If you really believe that the market’s going to crash...

Siegfried Layda | Getty Images

Then do something about it.

One frequently hears a handful of statements among those who are under-invested in equities. "I can't handle the risk." "They're in a bubble." "I could wind up losing every penny."

Working backward, these assertions are true, arguable and most likely false.

To be sure, there is nothing to stop every publicly traded equity from going to $0 tomorrow. If an event permanently and unimpeachably eradicated the future earning potential of every company in the world, this would in fact occur. For instance, imagine that the Messiah arrived and used divine law to banish corporate profits. Or that a meteor wiped out every human on this planet save for a sole tribe of notorious tightwads. In either case, there would be no sense in paying even a penny for an ownership stake in any corporation, and assuming that the surviving investors are economically rational, the would drop by 100 percent.

Unlikely as such events may seem, the potential for utter catastrophe plays an important role in modern financial theory.

Academics have long puzzled over why stocks have done so well as compared to bonds. Why, they wonder, has the stock market returned some 10 percent in the average year since 1928, while short-term Treasury bills have returned just 3 percent? If humans (or at least financial markets) are basically rational, then who are these saps buying Treasuries?

A compelling answer, as laid out by Martin Weitzman in his 2007 paper "Subjective Expectations and Asset-Return Puzzles," is that a large part of this "equity premium" exists to compensate investors for disasters that did not occur. Just because the worst didn't happen does not mean the worst could not have possibly happened, and objectively high rates of return may simply be viewed as compensation for "bearing the extra risk of rare disasters in the left tail of the distribution that happen not to have materialized within the limited sample."

Or as Nassim Nicholas Taleb put in his first book, "Fooled by Randomness": "One cannot judge a performance in any given field (war, politics, medicine, investments) by the results, but by the costs of the alternative (i.e., if history played out in a different way)." Perhaps stocks have performed so well in hindsight simply because potential catastrophic events were continually dodged, making investing in stocks akin to playing Russian roulette.

A delightful illustration of this argument, brought up by both Weitzman and Taleb, is known as the "peso problem." In the mid-1970s, the Mexican peso was pegged to the dollar. So why, some wondered, were Mexican bank deposits paying a higher yield than comparable American ones?

This question was said to be only answered later, when the peg broke and the peso lost nearly half of its value — a catastrophic event for those who had been in the process of scraping yield from Mexico.

But there's a problem with the peso problem. The relevant question is: How much would it have cost to insure the value of the Mexican peso as compared to the U.S. dollar? If one could do this nearly costlessly — as one would have needed to be able to in order for it to be true that investors saw almost no chance of the peso losing its value against the dollar — then adding this insurance component to the long-Mexican-notes short-U.S.-notes trade would have made it a slam dunk even in the face of this catastrophe. On the other hand, if the cost of buying such insurance was prohibitive, then we can categorically say it was false that people thought it out of the question that the peg could be broken.

Zooming out a bit brings the situation into greater relief. It is a tenet of finance that risk and reward are related; without one, there can be little of the other. And why should there be? Why should others simply hand you money for free?

One cannot earn more than the risk-free rate when protecting against all risks (here, overall global bond yield risk and currency risk — though we could also add sovereign credit risk, counterparty risk, et al into the equation) unless the market is broken. As a corollary, one generally must try very hard to guarantee earning less than the risk-free rate.

When it comes to the peso situation, it is certainly plausible that some traders completely ignored the chance that the peso's peg could break. But these traders needn't have waited until after they lost their money to learn that this was conceivable; the market was telling them that at the time. If it wasn't, then others could have secured the yield differential risklessly. And like a rack of chips dropped on a busy casino floor, that free money would not have stayed unclaimed for long — soon being arbitraged back down to the risk-free rate.

Getting back to stocks, a recent paper by Ivo Welch entitled "The (Time-Varying) Importance of Disaster Risk" attempts to mathematically assess the cost of preventing oneself against a market catastrophe. Welch found that the cost of insuring oneself against a drop in the S&P 500 of 15 percent or more in every month from 1983 to 2012 was about 2 percent, which means that disaster compensation could not have possibly accounted for more than a third of the 7 percent equity premium.

