Tail hedges with far-OTM puts, and VIX products

A tail hedge is not meant to protect against a normal decline. It is meant to pay a great deal in the rare month when everything falls at once, and to cost a small, fixed amount every other month. Done with far out-of-the-money index puts, it is a budgeted bleed with a convex payoff. Done with VIX-linked products, it is usually a worse version of the same idea with several traps attached. This lesson prices the first and explains the second.

The tail put

A portfolio of $100,000 tracking an index ETF at $400 (250 shares' worth). Ninety-day puts 30% out of the money, strike $280, trade around $0.60 per share, $60 per contract. That is more than a lognormal model would say, because index put skew makes far-OTM puts relatively expensive; it is what they cost.

Set a budget rather than a hedge ratio: 0.5% of the portfolio per quarter, $500. That buys about 8 contracts, which cover 800 shares' worth of downside below $280, more than three times the portfolio's size. That over-coverage is the point of the structure: the puts are cheap enough that a crash pays several times the loss they were bought against.

At expiration the puts do nothing until the ETF is below $280, so a 15% or 25% decline is unhedged. That is what "tail" means. In a 40% decline the hedge turns −40% into −8.5%. In a 50% decline the portfolio finishes up.

Why you do not wait for expiration

The table understates the hedge, badly, because a crash raises implied volatility. Suppose the ETF falls 25% to $300 in the first six weeks of the quarter and IV goes from 18% to 60%. The $280 put, now 7% out of the money with about 45 days left at IV 60%, is worth roughly $20, not zero: 8 contracts are worth about $16,000 against a portfolio loss of $25,000. The expiration table said −$25,500 for that outcome; the mark-to-market says about −$9,500, and only if you sell.

That is the discipline of tail hedging: monetize during the spike. Sell some or all of the puts when IV explodes, or roll them down to lower strikes and take the difference in cash. A tail put held through the spike and back to calm can round-trip to zero while the portfolio recovers, and the hedger who did not sell will conclude that hedging does not work.

Tail put value during a sell-off (schematic, $280 put, 90 days)

  Value
  $20 |                              *  (IV 60%, ETF 300, 45 days left)
      |                        *
  $10 |                  *
      |            *
   $0.60 |  *  *  *                     <- entry (IV 18%, ETF 400)
      +----+----+----+----+----+----+
      400  380  360  340  320  300    ETF, with IV rising as it falls

The bleed

A calm year costs 4 × $500 = $2,000, 2% of the portfolio. Five calm years cost about 10%. There is no version of the strategy in which that money comes back unless the crash arrives; it is the price of the convexity. The questions to answer before starting are the same as for any insurance: what is the loss you cannot recover from, how much of your expected return will you pay to remove it, and will you actually keep paying in year four when nothing has happened. Tail hedgers who stop in year four are the ones who fund the payoff for the ones who do not.

VIX products

The VIX index measures 30-day implied volatility of S&P 500 options. It spikes in crashes, which makes "buy the VIX" sound like the ideal tail hedge. Four caveats:

1. You cannot buy the VIX. You can buy VIX futures, options on VIX futures, and exchange-traded notes and funds built from the futures. Each is a different thing.
2. VIX futures are usually in contango. In calm markets the futures trade above the spot VIX and decline toward it as they approach expiry. A long VIX futures position, and every long-VIX ETN that rolls them, loses money continuously from that roll. The best-known long-VIX note has lost more than 99% of its value since inception through a series of reverse splits; that is the roll cost, not a series of crashes. As a permanent hedge, a long VIX ETN is a far worse bleed than the tail put.
3. VIX options are priced off the futures, not the spot. When the spot VIX jumps from 15 to 30 in a day, the two-month VIX future might go from 18 to 24, and a VIX call on that expiry moves with the 24, not the 30. VIX options also settle on a special opening quotation on a Wednesday morning that can differ materially from the previous close. Traders who buy VIX calls expecting spot-VIX behavior are frequently disappointed.
4. Inverse VIX products can go to zero in a day. On February 5, 2018 the VIX roughly doubled in one session and an inverse-VIX note lost about 96% of its value after hours and was terminated. Anyone using inverse products as a "volatility income" strategy carries that outcome as a possibility, not a theory.

VIX calls have a legitimate role as a small, deliberate complement to index puts, because VIX can spike on events that move the index only modestly. As the primary hedge for a retail equity portfolio, far-OTM index puts do the job with fewer surprises.

Key idea: A tail hedge is a fixed budget, about 0.5% a quarter, spent on far-OTM index puts that cover several times the portfolio; it bleeds 2% a year in calm markets and pays multiples in a crash, and most of that payout is available only if you sell into the IV spike. VIX products are futures-based, bleed from contango, price off the future rather than the spot, and can disappear in a day when inverse.

Try it: Price the 90-day put 30% out of the money on a broad index ETF. Compute how many contracts 0.5% of a $100,000 portfolio buys and the notional they cover. Then, in the options profit calculator, mark those puts to market with the ETF down 25% and IV at 60% with 45 days left, and compare that to their expiration value at the same price.

Recap

• Tail puts 30% OTM cost about 0.15% of the portfolio per quarter each; a 0.5% budget buys coverage of several times the portfolio.
• At expiration they do nothing in a 15–25% decline and turn a −40% into roughly −8%.
• During the sell-off IV lifts their value far above intrinsic; monetize into the spike or the hedge round-trips to zero.
• The bleed is about 2% a year and is only recovered if the crash arrives.
• VIX products: futures contango bleed, options priced off futures with a special settlement, inverse products that can lose nearly everything in a session.