The Free Fence

Question

You hold stock at 100. You buy the 90 put and finance it fully by selling a call, premiums net to zero. Describe your expiry payoff, explain what you gave up for the "free" insurance, and predict: given equity skew, will the zero-cost call strike sit closer to spot or further than 110?

Accepted Answer

The payoff. Stock + long 90 put + short K_c call clamps your terminal value: textvalue at expiry = minbig(max(S_T, 90), K_cbig) , floored at 90 (the put kicks in), capped at K_c (shares called away), one-for-one with the stock in between. A "fence" or collar. What you gave up: the upside beyond K_c. Zero cost is not zero price, you paid with the right tail. There is no premium check written today, but the position's expected return is reshaped exactly as if you'd bought insurance and funded it by selling your lottery ticket. (Identity: collar = bond paying 90 + the 90/K_c call spread, a fully bounded position.) Where skew puts the call strike. Equity skew prices the 90 put at a higher implied vol than symmetric-distance calls, you are buying the rich wing and selling the cheap one. Dollar-for-dollar, you must therefore sell more moneyness of call than you buy of put: the zero-cost call strike sits closer than 110: perhaps 106–108, i.e. the fence is asymmetric against you. Candidates guessing "110 by symmetry" have ignored both skew and the forward. (Working against that, the forward sits slightly above spot with rates, nudging call values up; in index markets the skew effect domina

The Free Fence

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