Protective puts and the cost of insurance

A protective put is the simplest hedge there is: own the shares, own a put, and the put sets a floor. Everything difficult about it is in the cost. Insurance that runs continuously costs a few percent a year, which over a decade is a large fraction of what the market returns, and the drawdowns it protects against do not arrive on schedule. This lesson prices the hedge honestly so that the decision to carry it, or not, is made with the numbers in front of you.

The menu

An index ETF at $400, 100 shares, $40,000. Implied volatility about 18%. Ninety-day puts:

The 5% put is close to the money and expensive; the 20% put is cheap because it pays only in a crash. Most continuous hedgers use something near 10% out, so take the $360 put as the working example.

P&L at expiration

100 shares plus one $360 put bought for $4.40.

100 shares + $360 put, 90 days

  +3,560 |                        /
         |                      /
       0 |--------------------/-----------
         |                  /
  -4,440 |________________/
         +----+----+----+----+----+----+
         280  320  360  400  440  480   ETF at expiry

The floor is at −$4,440, or −11.1% of the position: the 10% distance to the strike plus the 1.1% premium. Above $400 the hedged line runs $440 below the unhedged one. For the premium you have converted an unbounded loss into an 11% loss, and given up 1.1% of every quarter in which nothing happens.

The cost over time

Nothing happens in most quarters. Suppose the hedge is rolled every 90 days for ten years:

• Premium paid: about 4.4% of the position per year, roughly 44% of the starting value over the decade, before any change in IV.
• What it bought: a loss capped at about 11% in any single 90-day window.

Whether that is a good deal depends on how often and how far the market falls within a 90-day window, which is not knowable in advance. Over the long run, continuous full-size put protection on a broad index has cost more than it paid; that is the same volatility risk premium that funds the premium sellers in Modules 2 and 3, viewed from the buyer's side. It has also, in specific years, been the only thing between a portfolio and a 30% drawdown. The honest description is: a protective put is an expense, not an investment, and it is bought for the same reason as fire insurance.

Reducing the cost without removing the floor

• Hedge part of the position. One put against 200 shares halves the cost and halves the floor. The floor becomes about −20% on the whole position, which many holders find acceptable.
• Buy longer-dated, roll earlier. Option premium grows with the square root of time, so a one-year 10%-OTM put costs about $8.80, or 2.2% for the year, against 4.4% for four quarterly puts. Roll it when about 90 days remain, when it still has value, rather than letting it decay to zero.
• Hedge around known windows. Buy protection into an event or a period you are worried about and let it lapse otherwise. Cheaper, and it requires you to be right about when to be worried, which is a forecast.
• Use spreads or collars (next lesson) to sell something against the put.
• Monetize the hedge when it pays. A put does not have to be held to expiration. In a sharp sell-off IV rises and the put's value jumps by more than its intrinsic value; selling it then, or rolling it down to a lower strike and pocketing the difference, captures value that the expiration table does not show.

What the put does not do

• It does not protect against a slow decline that stays above the strike; at $380 the hedged position lost more than the unhedged one.
• It does not protect against a decline that starts after the put expires; the roll date is a gap unless you roll early.
• It does not reduce the position's delta by much until the market has already fallen; the $360 put's delta is about −0.22 at entry, so the hedged position still has 78% of the shares' exposure on day one. That is by design, and it is also why the first 10% of a drop is felt in full.

Key idea: A protective put sets a floor at strike minus premium and costs a few percent a year to maintain, which over time is more than it pays back on average; it is fire insurance, not a return-enhancer. Buy it for the tail, size it to the loss you cannot accept, use longer dates and early rolls to cut the cost, and sell it into the spike when it pays.

Try it: Price 90-day puts 5%, 10% and 20% out of the money on a broad index ETF. Fill in the cost table above with real numbers and annualize. Then price the one-year 10%-OTM put and compare its annual cost to four quarterly rolls. Decide which fraction of your own portfolio, if any, you would insure at that price and write down the resulting floor.

Recap

• A 90-day 10%-OTM put on a $400 ETF costs about 1.1% of the position, about 4.4% a year if rolled continuously.
• The floor is strike minus premium: −11.1% in the example, versus an uncapped loss unhedged.
• Over long periods, continuous protection has cost more than it paid; it is an expense bought for the tail.
• Cut the cost with partial hedges, longer-dated puts rolled early, event windows, or spreads and collars.
• Monetize the put during a volatility spike; do not wait for expiration.