Economists have long puzzled over the simultaneous demand from consumers for risk-reducing insurance and risk-increasing lottery tickets. Every year, people spend trillions of dollars on the two combined. These behaviors may seem unrelated, but they are actually symmetrical forms of risk transfer.
The insurance policy is a means of risk transfer in which a buyer pays to eliminate the possibility of an extreme, rare downside event—such as a premature death, destruction from an earthquake or hurricane or an equity market crash—while the lottery ticket is a means of risk transfer in which a buyer pays to create the possibility of an extreme, rare upside event.
The price of such a risk transfer decomposes into two parts: an expected payout; and a risk premium to compensate the seller for the uncertain nature of any payout, which may be sudden and dramatic. Financial markets are full of strategies resembling either insurance or lotteries.
For example, in options markets, the premium to compensate the seller for the uncertain nature of the payout is called the variance (or volatility) risk premium (VRP). This risk premium is rational for both the buyer and the seller.
The buyer willingly pays it to create, or to eliminate, uncertainty. The seller charges for taking the risk. And the evidence is that, the more remote the risk, the higher the ratio of risk premium to expected payout.
The bottom line is that over a large sample size, there is an expected fair value set by the probabilities of outcomes, and option sellers charge a premium to that fair value to compensate the seller for providing a risk-transfer service.
The VRP refers to the fact that, over time, the option-implied volatility has tended to exceed the realized volatility of the same underlying asset. This has created a profit opportunity for volatility sellers—those willing to write volatility insurance options, collect the premiums and bear the risk that realized volatility will increase by more than implied volatility.
Investors are willing to pay a premium, because risky assets—such as stocks—tend to perform poorly when volatility increases. In other words, the market tends to crash down, not up. Thus, the VRP isn’t an anomaly we should expect to be arbitraged away. Because the risks of the VRP (the selling of options performs poorly) tend to show up in bad times (when risky assets are performing poorly), we should expect a significant premium.