Defined-outcome ETFs, also commonly known as buffered ETFs, have become a popular way to package downside protection and upside sacrifice into a single product. These investment vehicles use an option-based strategy called a put-spread collar to provide a fixed amount of downside protection relative to a reference asset, such as SPY (the SPDR S&P 500 ETF), while simultaneously capping the upside potential above a predetermined return cap. The problem is that not all defined outcomes are created equal.
Ding Liu, author of the papers “Defined-Outcome ETFs with a Convex Payoff Profile, Part I: Motivation, Construction, Historical Simulation” and “Part II: The Downside-to-Upside Trade-Off,” published in the Summer 2026 issue of The Journal of Beta Investment Strategies, makes a useful contribution by asking: what if the payoff profile were convex rather than concave?
When the market rises, concave strategies reduce market exposure, while convex strategies increase it; concave structures tend to deliver incremental, limited gains, whereas convex structures are designed to produce higher returns at the extremes and lower returns near the average.
Conversely, when the market falls, concave strategies increase market exposure, while convex strategies reduce it. Liu argues that a convex structure may be more useful for investors who care most about large drawdowns and strong recoveries, even if it looks unattractive in ordinary market environments.
What Liu Studied
Part I introduces a defined-outcome ETF built with a convex payoff profile. Like today’s buffered ETFs, it is designed to provide a defined outcome without requiring an upfront cash outlay. But unlike the standard buffered structure, it offers a downside floor without capping upside potential.
To build that payoff, the authors combine a long out-of-the-money put, a short at-the-money call, and a long out-of-the-money call. They then simulate the strategy using SPX options data from 1996 to 2023 and compare it with the more familiar concave, or buffered, ETF structure. They also examine the probability of large one-year S&P 500 moves to assess when each structure is most likely to matter.
Part II extends the analysis by looking at the downside-to-upside trade-off across many full market cycles. It then breaks the data into moderate and deep drawdowns and recoveries to see whether the two structures behave differently depending on how severe the market move is.
What Liu Found

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