By Victor Haghani and James White¹
ESTIMATED READING TIME: 11 min.

Introduction

Is a stock market crash just around the corner? It’s a question on a lot of investors’ minds these days. In this note we’ll explore a few different approaches to answering this question, including a detailed explanation of our favorite.

Let’s start by reframing the question into something a bit more precise, namely: “What’s the probability that the U.S. stock market drops at least 30% from its starting level at any time over the next twelve months?”²

Before reading on, we’d appreciate it if you could share your personal estimate of the answer to this question here (note: at any time over the next year, not just at the end):

Pundits

Some well-known market observers see a big crash coming – e.g. Mark “the crash guy” Spitznagel, protégé of Black Swan author Nassim Taleb, Michael Burry of The Big Short fame, and Bridgewater founder Ray Dalio. For example, in a recent interview with the WSJ, Spitznagel said: “I do expect an 80% crash…but only after a massive, euphoric, historic blow-off rally.” A statement such as this suggests that Spitznagel believes there’s a greater than 50% chance of at least a 30% market sell-off coming in the foreseeable future, though he’s a bit vague about the exact timing, and the magnitude of the “blow-off rally” that will precede it. Amalgamating the statements of these market observers – even granting them credit for their past success – doesn’t seem like the best way to answer our question.

Prediction markets

With prediction markets all the rage these days, maybe we can find our answer there. Unfortunately, at the time of writing, Polymarket and Kalshi don’t have betting markets for the question we pose, though Polymarket takes bets on a “NYSE circuit breaker event in 2025”. This event traded at about 16% early in 2025, and has most recently traded at 4% with six weeks to go in 2025. A NYSE Level 1 circuit breaker event is triggered if the S&P 500 declines by 7% or more versus the previous day’s closing price.

Polymarket also has a listing for a U.S. recession by the end of 2026, and it’s recently traded at a 36% probability. The link between recession and a stock market drop isn’t a tight one, and also there’s only $30,000 wagered on this event. Who knows, maybe this note will encourage the listing of a prediction market on our definition of a stock market crash – that would be a welcome side-benefit to writing this note!

Surveys

As with the prediction markets, so with surveys; there aren’t any publicly available ones that ask our question. The closest one we’ve got is conducted by the Investor Behavior Project at Yale started by Professor Robert Shiller. Since 1989, it’s been collecting responses from individual and institutional investors to this stock market crash question:

What do you think is the probability of a catastrophic stock market crash in the U. S., like that of October 28, 1929 or October 19, 1987, in the next six months? (An answer of 0% means that it cannot happen, an answer of 100% means it is sure to happen.)

Unfortunately, their definition of a crash is not the same as ours, and we don’t have the detailed data from the survey. They publish an index of the percent of respondents who attach a probability of less than 10% of a stock market crash in the next six months. As of July 2025, 40% of institutions and 30% of individuals predicted a lower than 10% probability of a crash as defined in their survey.³

A rough conversion from the Yale survey result to the question we are asking might be to assign a 5% probability of a crash to those who answered “lower than 10%” and a 20% probability to those who estimated it above 10%. This gives us a blended probability of crash of 15% over the next six months, or a 30% probability of a “crash” in the next 12 months.

Ask the LLMs

ChatGPT, Claude and Perplexity gave estimates of 10%, 6% and 7% respectively. Their estimates were largely based on the historical frequency of such declines, slightly conditioned for current market valuation levels.

History

Following the lead of the LLMs, let’s take a look at U.S. stock market history. The chart and table below are based on daily U.S. stock market price data (excluding dividends). The frequency of stock market losses of greater than 30% over 12-month periods was 7%, spread over about ten episodes. Note that we’re measuring the maximum loss over the ensuing 12-month period from each date over the past 100 years.

In the table, we show the frequency of losses conditional on the starting level of the Shiller Cyclically-Adjusted Price-Earnings ratio (CAPE). While there was a slightly higher frequency of 30% or greater losses when CAPE was greater than 30x – 10% versus 7% – it does not strike us as being statistically significant.

The wisdom of crowds – what sayeth the options market?

