Put option strike versus deductible: what a fixed budget buys

A put's strike tells you where its expiry payoff starts; the number of covered units tells you how much of the portfolio receives that payoff. Under a fixed spending budget, those two quantities can move in opposite directions.

The main crash-protection article examines published evidence, contractual payoffs and recurring costs. This article instead holds starting capital and equity exposure constant to isolate a common analytical mistake: comparing strike percentages while ignoring coverage.

Key takeaways

• The strike sets where an expiry payoff begins; the covered quantity sets how much exposure receives it.
• Under a fixed budget, a higher strike can mean buying protection for fewer units.
• The invented premiums illustrate the arithmetic and do not quote executable protection or cap every portfolio loss.

Fix the portfolio before comparing contracts

Our hypothetical portfolio starts with $100,000: 980 equity units at $100, worth $98,000, plus $2,000 available for insurance. Three stylised puts share one expiry and the same underlying:

• A $95 strike costs $5 per covered unit.
• A $90 strike costs $2 per covered unit.
• An $80 strike costs $1 per covered unit.

These are invented teaching inputs, not observed premiums, current quotes or a valuation model. All amounts are nominal US dollars. There are no dividends, fees, taxes, interest or trading constraints. Payoff units are divisible for illustration, rather than actual exchange contracts.

We use at most $2,000 and never insure more than the 980 units owned. Money left over remains cash earning zero. That last rule prevents cheaper puts from silently turning the comparison into an oversized directional option position.

A higher strike can leave more equity uncovered

The $95 put buys coverage on 400 units, or 40.82% of the equity holding, using all $2,000. The remaining 580 units are unprotected.

The $90 put covers all 980 units, costs $1,960 and leaves $40 in cash. The $80 put also covers all 980 units, costs $980 and leaves $1,020. Equal spending caps do not require equal actual spending.

For each design, terminal wealth is:

980 × expiry price + covered units × max(strike − expiry price, 0) + residual cash

Values are hypothetical total portfolio wealth from the same initial $100,000. The strike, quantity and payoff CSV records all inputs and extra expiry-price scenarios.

At a 10% equity fall, the higher strike produces the largest portfolio value of these three designs. At a 20% fall, the $90 design produces more. The ranking changes because the $95 contract covers fewer units: once those 400 units are protected, the other 580 keep losing value as the underlying falls.

The deductible is not the portfolio's loss limit

A $90 strike on an underlying initially at $100 has a 10% spot-to-strike gap. Yet the fully covered $90 example ends at $88,240 for any expiry price below $90: an 11.76% loss on total starting wealth. The premium and the portfolio's initial cash allocation matter.

The deeper $80 design has a 20.58% maximum terminal loss here, equivalent to a $79,420 wealth floor under these assumptions. Its lower premium saves cash but leaves more of the initial equity loss with the owner. The $95 design has a higher per-unit floor, yet its uncovered units allow a 62% total loss if the underlying reaches zero.

For the distinction between the option's own profit and the package's return, see protective-put break-even.

What the comparison leaves open

It does not say which strike maximises geometric growth: no outcome probabilities or complete renewal path are specified. The assumed premiums deliberately create different coverage quantities; actual prices depend on maturity, implied volatility, skew and market conditions. A different price schedule can change the ranking.

The table also concerns a single expiry. It cannot show an intervening drawdown, a hedge sold early, or losses after the option expires. A fund holding different stocks from the option underlying has basis risk, even if its notional coverage looks complete. A standard contract multiplier may prevent the precise unit counts used here.