What Insurance Costs

Insurance is a transfer, not an investment

A hedge is an insurance contract, and insurance has a negative expected value by construction: the seller collects premiums that cover claims plus costs plus a margin. That is not a defect to be arbitraged away; it is the price of pooling a risk that would otherwise be borne entirely by one household. So the test that matters is not the average outcome. It is the specific question of whether the loss being insured would end the plan — a question the stress test in R12 is designed to answer. The cost is the part people underestimate. A put that costs 2.1% of the amount protected per quarter costs **8.4% a year**, and because it is rolled the cost compounds into a drag that is comparable to everything else in the plan: three years of continuous cover is 25% of the portfolio, or about $504,000 on $2,000,000. Against that, the payoff in a crash is the fall minus the distance to the strike — a 30% decline against a strike 5% out of the money pays 25%, or $500,000, so over a three-year window containing one generational quarter the hedge is nearly free. Over a decade containing none it is the most expensive line item in the plan. That asymmetry is the whole decision. The break-even per quarter is the premium plus the distance to the strike — **7.1%** in this example, since the market has to fall more than 2.1% of premium plus 5% of strike distance before the put pays anything at all. A market that falls 3% pays nothing, which is why a hedge sized for small wobbles is mostly a fee, and why a hedge worth having is one written against a loss the plan cannot absorb rather than against the discomfort of an ordinary correction. The hedge, priced — Premium per quarter: 2.1% of the protected amount · Cost per year: 8.4% — four rolls · Cost across three years: $504,000 — 25.2% of the portfolio ← · Payoff in a 30% quarter, strike 5% out of the money: $500,000 · Fall needed for one quarter to break even: 7.1% The strike distance and the premium both sit inside the break-even, which is why cheap-looking protection is usually protection that does not trigger.

Choosing the defence that matches the risk

Puts are one of five defences and rarely the best one, because each answers a different failure. **Cash** answers sequence risk and the need to fund spending in a bad year, and costs the return it does not earn. **Diversification across drivers**, from R10, reduces the size of the shock rather than transferring it. **Trend-following or a rules-based exit** was historically the most effective crisis defence of the cheap ones, because it reduces exposure after a decline begins rather than paying a premium in advance. **Shorter duration on the bonds**, after 2022, answers the specific failure of holding a long-duration asset as the ballast. And **options** transfer a defined loss to somebody else, at a cost that is high and certain. The choice follows from the diagnosis, which is why it belongs after the stress test rather than before it. If the scenario that breaks the plan is a 40% equity fall, then the answer is a smaller equity allocation, not a put programme. If it is a 40% fall in the next six months, with spending due inside that window, then cash answers it exactly and cheaply. If it is a tail so severe that no allocation change protects the plan, then options are the right instrument and the drag is the price of sleeping — paid knowingly, against a named loss, with the trigger written down and the roll schedule diarised. Two disciplines keep a hedge programme honest. The first is that the trigger and the size are decided in advance, because a hedge bought in the middle of a decline is expensive and one bought in calm markets is cheap; the decision to be protected belongs in the policy rather than in the mood. The second is that the cost is budgeted like any other expense rather than judged by whether it paid last year, because an insurance programme that is abandoned after two quiet years is almost perfectly designed to be uninsured in the third. Five defences, five failures — Cash: funds a bad year without selling — answers sequence risk · Diversification across drivers: shrinks the shock rather than transferring it · Rules-based exit / trend following: reduces exposure after a decline starts, with no premium · Shorter duration: answers the 2022 failure of long bonds as ballast · Options: transfers a defined loss — expensive, certain, and effective The most expensive version of this lesson is a hedge bought after the fall and abandoned after two quiet years. Both halves of that pattern cost money, and neither is a policy.