Welch's work is based on a simple strategy of buying put options (which give their owner the right, but not the obligation, to sell at a given price within a given time period) and holding them alongside equity holdings, a strategy which would have yielded more than 5 percent per year. Of course, it is theoretically possible that the S&P could fall by 14 percent for any given number of months. Yet not only does this appear at least as unlikely as a one-month decline of 90 percent (and probably more, since as Welch points out, there's not really a place for such a situation within the mosaic of economic reality), it is not what is meant by "disaster."

"Either crash risk was not that important or below-the-money puts were significantly underpriced," Welch concludes.

Further, such a put-buying strategy is eminently pursuable, meaning that it makes for a cogent retort to the accurate point that an investor could wind up losing every penny in the market: Not if you buy put options you can't. (Side note: Alright, in a true 100 percent drop, those who have sold these options to you may not be able to make good on their promises; while one does not actually take on credit risk when buying publicly traded options since they are cleared through a reputable middleman, such a situation may leave a surfeit of able payers, destroying the middleman and leaving the options buyers holding the bag. Yet such a situation would probably also entail the bankrupting of every major financial institution and possibly the U.S. government as one might ordinarily expect it to serve as a backstop, so it's not clear that any other strategy would have been preferable.)

Interestingly, this is an even better strategy for those who believe, for whatever reason, that the stock market is in a bubble at the time they are contemplating investment. To the modern mind, bubbles are characterized by hoary exuberance that culminates in a righteous crash of Biblical proportions (and don't look back, lest you be turned into a pillar of salt). If you think the market is in a bubble, then you do not think the market will fall by 1 to 14 percent. You think it will either continue to soar, or plummet fantastically. Pairing 15-percent-below-the-money puts with your stock exposure is a great way to play such a situation. Sure, you are sure to eventually lose 15 percent, but your expected upside should be much greater.

And as of October 31, 2016, it doesn't cost 2 percent a year to insure against a crash; it actually costs less than 1 percent, before transaction costs. So what are the bubble-vision investors complaining about? If the stock market is actually in a bubble, then the buy-and-protect trade is a home run.

Oh, but all that's not for me, some might say. Even knowing I could lose 14 percent would keep me up at night. That's OK, I'll just buy Treasury bonds.

First of all, "it helps me sleep at night" is not a better excuse for investors than it is for alcoholics. Some things that are good for us are difficult.

More to the point, the trouble is that sticking to bonds is risky as well, just in a subtler way. Inflation has been 3.6 percent in the average year since 1950. The decline in purchasing power is not an accident; it is explicitly baked into our monetary policy. The Federal Reserve has an inflation goal of 2 percent. In other words, Janet Yellen is telling you that she wants your hundred dollar bill to be able to buy just $67 worth of goods in 2036.

And inflation could well run above its target — as well as above short term yields. In eight of the past 13 years, 1-year bills have yielded less than the inflation rate.

To put that in practical terms, if you gave your money to the government on the day before Christmas and got it back, with interest, on the day before next year's Christmas, in most of the years since 2002, you would have been able to throw a more extravagant party had you just spent the money straightaway.

Here's something for the bondholders to ponder as they're hitting their pillows: What if inflation runs at 13.5 percent, as it did in 1980? Will you really feel better knowing that the amount of money you hold has remained stable, even as its value has plunged? (For the curious: The S&P returned 32 percent that year, while short-term bills returned 11 percent that year and 10-year bonds lost 3 percent, according to data compiled by Aswath Damodaran.)

Obviously stocks are not perfect for everyone in every situation. If you can't stand short-term volatility, say because you have a big payment to your sleep coach coming due, then you're probably better off keeping your money in something stable.

But in many cases, those who say stocks are risky for them have not considered the ways in which they could mitigate these risks, or the risks of investing in supposedly safer assets.

And in particular, those who believe stocks are in a bubble appear to be leaving a great deal of money on the table.