The options market is where we can find an estimate that has the weight of real money behind it and is also forward-looking. However, translating options prices into the probability we’re looking for requires a few steps:

1. Find the price of a put option with an expiration about a year from today and a strike price about 30% below today’s stock market level. You can find options prices on Yahoo Finance. At the time of writing (closes as of Friday December 5th), the S&P 500 was at 6870; the price of a put option with a strike price of 4800 – 30.1% below the current S&P 500 price – expiring on December 18, 2026 was 74.0. We’ll also need the price of a one-year put option struck close to the current level of the market (i.e. an at-the-money strike).
2. Calculate and take the average of the implied Black-Scholes volatility of these two options. Yahoo Finance provides an estimate, or you can ask one of the LLMs, or you can use an option pricing calculator yourself. For the 4800 Dec. 2026 put option above, the implied volatility is 29.8%, and the at-the-money one-year put option had an implied volatility of 18.8%. The average is 24.3%.
3. This next step is a bit fuzzy, but important. We think it likely that the market-implied volatilities include a risk-premium, in which case we’ll want to haircut the number we arrived at above. There are at least two reasons for this: 1) stock market implied volatility goes up when the stock market goes down. The correlation between one-year implied volatility, measured by ^VIX1Y and the S&P500 over the past 19 years using monthly data, was -0.7, implying a Beta to the stock market of 1.4, and 2) arbitrageurs selling out-of-the-money put options hedge their sales with the objective of making a profit, after costs of hedging, and therefore price the options above their “fair” value. We don’t know what the exact reduction should be arising from these two sources, and it probably changes over time, but let’s go with a 10% reduction of the implied volatility we calculated above from 24.3% to 21.9%.
4. Now that we have an estimate of the relevant expected variability of the stock market, we need an estimate of its expected return over the next year. Our suggestion here is either to use a consensus forecast of a dozen or so investment firms (e.g. Blackrock, Vanguard, Goldman Sachs, etc.) or to use the Cyclically-Adjusted Earnings Yield (1/CAPE) plus forecast inflation. We then need to subtract the dividend yield from the total return estimate to arrive at the expected price return. We estimate this figure at 4.5% (3.5% earnings yield + 2.5% inflation – 1.5% dividend yield).
5. Given an expected return, and a variability of returns, we can now calculate the probability that the stock market finishes the year with a loss of 30% or more. The probability we get using our inputs is a 4% chance of finishing the year with a loss greater than or equal to 30%.⁴
6. We’re not quite there though, because the probability we’re after is that of a loss of 30% or more at any point over the next 12 months, not just at the end of the period. It might be that the stock market goes down 40% over the next seven months, then rebounds to finish the year at down 28%. An approximation of the full-year probability is to double the period-end probability we just calculated above. To see why, imagine that for every time the market touches down 30%, there’s a roughly 50/50 chance that it finishes the remainder of the 12 months going up or down, and finishing above or below that 30% loss. This “reflection” approximation results in an 8% probability of the stock market dropping by at least 30% some time over the next year.⁵ Without the adjustments we made for stock market risk premium and for stock market volatility also including a risk premium, the probability of our stock market crash would be 14%, considerably higher than our estimate of the “real world” probability.

Connecting the dots

Knowledge is the antidote to fear.
    – Ralph Waldo Emerson

While the 8% one-year crash probability we’ve inferred from the options market is a significant risk, it is considerably lower than the probability reported from surveys of both individuals and institutions and even more at odds with the views of celebrated market observers with a bearish outlook.

What should you do with this 8% probability? First, we hope that simply knowing this probability, and where to find it whenever you want to, transforms stock market crash risk from an “unknown unknown” into a “known unknown,” making stock investing a little more comfortable. We all recognize that the reason that stocks generally offer an expected risk premium above the return of safe assets is because of the significant variability of stock market returns, and so we doubt any investors will be surprised that there is a significant probability of a drop of 30% over the coming year.

What may come as slightly more of a surprise is that, using the approach described above, we find the probability that the stock market rallies by 30% at some point over the next year is 11%, noticeably higher than our “crash” probability despite 30% out-of-the-money put options being priced at 29.8% volatility while 30% out-of-the-money call options are priced at a much lower 13% volatility.⁶

When it comes to asset allocation, the primary drivers of how much you should invest in equities – assuming you’re only considering stocks and low-risk bonds – are 1) their expected return in excess of bonds, 2) their risk, measured by their overall variability relative to their expected return, and 3) your personal degree of risk aversion. As we explained in our book The Missing Billionaires, for typical values of the primary inputs described above, the optimal allocation to equities is affected hardly at all by the shape of the distribution of outcomes, holding expected return and variability of returns constant.⁷ As such, the probability of a crash – or for that matter, the probability of a loss to any horizon – doesn’t play a direct role in the asset allocation decision, and should be viewed more as an output from the return and risk distribution that drives the asset allocation decision.

Elm survey running tally

May the spirit of Aumann agreement theorem be with us all!

