1. The protective put: what the insurance costs

Derivatives 5: Hedges and strategies

This whole level works with the same portfolio, so it is worth pinning it down now and not moving it: 200 units of an S&P 500 ETF trading at 500 dollars. One hundred thousand dollars exactly. Since each options contract covers 100 units, two contracts are enough to cover the entire portfolio. Every figure in the four modules comes from here.

The idea that organizes the level can be stated in one line: a hedge does not eliminate risk, it swaps it for something else, and that swap always has a price. The investor's job is not to learn recipes, it is to know how to work out that price and decide whether it is worth it.

What you are buying exactly

Buying a put is buying the right to sell at a fixed price. If the ETF collapses, that right is worth money; if nothing happens, it lapses worthless and the premium is gone. Suppose a put with a strike price of 450 — 10% below today's price — at twelve months, with an assumed premium of 15 dollars a unit. That is 1,500 dollars a contract and 3,000 dollars for the two: 3% of the portfolio's value, paid up front, to insure a year.

That premium is not the seller's whim. It comes out of implied volatility and the horizon, and what matters for what follows is that implied volatility has systematically exceeded the volatility subsequently realized. That difference has a name — the volatility risk premium — and it means that, on average, whoever buys protection pays an expected mark-up. It is not a swindle: it is what is charged by whoever agrees to take on your tail risk. But it is worth knowing that insurance is sold with a margin, just like any other insurance.

The policy's three numbers

A protective put is described completely by three figures, and in this order:

• The excess. Between 500 and 450 there are 50 dollars a unit that you pay in full. Ten percentage points of fall the policy does not cover.
• The premium. 3,000 dollars, 3% of the portfolio, unrecoverable whatever happens.
• The expiry. Twelve months. Once those months are up there is no cover, and renewing it means paying again at whatever the price is then.

Where the floor really sits

This is where most people's intuition fails. If the ETF sinks to 300, you exercise the put and sell at 450: the portfolio is worth 90,000 dollars. But you have paid 3,000 in premium, so your real wealth is 87,000 dollars, 13% below the starting point. The floor is not at the strike price; it is at the strike price minus the premium. And that floor does not fall even if the market collapses 60%: that is exactly the part you have bought.

Translated: you have paid 3% to turn an indeterminate worst case into a known worst case of 13%. It is worth putting it that way, because it is the only thing the policy really buys. It does not buy return, it does not buy a correct directional call and it does not buy peace of mind in the stretch from 500 to 450, which is where the vast majority of frights happen. It buys a limit.

When the market rises, the premium is a dead loss

Bullish scenario: the ETF closes the year at 560, 12% up. The portfolio is worth 112,000, the put lapses worthless and you have spent 3,000. Net result: 109,000, 9% against the index's 12%. You have not lost money, but you have given up a quarter of the rise. Repeat that through a long bull run and the difference stops being cosmetic.

The sum almost nobody does: repeating it for several years

3% a year does not sound like much. Compounded it is: five years of continuous protection leave a drag of around 14% on the portfolio's value, and ten years, around 26%. That is the cost of the policy before anything happens at all.

Let us set it against what the policy pays. With the 450 put and five premiums of 3,000, you have laid out 15,000 dollars. To get them back you need a payout from the option of 15,000, that is 75 dollars a unit below 450: the ETF would have to close below 375, 25% below the starting level. With a 30% fall, to 350, the put pays 20,000 and the protection has been worth it by 5,000 dollars. With a 20% fall, to 400, it pays 10,000 and you have lost 5,000 in the attempt. And if in those five years there is no fall greater than 10%, you have thrown away the whole 15,000.

That asymmetry explains an uncomfortable but well documented result: the indices tracking a systematic protective-put strategy on the S&P 500 show far smaller maximum drawdowns and lower volatility, but a cumulative return below that of the naked index over most of the long periods measured. Permanent protection works as protection; it does not work as a way of making more money. Whoever buys it is paying to sleep, and sleeping has a tariff.

A real anchor

In 2020 the S&P 500 fell around 34% between its high of February 19 and the low of March 23, and the VIX closed on March 16 above 82, its highest close on record. An investor holding the 450 put on that day had a valuable position. Now the part that rarely gets told: the market recovered its previous high in August of that same year. If your put expired in December and you did not sell it in the panic, it ended up lapsing worthless despite your having called the fall spot on. A hedge does not merely require the disaster to happen; it requires it to happen inside your window and it requires you to do something with it while it is worth something.