The Simplicity Tax

Why Retail Investors Pay More for Worse Products (And What It Reveals About the Limits of Behavioral Finance)

The Simplicity Tax: Why Retail Investors Pay More for Worse Products (And What It Reveals About the Limits of Behavioral Finance)

Here’s a simple test. I’m going to offer you two products.

Product A is a binary option. It’s a yes-or-no bet: if the S&P 500 is above a certain level when the contract expires, you get $100. If it’s below, you get nothing. Clean. Simple. Two outcomes.

Product B is a bull spread. It’s built from two call options. It starts paying out at a lower level than the binary — and the further the S&P goes up, the more you make, up to a cap that matches the binary’s $100. Below the bull spread’s lower strike, you get nothing, same as the binary. But between that lower strike and the binary’s strike, the bull spread is paying you and the binary isn’t. Above the binary’s strike, they both pay the same.

Here’s the key: Product B pays you at least as much as Product A in every possible state of the world, and strictly morein many states. There is no scenario — none, zero, not one — in which you’d be better off holding the binary.

So which one should cost more?

If you said B, congratulations, you have preferences that respect dominance. This is about the lowest bar in all of decision theory. An asset that pays more in every state of the world should be worth more. Full stop. This isn’t controversial. Toddlers understand this principle when applied to candy.

And yet.

The Finding

A new paper in the Journal of Financial Economics by Aaron Goodman and Indira Puri documents something remarkable. Analyzing a year of trading data from Nadex — a CFTC-regulated retail derivatives exchange — they find that retail investors routinely buy the dominated binary option at a higher price than the dominating bull spread that was available at the exact same time.

How often? 15% of S&P index trades. 19% of gold trades. 25% of silver trades. Consistently, across three different asset classes, over an entire year.

How much money are these traders leaving on the table? On average, 34% of the contract price. That’s not a rounding error. If you’re paying $50 for a binary, you could have bought a strictly superior product for roughly $33.

This is happening in a real market — over $1 billion in notional value annually — not a psych lab experiment with undergraduates choosing between hypothetical lotteries. These are people putting real money on the line and consistently choosing the worse product at the higher price.

What Makes This Different

Finance is full of anomalies. People overpay for out-of-the-money options. They hold losers too long and sell winners too soon. They buy high-fee mutual funds when low-fee alternatives exist. We have an entire field — behavioral finance — devoted to cataloguing and explaining these patterns.

What makes the Goodman-Puri finding special isn’t just that people are overpaying. It’s that the entire standard toolkit for explaining why people overpay doesn’t work.

The authors don’t just document the anomaly. They prove — mathematically, with formal propositions — that the following theories cannot capture this result, regardless of functional form or parametric specification:

Expected utility theory can’t explain it, because any utility function that respects dominance would prefer the bull spread. Obviously.

Prospect theory can’t explain it. This is the big one. Kahneman and Tversky’s framework allows for all sorts of departures from rational choice — probability distortions, loss aversion, reference dependence. But prospect theory allows for dominance violations only through distortions of the probability space. When the dominance is state-by-state — product B pays more than product A in every state — no amount of probability distortion helps. Distort the probabilities however you like; the bull spread still pays more everywhere. The proof is clean and general. It holds for any probability weighting function, any reference point, any utility function.

Ambiguity aversion can’t explain it. Whether you’re using max-min preferences or robust control, you’re choosing the worst-case probability distribution and optimizing against it. But the bull spread dominates the binary under everyprobability distribution. There is no subjective belief about the world under which the binary looks better.

Rational inattention can’t explain it. In the standard model, the probability of selecting an asset is proportional to its payoff. The bull spread has a strictly higher payoff. Rational inattention predicts more attention to the better product, not less.

Salience theory can’t explain it. The states where the two products differ most are the states where the binary pays zero and the bull spread pays something positive. If salience makes you overweight those states, it should make you moreattracted to the bull spread.

Stop and think about what this means. The five most prominent theoretical frameworks in behavioral decision theory — the ones that have launched a thousand papers, won Nobel prizes, and informed policy worldwide — all fail on the same anomaly. And they fail for the same fundamental reason: they all operate on payoffs and probabilities. They differ in how they distort or weight those ingredients, but they share the substrate. When the dominance is state-by-state, no distortion of payoffs or probabilities can prefer the dominated product.

The authors test the standard financial explanations too. Transaction costs? They include all explicit fees in their calculations. Collateral requirements? Neither product requires collateral since both have limited downside. Liquidity? The CME market where the bull spreads trade is more liquid than Nadex — investors should be willing to pay a premium to trade there, yet the dominating CME product is cheaper. Noise trading? They run a placebo test, constructing dominated bull spreads and checking whether those are overpriced too. The asymmetry is stark: binary overvaluation runs at 15-25%, but the placebo rates are 3-14%, and the difference is highly significant. Exchange-specific effects? They repeat the analysis within Nadex itself, comparing binaries to the exchange’s own call spreads. The dominance violations persist — in fact, they’re even more extreme: 91% of within-exchange comparisons show the binary overvalued.

What Does Explain It

After eliminating everything that doesn’t work, the authors point to a simple explanation: the binary is easier to understand.

Think about what your brain has to do to evaluate each product.

