cash settled transaction)" as a limitation of the futures route.

Options add one more: squaring off before expiry realises only the change in premium, so the Chapter 4 example of a dealer cancelling a hedge early leaves him with a net loss of Rs 550 on a position that had done its job.

Lots = round( Exposure face value ÷ Rs 2,00,000 )

Residual exposure = Exposure − (Lots × Rs 2,00,000)
                    positive → underhedged,  negative → overhedged

An exposure is perfectly hedgeable in amount only when
   Exposure mod Rs 2,00,000 = 0
   and its horizon coincides with a contract expiry
   and a contract exists on its own underlying.

Amount. A mutual fund must hedge Rs 5,37,00,000 of face value:

Exact requirement = 5,37,00,000 ÷ 2,00,000 = 268.5 lots

Sell 268 lots → Rs 5,36,00,000 hedged, Rs 1,00,000 exposed
Sell 269 lots → Rs 5,38,00,000 hedged, Rs 1,00,000 over-hedged

There is no third option. If yields then move 50 bp with a modified duration of 7, the residual Rs 1 lakh gains or loses about Rs 3,500 — small, but it is the hedger's, unavoidably.

Date. The same fund needs cover until 15 November. The November contract expires on the last Thursday of November — after the date needed — while the October contract expires before it. Rolling from October into November leaves the fund carrying two weeks of extra hedge it did not want, and the roll itself costs the bid-offer twice.

Underlying. The workbook's Chapter 5 case: a corporate will issue 10-year NCDs in a month, borrowing at about 50 bp over G-Secs, and hedges by selling IRF on the 7.59% GOI security.

Sold at    Rs 95.60   (yield 7.93%)
Settled at Rs 94.80   (yield 8.08%)
Gain       Rs  0.80 per bond

The gain reduces the borrowing cost. But the hedge was on a government bond and the exposure is a corporate one, so if the corporate spread widens from 50 bp to 80 bp while G-Sec yields are flat, the futures pay nothing at all and the NCD still prices 30 bp worse. That gap is basis risk, and it is not fixable within an exchange-traded contract.

Settlement. In the Chapter 5 scenario comparison, the hedged route produces the best outcome — Rs 5,08,81,527.78 against Rs 5,07,53,106.22 for selling into T-Bills and Rs 5,00,86,527.78 for doing nothing. It still carries listed limitations: impact cost in the IRF, expiry-price matching because the contract is cash settled, and opportunity loss if GOI prices rise instead.

The phrase recurs across four chapters. Chapter 2, section 2.6, gives it as a limitation of exchange-traded derivatives against OTC: standardisation may lead to imperfect hedge, and cash settlement may not help actual hedgers. Chapter 3, section 3.6, repeats it in the FRA-versus-futures comparison. Chapter 4, section 4.10, repeats it again for exchange traded options. Chapter 5 supplies the worked cases — the portfolio hedge in 5.2.2, the different-underlying hedge in 5.2.3, and the scenario limitations table in 5.2.1.

Questions ask why an exchange-traded hedge cannot be perfect, or which advantage OTC contracts retain over exchange-traded ones — the answer in both cases being customisation.

• Imperfect hedging is the price of standardisation, not a defect. The same standardisation buys liquidity, transparency and a central counterparty.
• Imperfect hedge and basis risk overlap but are not identical. Basis risk is the price-mismatch component; amount and date mismatches are imperfections that exist even when the underlying is identical.
• OTC contracts can hedge perfectly and still be worse. They carry counterparty risk, liquidity risk and are not accessible to all participants — the workbook lists all three.
• Cash settlement is a limitation for a hedger who needs the bond. He receives the profit and must still buy the security in the cash market.
• Rounding cuts both ways. Rounding down leaves an exposure open; rounding up creates a small speculative position in the opposite direction.
• Squaring off an option early realises only the premium change, which is why the workbook's dealer books a Rs 550 loss on a hedge that was never wrong.