Technical Appendix

For readers who want to take a deeper dive, here’s exactly what’s behind our rule-of-thumb described in Steps 1 – 6 above to estimate the probability of a 30% drop over the next year based on the traded stock options market:⁸

1. We used the Heston (1993) options model to fit one-year at-the-money and 70% of spot options prices, as well as a few other strikes.
2. We then reduced the starting volatility in the model by 10%, and we set the drift of the stock market to 4.5% (net of dividend).
3. Using the model dynamics with those altered inputs, we calculated the probability of the stock market being down 30% sometime over the next year.⁹
4. Finally, we looked for the simplest rule-of-thumb readers could use to get close to that probability, and that resulted in what we described in steps 1-6 in the body of the article.

Further Reading and References

• Beckers, S. (1980). “The Constant Elasticity of Variance Model and Its Implications for Option Pricing.” Journal of Finance.
• Black, F., and M. Scholes (1973). “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy.
• Cox, J., and Ross, S. (1976). “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics.
• Giglio, S., Maggiori, M., Stroebel, J. and Utkus, S. (2021). “Five Facts about Beliefs and Portfolios.” American Economic Review.
• Goetzmann, W., Kim, D. and Shiller, R. (2024). “Emotions and Subjective Crash Beliefs.” NBER Working Paper No. 32589.
• Haghani, V. and White, J. (2023). The Missing Billionaires: A Guide to Better Financial Decisions. Wiley.
• Heston, S. (1993). “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies.
• Martin, I. (2017). “What Is the Expected Return on the Market?” The Quarterly Journal of Economics.
• Merton, R. (1969). “Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case.” The Review of Economics and Statistics.
• Merton, R.C. (1973). “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science.
• Rietz, T. (1988). “The equity risk premium: A solution.” Journal of Monetary Economics.

1. Thank you to Dave Blob, John Campbell, William Goetzmann, Saman Majd, Vladimir Ragulin and Jeffrey Rosenbluth for their helpful comments on this note, and to Vladimir Piterbarg, Leif Andersen, Jesper Andreasen, Peter Jaeckel, and all the other quants who weighed in on our use of the Heston option pricing model. This is not an offer or solicitation to invest, nor are we tax experts and nothing herein should be construed as tax advice. Past returns are not indicative of future performance.
   
2. In price terms, not total return.
   
3. The July 2025 survey response is close to the long-term average of this survey, which finds 35% of institutional investors and 30% of individual investors estimating a lower than 10% probability of a “crash” in the next six months.
   
4. We’ll use the cumulative Normal probability function, assuming that stock prices are log-normally distributed. The calculation is \(N(\frac{ln(1 – 0.3) – r_s + \frac{\sigma^2}{2}}{\sigma})\) where \(N()\) is the cumulative Normal probability function, \(0.3\) is the loss fraction we’re interested in, \(r_s\) is the expected return of the stock market price (net of dividends), and \(\sigma\) is the relevant stock market volatility input.
   
5. Calculating this probability more accurately, taking account of the fuller dynamics of the assumed stock price distribution gives us a probability of 8.4%, pretty close to the rule-of-thumb doubling of the probability of finishing down 30% or more.
   A few readers have observed that we could shorten this estimation process by getting the price of a one-year “one-touch” option struck 30% below today’s stock market level. This is an exotic option that pays $1 if the stock market touches the down 30% level. Unfortunately, even if this option was publicly quoted or available on a betting platform like Polymarket, we’d still need to adjust it for the risk premium in the stock market and the volatility market, but it would be a useful price to be aware of. The same goes for using the price of a tight put spread to estimate the probability of being just below down 30% in a year – we still need those same adjustments.
   
6. The primary reasons for this are: 1) the stock market has a 4.5% expected return making the call option just 25.5% out-of-the-money, while the put option is 34.5% out-of-the-money, and 2) if we believe stocks are lognormally distributed, then in log-space the call is just \(ln(\frac{1.3}{1.045}) = 22\%\) out-of-the-money, while the put option is \(ln(\frac{0.7}{1.045}) = 40\%\), or almost twice as far out-of-the-money.
   
7. See Exhibit 18.2, page 283.
   
8. See Martin (2017) for a deeper dive on inferring risk premium and crash probability from options prices. However, our understanding, which may be mistaken, is that Martin does not adjust options volatility for a risk premium, as we do, but rather uses the risk-neutral measure of options volatility.
   
9. We got a similar result using the Constant Elasticity of Variance model of Cox and Ross (1976) and Beckers (1980).