Selling options and tail risk

Chapter 6 drew the seller's payoff: a flat capped gain and a sloping unbounded loss. This chapter is about why that shape fools people.

It works most of the time, by construction

Sell an out-of-the-money option and you win whenever the underlying fails to reach the strike. For a strike well away from the current price, that is most of the time.

So the experience of selling options is: small gain, small gain, small gain, small gain, for weeks or months. It feels like income. It feels like a system that works.

And it is working — doing exactly what it was priced to do. The high win rate is not evidence of skill. It is the shape of the instrument. An option priced so that it expires worthless 85% of the time will expire worthless about 85% of the time, and the premium reflects that.

Why a high win rate proves nothing

The arithmetic that settles it.

A strategy makes ₹5,000 on 85 trades out of 100 and loses ₹40,000 on the other 15:

85 × 5,000  = +4,25,000
15 × 40,000 = −6,00,000
net          = −1,75,000

An 85% win rate and a loss of ₹1,75,000. Both statements are true, and only one of them gets quoted.

This is the structural problem with any strategy whose wins are small and frequent and whose losses are large and rare. The win rate and the expectancy are different numbers, and a payoff shaped like a sold option guarantees they diverge.

Worse, the losses are not spread evenly. They cluster, because the events that cause them — a crash, a gap, a shock — are the same events.

The gap

The specific mechanism that turns a bad month into a ruinous one.

A stop-loss assumes you can exit at a price near where you decided to. Markets do not always offer that. On bad news the price can open far below the previous close, with no trading in between — chapter 2 of the markets subject's gap.

A short option position cannot be closed inside a gap, because there is no price inside a gap. You exit on the other side, at whatever is there.

So the risk management that works in ordinary conditions is least available in exactly the conditions that produce the loss. That is not bad luck; it is the definition of a tail event.

Margin accelerates it

Chapter 5's mark to market compounds the problem.

As the position moves against a seller, margin requirements rise — the position is now riskier, so more collateral is demanded. The seller must post more money at the moment they are losing it.

If they cannot, the position is closed at the worst available price. The loss is realised at the point of maximum stress, by somebody else's decision.

SEBI's measures of chapter 4 included increased tail risk coverage on the day of options expiry. A regulator demanding more collateral specifically where the tail lives is a statement about where this goes wrong.

Why sold puts are bounded and sold calls are not

A distinction worth keeping.

A sold put's worst case is the strike less the premium, because the underlying cannot fall below zero. Large, and finite, and calculable before you trade.

A sold call has no such bound. There is no ceiling on the underlying.

In practice both can exceed what the seller can pay, so the mathematical distinction matters less than it sounds. But a sold put at least permits the question "what if this goes to zero?" to have an answer.

Is there ever an edge in selling?

Honestly: there is a reasoned argument that options carry a premium for insurance, so sellers are paid for providing it over long periods. That argument is real and it is how the business works for institutions.

The conditions under which it works are the problem for an individual:

Capital large enough to survive the tail, not merely to margin the position.

Diversification across underlyings and time, so one event does not take everything.

Position sizing that assumes the worst case happens, rather than the expected case.

Not being forced out, which requires capital well beyond the margin.

An individual selling options at a size that makes the premium feel worthwhile has usually failed the third and fourth conditions by construction. The premium is worth collecting precisely in proportion to how much it could cost you.

The point

Selling options wins most of the time because it is priced to, so a high win rate is the instrument's shape rather than evidence of skill. Small frequent gains against large rare losses can be a negative expectancy at any win rate — and gaps prevent exit while rising margin forces it, in the same event.