Part XII · Strategy atlas · Chapter 12D

Advanced strategies

Ratios, diagonals and synthetic positions

1 · How to read this tier

The cards and the notation are those of Chapter 12C, with strikes numbered from lowest to highest, $K_1 < K_2 < K_3 < K_4$. A structure collects a net credit $C$ or pays a net debit $D$, the price at expiry is $S_T$, and dollars are points times $100. For positions that hold shares, $B$ is the cost basis per share. The premiums in the examples are illustrative, below what a pricing model gives, and the formulas hold at any premium.

Every entry here but the long condors has an unbounded or very large loss on at least one side. Find that side in the card before you read anything else.

2 · Naked structures

Short put, naked

The naked short put has the payoff of the cash-secured put of Chapter 12B, but it uses margin, so its buying-power requirement is lower. Under Reg-T the requirement is approximately 20% of the strike value less the amount the put is out of the money. Chapter 12G gives the full formula, which uses the underlying's value and adds the premium. The requirement is subject to margin expansion in stress (Chapter 2E).

Short call, naked

The naked short call is pure short volatility with no upside protection. It requires significant margin and explicit broker approval. With its unbounded maximum loss, it is rarely appropriate for a retail account.

The worked example is to avoid it, and to use the defined-risk call credit spread, the bear call spread of Chapter 12C, instead.

3 · Neutral structures

Short straddle

The short straddle takes the maximum credit for the maximum risk: pure short volatility with an unbounded loss, catastrophically dangerous in stress. Sold at the 80 points that Chapter 12C's long straddle cost, a short 6,000 SPX straddle breaks even at 5,920 and 6,080. A 10% fall to 5,400 would cost $600 - 80 = 520$ points, or $52,000.

Short strangle

The short strangle is a wider, higher-probability version of the short straddle, and a common vehicle for harvesting the variance risk premium (VRP). Used systematically with cash-secured collateral, as XSP strangles, it can be operationally viable.

Long call condor and long put condor

The long call condor has the same payoff shape as the iron condor, built from calls only; the long put condor builds it from puts. Traders use one when the puts are illiquid, or when skew makes one type cheaper. By put-call parity, a long call condor bought for $D$ is the iron condor with the same strikes sold for $W - D$, apart from interest (Chapter 5F). The CNDR evidence and the Edge Book's rejection of systematic condors therefore apply to it unchanged (Chapters 12C and 10I).

4 · Ratio spreads

Call ratio backspread

The ratio backspread's P&L is flat at $C$ below $K_1$. It falls with slope −1 to its low at $K_2$, then rises with slope +1, or +2 with three calls bought, without limit.

The put ratio backspread is the mirror image and the bearish backspread: sell 1 put at $K_2$ and buy 2 puts at $K_1$ below it. It profits big on a crash, which makes it an effective tail-hedge structure. Its maximum loss is $(K_2 - K_1) - C$, at $S_T = K_1$. It breaks even below at $2K_1 - K_2 + C$, and its profit reaches $2K_1 - K_2 + C$ if the underlying goes to zero.

Broken-wing butterflies

A broken-wing butterfly, often opened for a credit, is a butterfly with one wing wider than the other, which eliminates one side's tail risk. In the call version, you buy $K_1$, sell two $K_2$ and buy $K_3$, with the upper gap wider: $K_3 - K_2 > K_2 - K_1$. Opened for a credit $C$, it keeps $C$ below $K_1$ and makes its maximum, $(K_2 - K_1) + C$, at $K_2$. Above $K_3$ it loses $(K_3 - K_2) - (K_2 - K_1) - C$, and it breaks even at $2K_2 - K_1 + C$.

Suppose you buy the 5,950 call, sell two 6,000 calls and buy the 6,100 call for a hypothetical credit of 5. Below 5,950 you keep 5 points, and at 6,000 you make $50 + 5 = 55$. Above 6,100 you lose $100 - 50 - 5 = 45$ points, and you break even at 6,055. The put version widens the lower wing instead, which removes the upside risk.