A binary option has two outcomes. Win or lose. The expected value calculation is one multiplication: probability of winning times $100. A five-year-old could conceptualize it. Will the S&P be above 5300 on Friday? Yes or no. How much would you pay for that bet?

A bull spread has a continuum of outcomes across three regions. Below the lower strike: zero. Between the strikes: linearly increasing payoff. Above the upper strike: capped. Computing expected value requires integrating across a probability distribution, or at minimum doing piecewise reasoning over three regions. It’s not hard, exactly, but it’s more steps, more working memory, more cognitive load. Even when bull spreads are displayed on the same screen, prominently, with educational explanations — as they are on Nadex — the binary is just... easier.

The authors show that a formal theory of simplicity, developed by Puri (2025), captures the results. The idea is that investors derive disutility from product complexity, creating an effective complexity cost. When the payoff advantage of the dominant product is small enough relative to the complexity gap, the simpler product wins despite inferior payoffs. This framework also predicts the cross-sectional patterns in the data: as the degree of dominance increases (the bull spread gets even better relative to the binary), the frequency of overvaluation falls. Intuitively, there’s a tipping point: make the payoff gap large enough and even complexity-averse investors will switch to the better product. The data confirm this.

The Simplicity Tax

Let me put this in terms my fellow traders will appreciate.

Over 30-plus years of running money, I’ve learned something that sounds paradoxical but is absolutely true: signals you can’t understand often outperform signals that make sense. The elegant theory works in physics. In finance, the ugly model with no satisfying narrative frequently beats the one you can explain over dinner.

This used to baffle me. Shouldn’t understanding why something works make you more confident, help you size positions better, stick with the strategy through drawdowns?

No. And the Goodman-Puri paper shows why at the retail level, in its purest form. People don’t just prefer simplicity — they’ll pay for it. Real money. 34% of the contract price. They’re paying a simplicity tax: the premium you surrender because your brain would rather evaluate two outcomes than a continuum.

And this tax shows up everywhere, not just in binary options:

The growth of “zero-days-to-expiration” options — basically directional bets with binary-like payoff profiles — reflects the same preference. Robinhood just launched event contracts. Kalshi trades binary-style contracts on everything from Fed rate decisions to weather. The CME itself launched binary options explicitly to attract retail investors. The entire trend in retail financial products is toward simpler payoff structures. Supply-side actors aren’t correcting the simplicity preference; they’re catering to it, because there’s money in selling people the product that’s easier to evaluate, even when a better product exists.

My advice to aspiring traders has always been: test until you throw up. Test everything. Don’t trust stories, don’t trust elegance, don’t trust the narrative. Run the numbers. The Goodman-Puri result is the formal version of that advice. The numbers say the ugly product is better. But 15-25% of the time, people buy the pretty one anyway.

The Deeper Problem

Here’s what I find most interesting about this paper, and it’s something the authors are too polite to say outright (they’re writing for the Journal of Financial Economics, after all, not a Substack).

The failure here isn’t just empirical. It’s structural.

Behavioral finance spent forty years building increasingly sophisticated theories of choice under uncertainty. Prospect theory. Cumulative prospect theory. Rank-dependent utility. Ambiguity aversion. Salience. Disappointment aversion. Rational inattention. Each one relaxes a different assumption of expected utility theory. Each one adds a new mechanism — probability distortion, reference dependence, attention allocation, worst-case reasoning.

But they’re all doing the same thing. They’re all asking: given the payoff structure, what does the agent choose? They model the selection — increasingly exotic selection rules over the same underlying substrate of payoffs and probabilities.

This paper proves that approach has a boundary. The anomaly doesn’t live in the selection mechanism. It lives in the evaluation process — the computational cost of figuring out what the payoff structure even is. The binary option trader isn’t distorting payoffs or probabilities. The binary option trader hasn’t computed the payoff comparison, because the computation itself is the bottleneck.

That’s not a preference. That’s a constraint on information processing. And it requires a fundamentally different kind of theory — one that talks about computation, not utility.

There’s a phrase I’ve been using in my work: “conclusions without derivations are just opinions with fancy letterhead.” The behavioral finance literature has been, in a sense, providing increasingly fancy letterhead. More sophisticated utility functions. More elegant axiom systems. More Nobel-worthy mathematics. But the derivation — the part where you explain why the agent behaves as they do at the most fundamental level — has been stuck in one register: preferences over outcomes.

The Goodman-Puri result suggests we need a different register entirely. The binding constraint on human decision-making isn’t always what you prefer. Sometimes it’s what you can compute. And the difference between those two explanations — the one about preferences and the one about computation — turns out to have deep implications that go well beyond finance.

I’ll have much more to say about that soon.

---

Goodman, A. and Puri, I. (2025). “Overvaluing Simple Bets: Evidence from the Options Market.” Journal of Financial Economics, 172. Available here.

For aspiring traders: the lesson from this paper isn’t “avoid binary options” (though you probably should). It’s that the simplicity tax is real, it’s measurable, and it applies to your own cognition too. The strategy that feels clean and intuitive might be costing you 34% relative to the one that makes your head hurt. Test, don’t intuit.

For more on these themes — including why the same computational constraints that explain binary option mispricing also explain traffic jams, free will, and why a Supreme Court must exist — see my book The Science of Free Will.