4. What kills each combined position

Derivatives 8: Combined positions

This module closes the level and is the most uncomfortable of the four. The previous three have described structures; this one describes how they die. And the starting point is that they do not all die of the same thing: every combination has an executioner of its own, and mistaking the executioner is the fastest way to monitor the wrong risk.

The straddle is killed by the clock and by the deflation

The long 100 straddle cost 800 euros with the implied at 35% and thirty days ahead. If the index does not move, the value of an at-the-money straddle falls roughly with the square root of the time remaining:

• At 15 days: some 5.7 points, 570 euros. You have lost 230 with nothing happening.
• At 7 days: some 3.9 points, 390 euros. You are 410 down.
• The final stretch is the most brutal: half the value of a straddle evaporates in the last quarter of its life.

And the deflation of the implied moves faster still than the clock. With the index sitting at 100 and the implied falling from 35% to 20% over five days, the straddle goes from 800 to some 420 euros. Five days, no movement, almost half the money.

Hence the operational rule: a long volatility position has an expiry date and it has to be decided before opening it, not once it already hurts. Natenberg puts it another way: buying gamma is renting it, and the rent is paid every day.

The calendar is killed by the big move

The long calendar cost 210 euros and made 150 if the index stayed pinned at 100. Its executioner is the opposite of the straddle's: not silence, but movement.

• Index at 115: the position is worth some 20 euros. You lose 90%.
• Index at 85: it is worth some 10 euros. You lose 95%.

There is a second, quieter executioner that we have already seen: the inversion of the volatility curve. With the index still and the short implied jumping from 20% to 30%, the position loses 117 of the 210 euros. It is a risk that appears on no expiry payoff profile because it happens along the way.

And there is a third, specific to American-style options: early exercise of the short leg. If that call is deep in the money just before a dividend, you can wake up short the underlying with a stray long call, that is, with a position that is no longer the one you built.

The ratio is killed by the tail you left open

The 1x2 ratio lost 2,110 euros with the index at 130 and 4,110 with the index at 150. There is no executioner to explain: the position is designed for that and all it takes is for the market to pay it a visit.

What is worth underlining is the mechanism by which you are thrown out before getting there. The naked sold option requires margin, and that margin grows with the underlying and with the implied at the same time, exactly as level 6 described. Many ratio traders never get to see their position's final outcome: they leave earlier, liquidated, at the worst price available.

All of them are killed by execution

This is the common executioner, the least showy and the one that takes the most money. The Costs course already quantified commissions, spreads and slippage; here it only has to be applied to multi-leg structures, along with a detail almost nobody sees coming: the cheap legs are the ones with the proportionally widest spread.

Let us look at our options with realistic spreads:

• 100 call: quoted 2.25 against 2.35. Half spread: 0.05 points, 5 euros.
• 105 call: quoted 0.55 against 0.70. Half spread: 0.075 points, 7.5 euros.
• 110 call: quoted 0.05 against 0.20. Half spread: 0.075 points, 7.5 euros, on an option whose mid value is 12 euros. The spread is worth more than the whole option.

Complexity does not add costs, it multiplies them: you multiply legs and, on top of that, each additional leg tends to be cheaper in premium and proportionally dearer in spread. A straddle is two legs and some 10 euros of spread on 800 invested, 1.2%. A butterfly is four and the proportion rockets, as we are about to see.

There is also a risk that is not a cost until it is: legging in. If you send four separate orders and only three of them fill, the position you have open is not the one you wanted, and the previous module explained how expensive that difference gets. Executing the structure as a single combined order, where the market allows it, solves the problem at the price of a slightly worse spread.

Worked scenario: the full bill for a butterfly

Set out as the worked scenario, with the 100/105/110 butterfly that costs 120 euros and whose theoretical maximum is 380.

• Crossing half the spread on opening: 5 plus 15 plus 7.5, that is 27.5 euros.
• Crossing half the spread on closing: another 27.5 euros.
• Commissions at 1.50 euros per contract: four contracts on opening and four on closing, 12 euros.
• Total: 67 euros.

Against the 120 euros you are risking, that is 56%. Against the 380 of the best imaginable outcome, 18%. Before tax, and assuming you execute well.

Compare it with the straddle: some 10 euros of spread on 800 invested, around 20 there and back, 2.5% of the capital committed. The same desk, the same market, the same fee schedule, twenty times worse in proportion for the simple fact of having four legs instead of two and of two of them being worth next to nothing.

Close of the level, with the usual warning: this is education, not advice and not a recommendation to trade. Combined structures are neither better nor worse than a single option; they are more specific, and that specificity is paid for in execution costs and only collected if you get several things right at once. Before building any of them it is worth writing down three numbers: what kills it, what it costs to execute it twice, and what the worst case is if one leg never comes into existence.