Ratio Spreads And Backspreads

A butterfly spread buys and sells options in a fixed 1:2:1 ratio, and that particular balance is what caps its risk on both sides. Break that balance on purpose — buy one option and sell a different count of another, or sell one and buy more of another — and the payoff stops being a symmetric tent and starts leaning hard toward unlimited risk on one side, or unlimited reward on one side, depending on which way you tilt it.

Buying an insurance policy with someone else's premium

A ratio spread is like buying one flood insurance policy and, to help pay for it, selling two policies on a smaller, drought-prone patch of land you don't actually own — you collect enough extra premium from the two you sold to make the one you bought nearly free, but now you're exposed if that smaller patch floods badly, because you sold more protection than you bought. A backspread flips this: you sell one cheap, close-to-the-money option and use the proceeds to buy several further-out options, so you're paying almost nothing net (or even collecting a credit) for a position that does very little near the money but pays off explosively if the stock makes a big move — the opposite trade to a butterfly's bet on stillness.

The formula

A call ratio spread, selling $n$ options for every 1 bought:

$$\text{Payoff}_T = (S_T - K_1)^+ - n(S_T - K_2)^+, \qquad K_2 > K_1, \; n > 1$$

In plain English: below $K_1$ the payoff is zero. Between $K_1$ and $K_2$ it rises with the single long call, just like a normal call spread. Above $K_2$, the $n$ short calls now outweigh the 1 long call, and the payoff falls at a rate of $(n-1)$ times the stock's move — for every dollar the stock rises past $K_2$, you lose $(n-1)$ dollars, unbounded as the stock keeps climbing. Flip the direction — buy $n$ options at the higher strike, sell 1 at the lower — and you get a backspread: capped, small loss near the money, unlimited gain as the stock runs far past $K_2$, because now you own more contracts than you're short.

Worked example 1: a 1x2 call ratio spread, and where it turns dangerous

Buy one $100 call at $6.00, sell two $110 calls at $2.50 each. Net cost: $-6.00 + 2 \times 2.50 = -6.00 + 5.00 = -1.00$, i.e. you receive $1.00 up front. Below $100, payoff is $0, profit is $1.00 (the credit). Between $100 and $110, payoff is $S_T - 100$; at $S_T = 108$, payoff is $8, profit is $8 + 1 = 9$, i.e. $9. Above $110, payoff is $(S_T - 100) - 2(S_T - 110) = -S_T + 120$, which falls as the stock rises. At $S_T = 130$: payoff is $-130 + 120 = -10$, i.e. -$10, profit is $-10 + 1 = -9$, i.e. -$9. At $S_T = 150$: payoff is $-30$, profit is $-29$, i.e. -$29. There is no floor on the loss as the stock keeps rising — this trade looks like free premium collection right up until a large rally turns it into an uncapped loser.

Worked example 2: a call backspread, the mirror image

Sell one $100 call at $6.00, buy two $110 calls at $2.50 each. Net cost: $+6.00 - 5.00 = 1.00$, i.e. $1.00 received. Below $100: profit is a flat $1.00. Between $100 and $110: payoff is $-(S_T - 100)$, so at $S_T = 108$, payoff is $-8$, i.e. -$8, profit is $-8 + 1 = -7$, i.e. -$7 — this is the trade's worst zone. Above $110: payoff is $-(S_T-100) + 2(S_T-110) = S_T - 120$, which rises without bound as the stock climbs. At $S_T = 150$: payoff is $150 - 120 = 30$, i.e. $30, profit is $31. The maximum loss, -$7 at exactly $108 in this example (found by checking the boundary), is small and fixed; the upside above $110 is unlimited. This is a bet that either nothing happens or something big happens, and it loses in the narrow zone in between.

Start from a plain bull spread here to see the 1:1 balanced case, then imagine doubling the short leg's quantity — that's the ratio spread from Example 1, and the payoff line beyond the second strike tilts downward instead of staying flat.

What this means in practice

Ratio spreads are used to collect premium in range-bound markets when a trader is willing to accept tail risk on a big move, often paired with a stop-loss or a further hedge to cap the uncapped side — many brokerages require significant margin for exactly this reason. Backspreads are a favorite structure ahead of binary events (earnings, FDA decisions, court rulings) where a trader believes the outcome is either "nothing happens" or "something enormous happens," and wants to pay very little for exposure to the second case.