Married (Protective) Puts

A married put strategy involves buying an asset, such as shares of stock, and simultaneously purchasing put options for an equivalent number of shares. Each put option contract typically covers 100 shares and grants the holder the right to sell the stock at a predetermined strike price within a specified period, usually three months.

How it works:

Purchase Stock and Puts Simultaneously

You buy shares of a stock and at the same time, purchase put options for the same number of shares.

Set a Price Floor

The put options act like an insurance policy, setting a price floor for your stock. If the stock price falls below the strike price, you can sell the stock at the strike price, limiting your losses.

Let’s say you own 1,000 shares of ABC stock, purchased at $56 per share, totaling $56,000. To protect against a potential price drop, you buy puts for 1,000 shares at a strike price of $52. The total cost of the put options is $2,000 ($2 per share).

Write $S_T$ for the stock price at expiration and $K$ for the put’s strike. Your position value at expiration is $\text{max}<!--\; FUNCTION\; APPLICATION\; -->(S_T,K)\times 1,000$ — the shares are worth whichever is higher, because below $K$ the put lets you sell at $K$ — and your profit or loss against the $56,000 you started with is

Note what that produces at $50 — exactly the put’s breakeven, where the hedge has cost precisely what it saved:

Read the table, not the sales pitch. The put does nothing for you at $50 and costs you money in every scenario above it. Its entire value is delivered in the bottom row and everything below it: at $40 the unhedged position has lost $16,000 and the hedged one is still capped at $6,000, and that cap holds if the stock goes to zero. You are not buying a better average outcome — you are buying a floor, and paying about 3.6% of position value for three months of it. Whether that is worth doing depends entirely on whether a 40% drawdown in this position would change your life, not on whether you think the stock will fall.

To calculate optimal options strike prices in a protective put strategy, you need to balance the cost of the put option with the level of downside protection you desire. Let the current stock price be $S$, desired protection level $K$, and option premium for defined $K$ as $P(K)$. The trade-off lies in the strike price selection:

Higher Strike Price (Closer to S)

Offers more protection but comes with a higher premium.

Lower Strike Price (Further from S)

Reduces the premium cost but provides less protection. Higher potential returns if the stock doesn’t drop significantly.

Mathematically, the protective put position — stock and put together, which is the whole point — pays off at expiration as

where $S_T$ is the stock price at expiration and $S_0$ your entry price. The $\text{max}<!--\; FUNCTION\; APPLICATION\; -->(K-S_T,0)-P(K)$ formula you will see quoted describes the put alone, not the hedged position, and omitting the stock leg is how people talk themselves into believing a protective put is a directional bet. Since $S_T$ is unknown, the choice of $K$ is a choice about which outcomes you are willing to own.

Practical Applications The protective put is the right structure when you must hold the shares through a window in which you cannot afford a large decline — a planned sale for a known expense, a lockup, a concentrated position you are unwinding on a schedule — and the wrong structure as a standing policy, because the premium is paid every period and the floor is used in few of them. Its extension to positions you cannot sell at all is section “Asymmetric Tail Hedging for Concentrated Equity”.