Zero-Day Options

The risks and returns of selling lottery tickets
 

By: Noah Kreutter

About a year ago, the Chicago Board of Options Exchange implemented a noteworthy change to the options market: they began offering index options on the S&P 500 that would expire every trading day. Traders had long had a fascination with “zero days to expiration” options (aka 0DTEs) but, until this change, investors had to just buy longer-dated options on the day they happened to expire. However, the progressive march of financial innovation now empowers investors to express a view on intraday realized volatility every day of the week.

Trading these ultra-short-term options is fun, and this newfound accessibility predictably led to an explosion in 0DTE index options trading, as the volume chart below shows.

Figure 1: Short-Dated SPX Volume as a % of Total Volume

Source: RIA Advice

On the notorious WallStreetBets subreddit, retail gamblers share screenshots of explosive 0DTE trades, typically long volatility positions that blew out.

Figure 2: A Representative WSB Post

Source: Reddit

The potential for massive gains with a clearly defined maximum loss is psychologically appealing, as is the ability to construct a trade that is indifferent to the direction of the market move. Just think, for a modest payment of $2.00 per contract, an investor can fantasize about 10x-ing his money if the index moves 5% in the next 8 hours. All he must wager is that something will happen, and the internet is happy to provide an endless list of potential “somethings” to keep the punters engaged.

The expansion of 0DTE trading has been likened to an explosion in demand for lottery tickets, and the evidence thus far shows that retail investors are losing substantial sums buying these products. A recent paper by researchers at the University of Münster found that, since May 2022, retail investors have lost a total of $358,000 per day—$90M annually—trading 0DTE options and that they are, as a group, substantially skewed toward long volatility.

Now, the inverse of a stupid trading strategy is not necessarily an intelligent trading strategy. Most bad strategies are bad because they take on uncompensated risk and incur substantial transaction costs. These properties are preserved when one flips the sign on the trades.  But we think that a (small) allocation to short 0DTEs does make sense for many portfolios. We believe 0DTEs are typically overpriced, even after accounting for risk and transaction costs, and that selling these lottery tickets can be a profitable strategy, presuming the allocation to this strategy is kept sized small as appropriate given the high risk.

Selling ODTEs has a very different risk profile to traditional long-only investing because, with options, you can lose more than everything. If you allocate 5% of your portfolio to shorting something that returns 20x one day every 10 years, you will go bankrupt every 10 years. If you allocate 5bps to that same strategy, then once every 10 years you will have an annoyingly bad day where you eat an unexpected 1% loss.

To determine the optimal sizing of this type of strategy, we assume that we want to lose no more than 2% if SPX moves 10% open to close, something that has not happened in the last 30 years. We believe investors could earn 1.6% per year on a portfolio by only allocating 16bps to shorting the 0DTE straddle (assuming a 15% implied volatility, a 14.25% fair volatility, and using a standard Black-Scholes model. These assumptions are justified in a technical appendix that follows this piece). Under these assumptions, selling 0DTE straddles ought to realize an expected Sharpe Ratio between 0.85 and 1.4. This is an attractive Sharpe on its own terms, never mind for a strategy which is at least locally uncorrelated with the broader market. Simulated performance of such a strategy over 10 years is shown below, although readers should bear in mind that this is only one simulated path of many and that real-world tails are fatter than those commonly assumed in options theory.

Figure 3: Simulated Performance of 16bps Allocation to 0DTE ATM Straddle

Source: Verdad analysis. Note: Assumes 15% implied volatility, 14.25% fair volatility, returns shown net of transaction sosts.

In 0DTE options, market-makers operate a casino for which there is irrational demand. So long as that irrational demand persists, there’s an opportunity to sell these lottery tickets. The challenge facing the sober-minded trader, then, is controlling greed by sizing the position small and conquering fear by taking the risk of being short volatility in a world that’s full of risks.

Technical Appendix - Why Do We Think These Things Are Overpriced, Anyway?

To better understand the merits of the short 0DTE trade from the point of view of a typical investor, it is useful to analyze the trade from the point of view of the market-maker. This will allow us to estimate the degree to which 0DTEs ought to be overpriced. This is because market-makers are net short these options and therefore set the price at which they trade. This in turn happens because retail investors are net long, and other sophisticated institutions, like banks and asset managers, face regulatory, technical, and reputational barriers that prevent them from meaningfully competing with market-makers to drive down the price. And if market-makers set the price, this means that the expected risk-adjusted returns to the trade, from the market-maker’s point of view, must be quite attractive. Market makers are not in the business of 1.0 Sharpe trading strategies. They are in the business of making money every trading day of the year.

An at-the-money 0DTE straddle is the purest way to speculate on realized versus implied volatility. If expected realized volatility (i.e., fair volatility) is lower than implied volatility, then the seller of the straddle will make money over time. The volatility of this PnL can be reduced by delta hedging the short straddle, that is to say, buying SPX when the market goes up and selling when it goes down, although this will incur transaction costs that depress expected returns. So if we can estimate the expected difference between fair and implied volatility based on the market-maker’s risk aversion, we can simulate the trade as it would be experienced by a low-frequency trader.

Using the standard Black-Scholes option pricing model, we ran two Monte Carlo simulations of a short 0DTE straddle position with an implied volatility of 15% (We chose 15% because it’s close to the long-run realized volatility of the S&P 500. But this argument generalizes to other levels of implied volatility).  The first simulation is from the point of view of the market-maker: they collect a 1% spread to put on the trade and hedge their deltas every five minutes above a certain threshold, paying only 0.5bps to do so. The second simulation is from the point of view of an ordinary investor: they pay the spread to sell the straddle and do not delta hedge. Over thousands of trials, we simulated the expected Sharpe Ratio of the short straddle for both parties at fair volatilities ranging from 13% to 15%. The results are shown below.

Figure 4: Simulated Performance of Short 15 IV 0DTE ATM Straddle, Hedged, Collecting a 1% Spread

Source: Verdad research, Monte Carlo simulation, 1000 trials per fair volatility

Figure 5: Simulated Performance of Short 15 IV 0DTE ATM Straddle, Unhedged, Paying the Spread

Source: Verdad research, Monte Carlo simulation, 10,000 trials per fair volatility

If fair volatility equals implied volatility, then the market maker receives a negative Sharpe Ratio owing to the cost of their hedging. At 14.5% fair volatility, then the market-maker profits in expectation but receives an unacceptably low Sharpe Ratio by the standards of high-frequency traders. It is not until fair volatility approaches 14% to 14.25% that the expected Sharpe Ratio of the short straddle position is above 4.0. What this tells us is that, in an equilibrium where risk-averse dealers set price owing to otherwise imbalanced flow, we ought to expect the 0DTE ATM straddle to be overpriced by roughly 0.75-1.0 vol points, which permits ordinary investors a Sharpe Ratio in the range of 0.85 to 1.4. since the market maker Sharpe becomes attractive to them at 14-14.25 fair vol, we can look at the Sharpe the low frequency trader receives at the same range in order to gauge what we ought to expect.