Buying AMZN puts: hedge math and breakevens

A long put is the right to sell 100 shares at $270 until August 28, 2026. Max loss is the $850 premium; max profit is $26,150, reached only if AMZN goes to zero.

Below $261.5 the position is in profit at expiry, gaining one-for-one with each dollar the stock falls. Above $270 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 $270 at the cost of 3.1% of position value — an annualized drag of 42.3% 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 $270 at August 28, 2026 costs the full $850, and stocks drift up more often than down.

If you are hedging, be clear about what you are insuring. One put covers 100 shares — $27,158 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 Aug 28 strikes are $5 apart near the money (1.84% 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. 16k contracts of open interest on Aug 28 is workable around the money and thin in the wings — width costs more here than the ladder suggests. 23 strikes on that expiry — 50% 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.

Skew is inverted: the 25-delta CALL implies 1.3% more vol than the put. That is the market pricing upside risk above downside risk — a squeeze, a takeover rumour, or a crowded short. Owning upside on an inverted skew means paying the expensive side of the surface, which is worth knowing before you buy the call. The term structure is flat inside 1.5% between the two captured expiries, so there is no calendar edge to harvest and no event visibly priced into one month over the other.

At 33% ATM implied vol, the Aug 28 options are pricing a one-standard-deviation move of $24.05 over 27 days — roughly −8.9% to +8.9%, or $247.53 to $295.63. 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.