The 1x2 Call Ratio: A 'Spread' With a Naked Second Short
Nifty is 24,000 with three weeks to the monthly expiry and implied volatility at 13%. A trader buys one 24,000-strike call at ₹300 and sells two 24,300-strike calls at ₹172 each, taking a net credit of ₹44 - ₹3,300 on the 75-unit lot. His note to the risk desk reads: 'This is a spread. The long call covers both shorts, so my maximum loss is the credit I received, my maximum profit is ₹344 at 24,300, and the margin blocked is only ₹2.1 lakh.' The desk sees a different position. Nifty options are European and cash settled; the trader has ₹5 lakh of free cash and no other F&O positions. Three sessions later the index is at 24,560 and he still holds everything, telling the desk he will 'roll the shorts up if it keeps going'.
1. Draw the expiry payoff, compute the breakevens, and calculate the P&L at 24,600, 25,200 and 26,000. Why is the margin charged like a naked short call?
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Payoff components: long 24,000 call, short two 24,300 calls, net credit ₹44.
- Below 24,000: +₹44 (₹3,300 per lot).
- At 24,300: 300 intrinsic on the long + 44 credit = +₹344 (₹25,800), the maximum.
- Above 24,300: profit = 344 − (S − 24,300), falling by one rupee per index point.
Breakevens:
- Upside: 344 − (S − 24,300) = 0 → S = 24,644, only 2.7% above spot - well inside a normal three-week range for Nifty.
- Downside: 24,000 (below it, the ₹44 credit is the loss).
P&L at selected levels:
| Expiry | P&L per unit | Per lot |
|---|---|---|
| 24,600 | +44 | +₹3,300 |
| 25,200 | −556 | −₹41,700 |
| 26,000 | −1,356 | −₹1,01,700 |
Above 24,300 the loss is unbounded - there is no ceiling, only the index's own ceiling.
Margin: only one of the two short calls is covered by the single long call. The second is a naked short call on ₹24.3 lakh of notional and attracts SPAN plus exposure margin on that basis, which is why the desk blocks far more than the ₹3,300 collected. The '₹2.1 lakh blocked' the trader quotes is precisely the tell that the position is not a spread.
2. The trader argues that the long call 'covers' both short calls. Refute this with delta, slope and gamma reasoning, and describe what his 'roll the shorts up' plan will actually look like at 24,560.
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Coverage is a price-point claim, not a position claim. A long call is a claim on one lot of the index, not two.
Delta: at 24,300 the long call's delta is about 0.5 and each short call's delta is about 0.5, so local delta is roughly 0.5 − 1.0 = −0.5... which is why the position feels 'covered' near the money. Above 24,300 the long call goes deeper in the money and its delta tends to 1, while both shorts' deltas also tend to 1, giving net delta → 1 − 2 = −1. From there, every 100-point rally costs ₹7,500 per lot.
Slope: for S > 24,300, dP/dS = −1 exactly. That is the mathematical definition of a naked short call, offset by nothing.
Gamma: the position is short gamma through 24,300 - as the index rises, delta becomes more negative, so losses accelerate rather than stabilise. The trader's intuition (long call available to cover) is a story about the terminal payoff at one point, not about the path.
The roll plan at 24,560:
- The 24,300 shorts are ~260 points in the money; buying back two of them costs roughly 2 × 290 = ₹580 per unit against ₹344 of maximum profit - the roll crystallises a loss well beyond the credit.
- Rolling up means buying back the two 24,300 calls and selling two higher-strike calls, converting a bull ratio into a higher, larger naked ratio with fresh margin. In a trending market this is a known way to compound the loss.
- The honest description: 'a bull call spread plus a naked short call, financed by the premium of the naked call.' The extra ₹172 per unit is not free money; it is the price of the unhedged tail.
3. Propose two ways to convert the structure into defined risk, quantify each, and state which is appropriate to the trader's actual view.
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Fix 1 - buy back one short call (make it a plain vertical).
- Buy 1 × 24,300 call at ₹172: net position is long 1 × 24,000 at ₹300, short 1 × 24,300 at ₹172 → net debit ₹128.
- Maximum gain 300 − 128 = ₹172 (₹12,900); maximum loss ₹128 (₹9,600); breakeven 24,128.
- Clean, cheap, defined on both sides, but it gives up most of the credit that motivated the trade.
Fix 2 - add a higher long call (1x2x1 'Christmas tree').
- Buy 1 × 24,600 call at roughly ₹90 (three weeks, 13% vol), turning the net ₹44 credit into a net ₹46 debit.
- Payoff: at 24,300, 300 + 44 − 90 = +₹254 (₹19,050); at ≤24,000, −₹46 (₹3,450); at ≥24,600, −₹46 - the upper tail is now capped and flat.
- Defined risk ₹3,450 per lot versus the current exposure of ₹41,700 at 25,200 and ₹1,01,700 at 26,000. This keeps the shape of his view (bullish, stalling just above 24,300) at a fraction of the tail risk.
Which fits his view: his thesis is 'the index stalls below 24,400 into expiry' - that is a pinning view, which is precisely what the tree expresses and what the naked ratio does not. The vertical is the better choice if he genuinely expects a move to 24,300-24,500.
The general rule: a ratio spread is a position short the tail on one side, whatever the premium looks like. It should only be put on with (a) a hard exit at the short strike, (b) margin sized for the naked leg, and (c) a view that the underlying pins, not merely drifts in the right direction.