The price of insurance rises when you want it

A rolling hedge has a property that makes it different from any other recurring expense: its cost is not stable, and it moves with the same fear that makes you want it. Option prices rise with implied volatility, and implied volatility rises when the market is falling. So the month a hedge feels essential is the month it is most expensive, and the month it is cheapest is the month it feels unnecessary. The decision to start a hedging program is therefore usually made at the worst possible moment for the price, and the discipline that makes it work is the refusal to time it: a program is bought on a schedule, or it is not a program. The shape of the pricing is worth knowing precisely because it explains why naïve hedges disappoint. Downside puts are systematically more expensive than an at-the-money option implies, because the market charges more implied volatility for lower strikes — the skew. Part of that is crash insurance, part is the natural demand from holders protecting positions, and part is supply: writing downside puts is a business that blows up occasionally, so it is priced accordingly. A hedge bought at the bottom of the skew therefore has a permanently higher cost than the expected-move arithmetic suggests, and a hedge bought at a higher strike near the money is cheaper per unit of protection but pays out less when it is needed. That combination — cyclical cost, skewed price — is why a rolling program has to be evaluated over a full cycle rather than over a quarter. Three quiet years of premium is the price of being able to hold the position through the year that matters, and it is also the reason a hedge is a decision about whether you can tolerate the drawdown, not a way to improve the return. If the cost of cover over a cycle exceeds the damage of the drawdown you are insuring against, the honest conclusion is that you have chosen the wrong defence — smaller size or a different asset mix rather than a rolling option purchase. What makes the hedge expensive or cheap — Calm market: Cheapest cover, and the month it feels least necessary · Falling market: Most expensive cover, and the month it feels essential · Lower strikes: Extra cost from the skew: crash insurance is priced as such ←

Basis risk: hedging with something that is not the thing

A hedge is usually too small when it is designed and too late when it is needed, and the reason is that the instrument doing the hedging is almost never the thing being hedged. You own a stock and you short a sector fund, an index future, or a peer. What remains after that, when the two do not move together, is **basis risk**, and it is the part of the exposure the hedge does not address. The arithmetic is worth stating plainly. The residual exposure is the position’s own risk minus the part that the hedge explains, and the part it explains is set by the correlation between the two instruments — which is an estimate from a sample, and it changes. Two consequences follow. A hedge sized to a correlation of 0.9 leaves exposure that is real but often invisible, and the exposure grows if the correlation falls at the moment of stress, which is the usual direction. The classic version is the pair that diversifies in calm markets and converges in a crisis, when the common factor — a market-wide de-risking — overwhelms the difference between the instruments. The second source of basis risk is structural rather than statistical. A sector ETF may not hold your company’s weight in its index; a future may be cash-settled and expire before the risk does; a currency hedge may cover the translation exposure and not the economic one; an option may hedge the downside and cost a premium that must be funded from somewhere. Each of these is a difference between the hedge and the thing, and each shows up as a residual the plan has to own. There is also the distinction that decides which tool belongs in the plan: hedging and diversifying are different acts. Diversifying means holding exposures that do not all move together, and it is cheap and permanent. Hedging means taking an offsetting position against an exposure you already have, and it is a transaction with a cost, an expiry and a decision to reverse it. A portfolio of uncorrelated positions does not need a hedge; a concentrated book does, and it needs to know which correlations it is relying on. The practical discipline is to measure the hedge rather than to assume it. Track the correlation of the position and the hedge over a rolling window, and track the residual volatility with the hedge in place. A hedge that is not reducing the measured swing is not a hedge, it is a second position with an explanation. And size the hedge from the residual exposure you are willing to carry, not from the gross exposure you found uncomfortable — those are different numbers, and only one of them describes what is left after the trade. • A hedge is only as good as the correlation, and correlations fall when they are needed. • Index weights, settlement, expiry and currency each add basis risk that is structural. • Diversifying is cheap and permanent; hedging is a transaction with a reversal decision. • Measure the residual swing with the hedge on; if it has not fallen, the hedge is not one. The hardest version of basis risk is the hedge that works until it matters: two positions that are uncorrelated in ordinary markets and both long the same liquidity risk in a stressed one. Any pair whose common feature is “it works when the market is functioning” should be counted as one position.

Sources

• Negative expected value as the price of risk transferStandard insurance economics; expected-value pooling arithmetic
• Put options as portfolio insurance and its costOptions Industry Council education on protective puts; Taleb, "Dynamic Hedging"
• Trend following and cash as alternative crisis defencesHurst, Ooi & Pedersen, "A Century of Evidence on Trend-Following Investing"
• Tail-risk hedging programmes and their dragStandard practitioner literature on tail-hedging cost and carry