RET-PUT-001 · Read me first

Protective puts, and the benchmark almost nobody uses

The question. A retiree buys a rolling protective put. The insurance is overpriced — that is what insurance is. Does it still help? And crucially: does it help more than the free alternative of simply holding less equity, which also cuts drawdown and costs nothing?

Almost every published comparison sets hedged equity against unhedged equity. In that table the hedge always wins on drawdown and always loses on return, so both sides of the argument walk away with the answer they arrived with. It is not a test.

The test is the de-risked arm: no options at all, just a smaller share of equities with the rest in T-bills, swept across every weight from 100% down to 40%. That curve is what a plain two-fund portfolio delivers for nothing. A hedge has to land above it to have bought anything.

The four arms

All four withdraw the same real dollars on the same day from identical market paths.

Unhedged — 100% equities, selling shares to fund withdrawals. This is the arm carrying sequence-of-returns risk: a withdrawal during a drawdown removes shares permanently.
Protective put — the same, plus a rolling long put. The premium is paid by selling shares, because that is what it actually costs: shares gone, permanently, every roll, whether or not the hedge ever pays.
Collar — the same put, part-funded by a short call at the same tenor.
De-risked — no options. Equities and T-bills, rebalanced annually.

The put wing, and the mistake that was nearly made

Out-of-the-money puts cost more than at-the-money ones, because everyone wants crash protection and nobody wants to sell it. WHL-001 measured that skew properly from the Cboe SPY option chain and got −0.955 — but it fitted that on 30-delta puts one month out.

This study buys 15-delta puts three months out: further from the money and further out in time, in both cases outside the region where the number was measured. Re-measuring on the same chain at the strikes and tenors actually traded:

Window	Actual IV	Straight-line model	Error
20–40 DTE, 5–20 delta — the fit region	19.13%	19.16%	+0.03 pts
60–120 DTE, 5–20 delta — what this study buys	22.92%	26.78%	+3.86 pts

The fitted wing slope falls from −0.968 at one month to −0.646 at three. So the old number would have overcharged this hedge by nearly four volatility points — biasing the study toward the conclusion it already expected. The default here is the tenor-aware measured curve. Set the skew control to −0.955 to see what the unchecked extrapolation does to the answer.

Report every result at more than one price. A conclusion that only holds when the hedge is expensive is not a conclusion. The skew control exists so you can make the insurance cheaper than anyone could defend and see whether the answer survives.

Why risk is measured on NAV, not on your balance

Maximum drawdown of a withdrawing balance conflates two completely different things: a market crash, and slowly running out of money. A portfolio bleeding 3% a year in premium posts an enormous balance drawdown with no crash anywhere in it.

The first version of this study used balance drawdown and duly reported the hedged arm as riskier than the unhedged one — which a long put cannot be. So risk here is measured on NAV: the strategy's unit value, with the withdrawal treated as an external cashflow and the option premium charged to the strategy where it belongs. The balance drawdown is still reported beside it, because for a retiree it is a real question — it is just not a measure of market risk.

The mechanism that decides the answer

A 15-delta three-month put needs the index to fall about 9.5% inside a single quarter before it pays for itself. What that means for real declines:

A 45% fall…	Premium paid	Payoff	Share of the fall covered
in one quarter	0.82%	36.30%	80.7%
over three quarters	2.45%	27.89%	62.2%
over six quarters	4.90%	4.78%	10.6%
over ten quarters	8.17%	0.00%	0.0%

The strike resets at every roll, so a decline arriving in instalments is never seen. This single fact dominates everything else on the page — move the roll frequency and watch it.

Verification

Set the put delta to 0 and the strategy reproduces the unhedged benchmark exactly, in your own browser. Set the collar's call delta to 0 and the collar collapses onto the plain hedge, bitwise.
With skew at zero the option price matches textbook Black–Scholes, and put–call parity holds to 1e-8.
The unhedged arm reproduces RET-BILL-001's published equity survival rate on an independent random stream — 88.8% against 88.6%.
The bootstrap delivers falls of 9.5%-in-a-quarter at 1.01× the rate the real SPY series did, so the hedge is not being denied the events it exists for. (Measured against rolling 63-day windows; comparing against non-overlapping calendar quarters instead reports 2.15× and is a like-for-unlike comparison.)

What is not modelled

Every option is held to expiry. No selling the put into a volatility spike, which is how real tail programmes make their money. This caps how well the hedge can do here, and it is the most important limitation on the page.
No taxes. The premise is an IRA, which is also what makes cash settlement exact.
No timing. Hedging is unconditional and calendar-driven, not switched on when implied volatility looks cheap. That is the honest baseline any timing rule has to beat.
Contracts are continuous. Real puts come in 100-share lots, so a small portfolio cannot hedge precisely at all.
Fixed horizon, no mortality, and no Social Security or other income, so the portfolio carries all of spending.
Nothing here applies to tail funds. Deep out-of-the-money systematic long-volatility programmes buy convexity rather than insurance and monetise volatility spikes rather than holding to expiry. They are a different strategy and this says nothing about them.

Reproducing it

The engine on this page is a port of the reference implementation, and the two agree. Both are driven by the same measured pricing map.

RET-PUT-001/engine/verify.mjs — the gates above
RET-PUT-001/engine/run.mjs — the study
RET-PUT-001/notes/check-far-wing.py — the wing re-measurement
RET-PUT-001/engine/payoff-check.mjs and crash-shape.mjs — the mechanism table and the bootstrap check

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Model-based research, not investment advice and not a recommendation about any portfolio or strategy. Option prices are generated from realised volatility plus stated implied-volatility and skew assumptions, not from live quotes.