What portfolio protection costs, and why volatility cannot time it

The short answer

Protection has a fairly stable price, and volatility cannot tell you when to buy it. Insuring a broad index fund with a one-year at-the-money put cost about 4.3% a year, which came to roughly 39% of what the fund returned over the same period. On a single stock the same insurance cost between about 8% and 10% a year, depending on the group. That cost held steady across three decades and four separate groups we tested, staying within about a point and a half either side of each group's own average.

The timing question came back the other way. Buying protection when a stock's own volatility was cheap looked like a good idea in the years since 2011 and a bad one in the years containing the dotcom decline and 2008. Not weaker in one and stronger in the other. The opposite sign, in every group we measured.

Cheap volatility does reliably buy you a cheaper contract. It does not buy you cheaper protection, because the contract is cheap in exactly the conditions where it is least likely to pay.

This is a study of market history. It is not advice, and it is not a strategy we sell.

What we tested

At every entry we recorded the underlying's trailing 63-day realized volatility as a percentile of its own prior three years, priced a one-year at-the-money put with Black-Scholes, and settled it against the price a year later. We also scored the pairing a portfolio owner actually holds: the underlying plus the put, against the underlying on its own. The gap between those two is the cost of being insured, and it is the number most of this study is about.

That ran over four groups and produced 100,469 entries from 435 instruments with enough history to measure. Two groups are single stocks: 144 our own screens rated favourably, and 275 others as a control. Two are funds: seven broad index funds and nine sector funds.

The funds are not padding, and for a study about puts they carry the result. Both stock groups are drawn from companies still tracked today, so firms that went to zero never appear. In our study of calls that gap flattered the numbers and made a negative finding safer to trust. Here it cuts the other way: it removes exactly the collapses that make owning a put worth it. An index fund cannot be picked for having survived, so where the funds and the stocks agree, the finding is safe. They agreed on everything below.

What insurance costs

The cost of holding the underlying plus a one-year at-the-money put, against holding the underlying alone.

A broad index fund returned 11.1% a year on average across these entries. Insured the whole way, it returned 6.8%. Over the whole sample, protection consumed between 36% and 43% of the return depending on the group. Split by period that share moves around a good deal more, between roughly 29% and 49%, because what the underlying returned moved too.

The steadier number is the cost itself. Within any one group it stayed within about a point and a half of its own average from one period to the next, which is what makes it worth quoting at all.

Buying a strike 10% below the current price costs less, as you would expect. On a broad index fund it ran about 2.7% of the fund's price against 6.2% for the at-the-money contract, and about 2.4% a year of drag against 4.3%. Single stocks are far dearer at both strikes, nearer 12% and 17% of the share price, which is most of why insuring one costs what it does. Treat these as a floor rather than a quote. Puts below the current price trade at higher implied volatility than the ones we could model directly, so the real figure is worse than the one we can show.

Cheap volatility did not time it

We applied the same signal from our study of calls to puts. The number below is how much better the cheap-volatility entries did than the expensive ones. Positive means buying when volatility was cheap was the better moment.

Every group changes sign between the last two columns. In the years containing a real decline, the expensive entries were the better ones, because volatility being expensive is itself the signal that something is going wrong. In the years without one, cheap entries won by default: almost nothing paid off, so paying less for it was the only thing left to measure.

The first column does not fit that explanation, and we would rather show it than leave it out. The years before 1996 contain 1973, 1987 and 1990, yet the number leans the same way as the calm period. It is the weakest column here: no funds existed to test, and the only companies old enough to appear are the ones that lasted. We take it as a reason to hold the explanation loosely, not as support for the rule.

A rule that reverses depending on whether the period contains a crash is not a rule. Fitted to the last fifteen years, it would have looked convincing right up to the first serious decline, which is the moment anyone holding it would be counting on it.

A fall inside the year is not the same as a payout

This one surprised us, and it is the most useful thing here for anyone actually considering a hedge. A standard put pays on where the price finishes, not on how far it fell along the way.

The gap between the first two columns is the part worth understanding. A fund that dropped 25% in the spring and finished the year down 5% never reaches the second column, and the put covering it was worth a fraction of the fall it appeared to insure against. In a smaller set of cases the fund fell more than 20% and still finished the year higher, so the put expired worthless in a year containing exactly the event it was bought for.

Scoring those windows by what the put actually returned, rather than by where the price went, gives the sharper version. Among the windows that did contain a 20% fall, an index put still lost money 38% of the time and expired worthless in about a quarter of them. On the rated stocks it lost money 55% of the time.

That is a fact about the contract, not about hedging in general. A position you can sell during the decline behaves differently, and this study does not model that.

It does work when the tail arrives

Restrict to the entries where the underlying really did finish at least 20% down, and the picture reverses. Index puts paid in every one of those 112 cases, averaging about four and a half times the premium. On single stocks they paid in about 89% of 5,743 cases, averaging a little over twice the premium.

The 100% is arithmetic rather than an achievement, and it would be misleading to present it as a result. A put struck at the current price on a fund that finishes 20% down is worth about 20% of the price against a premium near 6%, so it can hardly fail to pay. Single stocks fall short of 100% only because their premiums are so much larger that a 20% fall does not always cover the cost.

The instrument does its job. The difficulty is that you pay for it in every year the job does not come up, and those are most years.

What this study cannot tell you

The limits matter more here than another table would.

• No delisted companies, and it cuts the other way this time: the two stock groups contain only companies still tracked today. In our study of calls that flattered the results. In a study of puts it removes the collapses that would most favour them, so it makes these negative findings look better than they should. The fund groups carry the result for that reason.
• The strike most people buy is priced generously: we modelled the 10% out-of-the-money put at the same implied volatility as the at-the-money one. Real markets charge more for downside strikes, so that contract costs more than we show and the drag is worse. We did it that way on purpose: a discouraging result under generous pricing stays discouraging under real pricing.
• We had to estimate what the options cost: no long-dated implied volatility history exists to buy, so each contract is priced off the underlying's own realized volatility. We checked that estimate against live quotes for the earlier study and found it close. It is still an estimate.
• Held to expiry, never managed: no rolling, no adjusting, no selling the put into a decline. The finding about missed drawdowns follows directly from that choice, and a managed position would score differently.
• Overlapping windows: entries a month apart share most of the following year, so the real sample is far smaller than 100,469. That is why this study reports period splits and group comparisons rather than significance tests. No p-value here would be honest.
• Two errors that point in opposite directions: the price series adds dividends back, which understates what puts are worth, while the flat interest rate we used overstates it in the low-rate years. We have not tried to net them off, and we would rather say so than imply a precision we do not have.

What we did with the answer

We built nothing. This is the second options feature our own calibration step has stopped before we wrote any of it, and both times the study cost an afternoon against a year of waiting for a one-year contract to report.

The cost figures we kept, because they answer a question people actually have and the answer turned out to be stable. The timing signal we published as a failure, next to the earlier one, for the same reason we publish our misses elsewhere. You can see what we do publish, scored against what happened, on the public track record.