Puts are valuable beyond their payoffs

Loss comes with loss of opportunity

For the business of options market making to be viable, options have to be sold on average above their cost of hedging. Hence, the volatility risk premium. This means options on average are sold above their expected payoffs. This is no different than a manufacturer charging a price above cost of goods sold.

What's in it then for the buyers?

In short, continued access to optionality. Options are insurance. It's valuable beyond expected payoffs because when you lose, you actually lose twice. Whenever you lose money, you also lose access to the opportunity set of the money you lost.

A real world example can be found in option market making.

Market makers buy out-of-the-money puts, knowing full well they're expensive in terms of volatility risk premium. But volatility risk premium doesn't tell the full story. It's an objective metric. It ignores the subjective value for the market maker to continue doing business during the times where these puts pay off.

When volatility picks up, the profitability of market making increases exponentially: higher volume, wider spreads, and market share concentration. A market maker can't afford to be constrained by losses or elevated margin utilization during these windows of opportunity and should be willing to pay for options that allow monetizing a fast market.

In other words, they pay premium to operate in prime market conditions.

Puts if you're bullish?

The same duality between the objective value of payoffs compared to the subjective value of optionality takes center stage when debating the simple question of whether it's worth hedging a long position with puts.

As a starting point, if you systematically buy puts, you should expect to lose money. The puts stand-alone will cost more in premium than they give back in payoff, especially for an asset like Bitcoin, which drifts upwards over time.

The merit of tail hedging could be dismissed on these grounds. The puts lose money so you're better off not hedging?

This misses the optionality of reinvesting the payoffs from puts.

If you buy and hold Bitcoin and protect downside with puts, the cash you get during drawdowns can be used to buy more Bitcoin.

Think of the puts as midfield defence. Their job is to intercept the ball and start a counter-attack. At a portfolio level, the puts 'intercept' losses and allow to counter-attack by buying the underlying during dips.

While the puts may be a losing trade in isolation, their effect at the level of your portfolio, if rebalanced, is to increase your Bitcoin exposure over time.

By reducing risk, the hedge pays itself back by allowing you to take more risk over time.

Implementation questions

While the concept of a tail-hedged long portfolio is straightforward, there are many implementation details to consider. For instance:

• Which strikes and maturities do you select for the puts?
• Do you delta-hedge the puts?
• What is your rolling strategy over time?
• How do you monetize the puts?
• How to adjust for cheap versus expensive IV?

For further reading on this topic, we recommend Common Hedging Discussions part one & two by Benn Eifert, which can be found under QVR's research section on their website: Research — QVR Advisors.