Why "Worst-Of" Is Worse Than You Think

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Why "Worst-Of" Is Worse Than You Think

Picture yourself at breakfast at an average hotel. They serve coffee and tea from a big pot, and the quality is inconsistent day to day. Sometimes a cup turns out great, sometimes it's fine, and on other days it tastes bitter, all with equal probability. You don't know upfront how either will taste, so you might reason: it doesn't matter whether I pick coffee or tea, the expected outcome is the same either way.

That's a reasonable instinct, and it's consistent with how humans generally navigate uncertainty. Some days don't go your way, but that gets offset by the days that do.

Now let's change the game. The hotel staff, feeling mischievous, actually knows in advance which drink will be the bitter one that day, and they serve you that one. You're worse off, obviously, but by how much? Your first instinct might be to think you're still fine: each drink is decent on average, so even getting the worse one, shouldn't you still land somewhere decent over many days?

That turns out to be wrong, and two things are going on.

First, we often get the order of operations backwards. If the expected tastes, E[coffee] and E[tea], are both decent, we assume that taking the worse of the two, day after day, still averages out to something decent. It doesn't. The expectation of the minimum is not the minimum of the expectations, and the gap between the two grows the more the two drinks vary independently of each other.

Second, we forget that the assignment compounds and that roles can switch. Today coffee is the bad one, so you get coffee. Tomorrow the worse one might be tea, and you get tea. Over time you're not sampling from "coffee" or "tea." You're sampling from "whichever one is worst today," which is a distinctly worse thing to hold.

Put differently: picking randomly and being assigned the worse one are very different games, even when each underlying option is decent on its own. Knowing that either component is fine in isolation tells you nothing about what you get when the payout is defined as the worst of the two.

Going back to structured notes: between 30% and 50% of multi-asset notes reference the worst-of the underlying assets¹, and it's unclear how well investors understand the mechanics. This gap caught regulators' attention too. In May 2026, FINRA announced a targeted review of non-principal-protected worst-of structured notes, examining how firms supervise concentrations in these products and how they're recommended to clients under Regulation Best Interest.² A worst-of note isn't just a riskier version of a single-stock note. It behaves differently in ways that may not be obvious on the term sheet.

In this article, we unpack the dynamics and math behind a "worst-of" payout.

The Math Behind the Gap

Take two dice. Each one, on its own, averages 3.5 over many rolls. If you rolled just one die and it were somehow tied to a payout, 3.5 would be the fair value to expect.

Now roll both dice and take the higher of the two. The average climbs to about 4.47. Take the lower of the two instead, and the average falls to about 2.53. Both are meaningfully different from 3.5. To illustrate this point further, we created a small simulation where you can roll two dice thousands of times, and check the outcomes of different metrics: Lati Capital's Worst-Of Lab

Before we can tie this back to asset prices, we need to introduce correlation. Correlation tells us how much two random variables move together. Dice are uncorrelated, but equity assets are often correlated, dampening the effect somewhat. If we believe that two equity indices return 6% over a long period, and further assume a volatility of 16% for each, we can quantify the effect the "worst-of" payout has, compared to the average payout, for a few correlation assumptions:

This result is worth emphasizing: two assets, each with a positive expected return of 6%, and combining them the "worst of" way can turn your expected outcome negative, at a correlation of ~0.56, which is common between two equity indices, and continues to worsen below that. Only once the two move almost perfectly together does the drag disappear.

How to Make It Even Worse

The lower expected return is already a real cost. But there is a second effect at work, and it is more subtle, because on the surface it looks like good news.

If you measure the volatility, the year-to-year variability, of a worst-of outcome, it is usually lower than the volatility of either index on its own. That sounds like a benefit for a variety of reasons: Lower volatility is normally something investors want and they may conclude the worst-of note is, in some sense, the calmer investment. And because structured notes have option-like payoffs where the investor is "short volatility", lowering it seems to be a benefit.

But that ignores a subtle detail: Taking the worse of two outcomes clips the upside. You get the smaller of two numbers, which means on your best days you're never rewarded for your best-performing index, only for your worst-performing one. That's where the "missing" volatility went: out of the good scenarios, not the bad ones. The downside is left untouched. In the years that matter, the ones where an index actually falls, the worst-of note behaves exactly as badly as its worst-performing reference, with none of the protection its lower headline volatility seemed to promise.

A single volatility number, quoted on a term sheet or a fact card, describes the whole distribution as if it were symmetric. Worst-of outcomes are not symmetric. The number is technically correct and still tells you the wrong thing, because it's calm on the side you don't care about and unchanged on the side you do.

What This Means for You

None of this makes worst-of notes uninvestable. It means they need to be evaluated for what they actually are, not for how they're described.

This is also, in part, why FINRA has turned its attention to these products. The 2026 review of non-principal-protected worst-of structured notes looks closely at how they are supervised and how they are recommended to clients.² Regulators are not scrutinizing the concept of combining multiple assets. They are scrutinizing the gap between how these notes are sold and how they actually behave, the same gap this piece has tried to walk through.

A few questions are worth asking your advisor before buying a worst-of note:

• What is the correlation between the referenced assets, and how does it affect the expected outcome?
• Does the quoted volatility reflect the whole distribution, or only the average behavior?
• What happens to the note in the specific scenario where one reference asset underperforms the others?

You may want to be skeptical if an advisor tells you:

• "The underlying assets both have good returns, so it doesn't matter that the note references the worst performing one": as we have seen, the expected value can decrease below the worse one
• "There's a diversification benefit of having multiple assets": True in a portfolio, wrong when only referencing the worst-of

If you hold, or are considering, a worst-of structured note, we're glad to walk through the specific mechanics with you.

Appendix: The Math

For any two random variables $X$ and $Y$:

$\min(X,Y) = \frac{X+Y}{2} - \frac{|X-Y|}{2}$

This is just arithmetic: If $X \le Y$, the right-hand side reduces to $X$. If $Y \le X$, it reduces to $Y$. Either way, it equals whichever is smaller.

Taking expectations of both sides:

$E[\min(X,Y)] = \frac{E[X]+E[Y]}{2} - \frac{1}{2}E|X-Y|$

This holds for any two variables with finite means, no assumption of normality required. It says something simple: the expected worst-of outcome is the average of the two expected outcomes, minus a penalty equal to half the expected absolute difference between them. The more the two variables tend to diverge from each other, the larger that penalty, regardless of what either one is doing individually.

To get a closed-form number, we do need a distributional assumption. If $X$ and $Y$ are jointly normal, with the same mean $\mu$ and standard deviation $\sigma$, and correlation $\rho$, then $X - Y$ is itself normal, with mean 0 and variance $2\sigma^2(1-\rho)$. For a mean-zero normal variable with standard deviation $s$, $E|X-Y| = s\sqrt{2/\pi}$. Substituting:

$E[\min(X,Y)] = \mu - \sigma\sqrt{\frac{1-\rho}{\pi}}$

This is the formula behind the table in the earlier section. The penalty grows as $\rho$ falls, disappears entirely as $\rho \to 1$, and scales with $\sigma$: the more volatile the underlying assets, the larger the drag from taking the worse of the two, at any given correlation.

¹ Source: Lati Capital survey of recent SEC Form 424B2 filings.
² FINRA, "FINRA Announces Review of Higher-Risk Structured Products," 2026. finra.org