Buying AMZN puts: hedge math and breakevens

A long put is the right to sell 100 shares at $250 until October 30, 2026. Max loss is the $1,115 premium; max profit is $23,885, reached only if AMZN goes to zero.

Below $238.85 the position is in profit at expiry, gaining one-for-one with each dollar the stock falls. Above $250 it expires worthless — which is the good outcome if you own the shares.

Puts carry a structural headwind: skew. Downside strikes on AMZN trade at higher implied vol than equivalent upside strikes because everybody wants the same protection at the same time. You are buying the expensive wing, always.

As a hedge on 100 shares, this put caps the loss below $250 at the cost of 4.5% of position value — an annualized drag of 49.4% if you run it continuously. That is the honest price of permanent protection, and it is why most people don't.

The modal outcome for a bought put is expiring worthless. AMZN above $250 at October 30, 2026 costs the full $1,115, and stocks drift up more often than down.

If you are hedging, be clear about what you are insuring. One put covers 100 shares — $24,967 of AMZN. A hedge that covers a quarter of your position is a quarter of a hedge.

Time is the cost you cannot hedge. A debit structure needs the move and needs it before expiry, and being early is indistinguishable from being wrong once the contract settles.

Amazon's directional character is two-sided in a way the mega-cap peers are not: retail margin and cloud growth pull the stock in different directions on the same print. A call spread expresses the cloud view and a put spread expresses the margin view, and traders who hold both at once discover they have paid twice for one opinion.

AMZN's Oct 30 strikes are $5 apart near the money (2.00% of spot). On a ladder that wide, "pick the 0.30 delta strike" resolves to whichever rung happens to be closest — sometimes not close at all. 146k contracts of open interest on Oct 30 is deep enough that multi-leg orders fill near mid at retail size. 29 strikes on that expiry — 100% of the board — carry prints that agree with their own implied volatility and hold up across the ladder, and those are the strikes priced here. Deep at every strike; the far-dated back month a calendar needs is liquid enough to leg if you must.

The surface is close to flat: only 0.2% between the 25-delta put and the 25-delta call. With so little skew, the wings on either side cost about the same in vol terms — unusual, and worth exploiting if your view is one-sided. The term structure is backwardated — Oct 30 implies 2.0% MORE vol than the following month. That is the signature of a dated event inside the front month, and it is the strongest argument for picking the expiry that sits behind it.

At 40% ATM implied vol, the Oct 30 options are pricing a one-standard-deviation move of $30.04 over 33 days — roughly −12.0% to +12.0%, or $219.63 to $279.71. Compare that with where the short strike of the structure above sits. A target inside the implied move is one the market already thinks is likely; a target outside it is the one you are actually being paid for.

The AMZN-specific failure mode: Buying the holiday-quarter straddle because the narrative is loud. That print's implied move is usually the year's largest and usually adequate.