Are investors too complacent about the likelihood of black swan events? Most of them are unwilling to hedge their equity portfolios against the possibility of disastrous loss even at times of huge market stress, such as during the global financial crisis. Perhaps the lack of observable black swan events—it is arguable whether the global financial crisis should be classified as a black swan event—has convinced investors they do not exist.

This belief has undoubtedly contributed to the large equity premium of stocks over government bonds. The author sets out to uncover just how much of this premium is actually due to the risk of a portfolio wipeout.

The so-called equity premium puzzle has been the subject of many earlier studies by academics. These studies have variously attributed the equity premium to tax distortions, market failures, implied volatility, and certain equity characteristics.

The author suggests a new approach to studying the equity premium. This approach relies on analyzing returns from 1983 to 2012 to see how much of the 7% a year equity premium was compensation for disasters that did not actually occur, which allows for determining the extent to which unrealized black swan events are responsible for the equity premium.

Disaster risk as a possible source of the equity premium has been examined before, but this study is the first to quantify that risk using put options. The author believes that analyzing the prices of deep-below-the-money index put options provides a more accurate measure of disaster risk. Indeed, buying such options enables investors to get protection against extreme market crashes in any one month. Such a hedge is comparable to getting protection against a one-off earthquake in an area that sits on a fault line but has not experienced any earthquakes in recorded history. So, deep-below-the-money index put options are a way to get protection against a plausible but infrequent occurrence—a black swan event.

Compared with a naked stock portfolio, a put-protected stock portfolio is much less affected by extreme market crashes, losing at most 15% in any one month. The total cost of the monthly put protection over the 29-year period was less than 2% a year. So, the “crash-insured” stock portfolio yielded about 5% a year.

This finding implies that sudden and huge stock market disasters account for around 2% of the 7% equity premium, which is sizable but clearly means that unrealized black swan events are responsible for only less than a third of the equity premium. To put this into context, the average sampling variation, whereby using different data gives different results, is 3%.

The author estimates that over the 29-year period, there was a 37% probability of a stock market disaster larger than the one in 2008. In terms of the magnitude of such a disaster, the author calculates a maximum crash of 60%–80%.

Intriguingly, the author found that fear of tail risk, as implied by the prices of the put options, was no greater than fear of ordinary volatility risk either before or after the global financial crisis.

For an investor, it is not irrational to believe in the possibility of an unprecedentedly terrible stock market crash, despite no record of such a crash occurring. Given the relatively recent return history, this study suggests that there is still a 37% probability that black swan events exist.

At most, a third of the superior stock market performance in the modern era can be attributed to black swan events. For an investor, this finding means that a drag of less than 2% a year is the cost of getting protection against extreme market crashes. The fact that few, if any, investors take out protection is a matter for reflection, particularly given the author’s showing that getting disaster risk protection is relatively cheap and does not have a material effect on fund performance.