1. Straddle and strangle: movement, not direction

Derivatives 8: Combined positions

The first six levels dealt with the instruments one at a time and the seventh changed the object of study: from the price of the underlying to the price of volatility and its shape by expiry. From here on you no longer buy an option, you build structures with several legs. The oldest of them consists of buying two options at once so as to get paid if the market moves, without committing to a direction.

Straddle and strangle: two ways of buying movement

A long straddle is the simultaneous purchase of a call and a put with the same strike and the same expiry. A long strangle is the same idea with different strikes: the call above the current price and the put below it.

In both cases the overall delta starts close to zero. What is being bought is not direction: it is positive gamma and positive vega, and the bill arrives in the form of negative theta. Level 4 explained those three letters and level 7 put a price on them; here they are simply used.

It is worth saying from the first line what Natenberg repeats every time he deals with these positions: buying a straddle is not betting that there will be movement, it is betting that there will be more movement than is already paid for in the premium. They are two different bets and they are constantly confused.

The position we will use across the four modules

An index trades at 100 points. Its options have a multiplier of 100 euros per point, so one point of premium is 100 euros. We work with the 30-day expiry.

There is a known event two weeks away: a central bank meeting whose outcome is genuinely open. That is why the implied volatility of the short expiry is at 35%, well above the 20% that market runs at in calm conditions. Level 7 explained why the curve bulges precisely at the expiry containing the event; it is not re-explained here, it is paid for.

At that implied, the starting prices are:

• 100 call: 4 points, that is 400 euros.
• 100 put: 4 points, another 400 euros.
• Long 100 straddle: 8 points, 800 euros per structure.
• 105 call and 95 put: 2 points each. The long 95/105 strangle costs 4 points, 400 euros.

How far the index has to move to break even

The straddle recovers what was paid when one of the two legs is worth on its own the 8 points laid out. That happens at 92 and at 108: it takes an 8% move in thirty days, in either direction. Some specific outcomes at expiry:

• Index at 100: both legs die worthless. You lose the full 800 euros.
• Index at 104: the call is worth 4 points, 400 euros. You lose 400.
• Index at 108: the call is worth 8 points. You break even exactly.
• Index at 115: the call is worth 15 points, 1,500 euros. You make 700.
• Index at 85: the put is worth 15 points. You make another 700.

The strangle breaks even when the winning leg covers the 4 points paid, counting from its own strike: at 91 and at 109, a 9% move. It costs half and demands one percentage point more.

When the strangle is worth it and when it is not

The difference between the two lies not in the cost but in the shape of the loss. The straddle loses its maximum at a single point, exactly 100. The strangle loses its maximum across the whole band between 95 and 105: there both legs die and you are out the 400 euros.

Compared point by point, the strangle only beats the straddle if the index ends between 96 and 104. At 104 and at 96 they tie. Outside that band, the straddle comes out exactly one point ahead, 100 euros, whether the index runs to 120 or sinks to 80. In short: the strangle is cheaper and harder to collect on, and its advantage is concentrated in the mediocre outcomes.

Getting the movement right and losing anyway

Here is the point almost nobody sees coming the first time, and it is not a curiosity: it is the usual way of losing money with a long straddle.

You paid 8 points with the implied at 35%. Those 8 points already contain the event. The market has not sold you a cheap option while waiting for something to happen: it has sold you the event with its price attached. To win, the movement has to exceed the one already priced in.

Scenario: the day arrives, the central bank decides, the index rises to 103. There has been movement and in the direction you expected, at that. But the uncertainty has been resolved, the short expiry's implied falls from 35% to 20% and 25 days remain. With those inputs:

• The 100 call is now worth around 4 points.
• The 100 put settles at around 1 point.
• The straddle is worth some 4.9 points, that is 490 euros.

You paid 800 and you have 490: you lose around 310 euros, almost 40%, with the index rising and twenty-five days still ahead. The deflation of the implied after an event is entirely foreseeable: uncertainty was the merchandise and it has been consumed.

Worked scenario: buying the event and paying for the deflation

We set out as the worked scenario, with the figures above, the complete case. You buy ten straddles: 8,000 euros. The index moves 3% and the implied returns to 20%. The position is worth 4,900 euros. Loss: 3,100 euros, 39%, having been right that the event would move the market.

To have broken even you needed a close at 92 or at 108. In other words: it was not enough to be right that there was movement, you had to be right that it would be almost three times larger than it was.

There is a real case that illustrates the other extreme. At the British referendum of June 2016 sterling's one-month implied shot up to levels not seen since 2008, and even so the subsequent move exceeded it: sterling fell of the order of 8% against the dollar in a single session. The exact figures vary by source, so hold on to the order of magnitude.

The lesson brings the two cases together: buying a straddle ahead of an event is betting against the consensus about the size of the move, not about its existence. Sinclair presses that distinction because it is what separates a volatility position from a hunch in disguise.