Straddle or Strangle: Do the Breakevens

Question

Stock at 100. The 100-strike straddle costs 8. The 90/110 strangle (long 90 put, long 110 call) costs 3. Compute the expiry breakevens of both positions. What is the strangle's UPPER breakeven, and what's the real trade-off between the two structures?

Accepted Answer

Straddle (K = 100, cost 8): payoff |S_T - 100| must cover 8: S_T = 92 quadtextorquad S_T = 108. Strangle (90 put + 110 call, cost 3): below 90 the put earns 90 - S_T; above 110 the call earns S_T - 110; in between both die. Cover the 3: S_T = 87 quadtextorquad S_T = mathbf113. The trade-off, precisely: - Cost & worst case: strangle risks 3 vs the straddle's 8, but the straddle loses its full premium only at exactly 100, while the strangle loses everything anywhere in the whole 90–110 corridor. - Breakeven width: straddle needs an 8% move; strangle needs 13%. Wider goalposts are the price of cheaper entry. - Payoff convexity per dollar: on a 20-point move to 120, straddle nets 20 - 8 = 12 (1.5× premium); strangle nets 10 - 3 = 7 (2.3× premium). The strangle is the higher-multiple, lower-probability ticket, more "lottery-like" per dollar. - Greeks: the strangle carries less gamma and vega per structure (wing options), but much more per premium dollar, which is the budget that actually binds. The interview reflex: never compare option structures by premium alone; compare breakevens against your forecast distribution. If you expect a grind of 10%, the straddle wins (108 < your target <

Straddle or Strangle: Do the Breakevens

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