Skip to content
Financial Context Wiki

Put Ratio Backspread: Crash Convexity with a Middle Loss Zone

For educational purposes only; not investment advice.

Direct answer

Section titled “Direct answer”

This article defines a 1-by-2 put ratio backspread as selling one put at a higher strike K_H and buying two puts at a lower strike K_L, with one expiration and K_H > K_L. It exchanges a loss zone near the lower strike for increasingly positive downside exposure below a lower breakeven.

The structure may open for a credit, zero cost, or a debit. A credit does not eliminate risk: the largest expiration loss occurs at K_L, where the short put is fully in the money by the strike width but the two long puts have no intrinsic value. A sufficiently deep decline makes the two long puts outweigh the one short put.

Names are not standardized across platforms. “Ratio spread” can also describe the opposite quantity relationship, which has a very different tail. Record every signed leg before using the name.

Piecewise expiration payoff

Section titled “Piecewise expiration payoff”

Let C be the net credit per share; use a negative C for a debit. Expiration profit per share is:

Π(S_T) = −max(K_H−S_T,0) + 2max(K_L−S_T,0) + C

  • S_T ≥ K_H: every put expires worthless; profit is C.
  • K_L ≤ S_T < K_H: only the short put has intrinsic value; profit is S_T − K_H + C. The upper breakeven is K_H − C.
  • S_T < K_L: both long puts contribute; profit is 2K_L − K_H − S_T + C. The lower breakeven is 2K_L − K_H + C.
  • The minimum occurs at S_T = K_L: C − (K_H − K_L). Maximum loss is therefore K_H − K_L − C, when positive.

For an equity bounded by zero, maximum expiration profit occurs at zero and is 2K_L − K_H + C per share. The downside gain is large but not mathematically unlimited. Before expiration, the two long puts usually give positive downside convexity and positive Vega, but actual Greeks vary with spot, time, volatility skew, and premium.

A 100/95 one-by-two backspread

Section titled “A 100/95 one-by-two backspread”

With the stock near 100, sell one 100 put, buy two 95 puts, and receive a 1.00 net credit. Using a 100-share multiplier and ignoring fees:

Stock at expiration Option payoff per share Profit/loss per share Position profit/loss
105 or 100 0 1 +$100
99 −1 0 $0
95 −5 −4 −$400
91 −1 0 $0
85 5 6 +$600
50 40 41 +$4,100
0 90 91 +$9,100

The upper and lower breakevens are 99 and 91. Maximum loss is $400 at 95; profit then rises as the stock falls below 91. A different net premium shifts both breakevens and the maximum loss, so the actual combination fill matters.

This is not the same as simply buying two puts. The short 100 put finances part of the purchase but creates the loss valley and an assignment obligation. It also differs from a bear put spread because the extra lower-strike long put restores increasing crash participation.

Risk and implementation checklist

Section titled “Risk and implementation checklist”
  • Confirm the −1/+2 quantities, common expiration, multiplier, and net credit or debit; reversing the ratio reverses the tail risk.
  • Calculate both breakevens and the loss at K_L, not only the attractive zero-price outcome.
  • Treat a credit as entry cash flow, not guaranteed profit. The underlying can finish in the middle loss zone.
  • American-style short puts can be assigned early. Assignment creates a stock purchase obligation even though long puts remain in the account.
  • Confirm cash, margin, and broker liquidation policies. A broker may close one leg if the account cannot support assignment.
  • Use a multi-leg limit order and inspect the combination market. Two long legs can magnify spread costs and slippage.
  • Stress test a slow decline, no move, volatility collapse, skew changes, and passage of time; the strategy is not a pure spot-only hedge before expiration.
  • Plan expiration around both strikes, including pin risk and whether the account can carry any resulting shares.

Common misconceptions

Section titled “Common misconceptions”
  • “The credit means there is no loss.” The strike-width loss near K_L can exceed the credit.
  • “It profits from every decline.” A moderate fall between the strikes can produce the maximum loss.
  • “Crash profit is unlimited.” For ordinary equity, zero bounds both the stock and the expiration payoff.
  • “Two long puts automatically prevent assignment.” They do not cancel the short put holder’s exercise right.
  • “It is just a cheaper long put.” It has two breakevens, an assignment obligation, and a distinct middle loss valley.
  • “A high IV always helps.” Skew and each leg’s IV can move differently, while time and spot also change net Vega.
Section titled “Related topics”

Authoritative sources

Section titled “Authoritative sources”