5 · Income variants

Covered short straddle

Below the strike, the shares and the short put both lose, so the P&L falls with slope 2: highly negative gamma and double assignment exposure. Through put-call parity, shares plus a short call are a short put (Chapter 5F). The whole position is therefore effectively two short puts.

Suppose a stock is at $100 and you sell the 100 straddle for a hypothetical $8. The breakeven is $(100 + 100 - 8)/2 = \$96$. At $80, the shares lose $20 a share, the put costs $20 and the credit returns $8, a loss of $32 a share against $20 for the shares alone.

Covered short strangle

A covered short strangle holds 100 shares and sells an out-of-the-money put at $K_1$ and an out-of-the-money call at $K_2$, for a credit $C$. It gives modest income with less assignment pressure than the covered short straddle. The out-of-the-money strikes give the underlying room to move before either short leg goes in the money. Its maximum profit is $(K_2 - B) + C$ per share, and its maximum loss $B + K_1 - C$, if the stock goes to zero. The breakeven is $B - C$ if that lies above $K_1$, and otherwise $(B + K_1 - C)/2$.

6 · Other directional structures

Ladders

A ladder is a three-strike asymmetric structure: premium income with a capped profit zone and uncapped risk on one side. The bull call ladder buys a call at $K_1$ and sells calls at $K_2$ and $K_3$, which leaves an unbounded loss above $K_3$. For a net debit $D$, or a credit if $D$ is negative, it makes at most $(K_2 - K_1) - D$, between $K_2$ and $K_3$. It breaks even above at $K_3 + (K_2 - K_1) - D$.

The bear put ladder is the mirror image: buy a put at $K_3$ and sell puts at $K_2$ and $K_1$. It makes at most $(K_3 - K_2) - D$, between $K_1$ and $K_2$, and its loss grows below its lower breakeven, $K_1 + K_2 - K_3 + D$. Reversing every leg of a ladder turns it into its opposite, a position that pays for a large move on the open side.

For example, a bull call ladder on 6,000, 6,100 and 6,200 bought for a hypothetical 20 points makes at most 80. It breaks even above at $6{,}200 + 100 - 20 = 6{,}280$, and loses a point for every point beyond that.

Jade lizard

Provided the total credit is at least the call spread's width, a jade lizard has zero upside risk, leaving all of its risk on the downside. That condition is the defining feature of the structure. With a credit below the width, you hold a short put and a short call spread with risk on both sides, not a jade lizard.

Many published jade lizard examples, and some trading-platform builders, quote a call spread wider than the credit and still call the structure a jade lizard, which it is not. Verify that the credit covers the width before you rely on the no-upside-risk property.

The reverse jade lizard is the mirror image: a short out-of-the-money call and a short out-of-the-money put credit spread. It has no downside risk if the credit is at least the put spread's width. Its loss above the call strike is unbounded, from a breakeven at the call strike plus the credit.

Call and put ratio spreads, debit version

A ratio spread buys one in-the-money option and sells two out-of-the-money ones. It is a modest directional bet with premium income, but its risk is uncapped if the underlying moves through the short strikes. The call version buys $K_1$ and sells two $K_2$, for a net debit $D$. It makes at most $(K_2 - K_1) - D$, at $K_2$, and breaks even at $K_1 + D$ and at $2K_2 - K_1 - D$, above which the loss has no limit. The put version buys $K_2$ and sells two $K_1$. It makes at most $(K_2 - K_1) - D$, at $K_1$, and loses below $2K_1 - K_2 + D$.

The figure opens on the worked example's jade lizard. Lower the put premium or widen the call spread until the credit falls short of the width, and the right side of the chart turns from profit to loss.

put premium

42

call spread credit

9

call spread width

30

credit C = 42 + 9 = 51 ($5,100)

strikes 5,950 / 6,080 / 6,110

above 6,110: +21 points

breakeven K₁ − C = 5,899

A jade lizard. The credit of 51 covers the 30-point width, so above 6,110 the position keeps 21 points: no upside risk.

7 · Check yourself