a quantitative tool to answer qualitative questions
For decades, the financial world has applied the logic of liquid markets to assets that refuse to behave like them — private equity investments that cannot be priced in real time, hedged easily, or sold on demand. Researchers Alexander Lipton and Marcos Lopez de Prado, working at one of the world's largest sovereign wealth funds, have proposed a framework that meets private assets on their own terms, using utility maximization and indifference pricing to account for the irreducible individuality of each investor's risk tolerance and time horizon. The work arrives at a moment when private equity has grown too large and too consequential to be governed by borrowed mathematics.
- Trillions of dollars flow into private equity annually, yet the tools used to justify those allocations were designed for markets where prices update by the second — a fundamental mismatch that leaves portfolio managers navigating in the dark.
- Traditional arbitrage pricing theory quietly assumes investors can hedge, trade, and exit at will; strip those assumptions away and the math that underpins most valuation models quietly collapses.
- Lipton and Lopez de Prado's framework replaces the fiction of a universal fair price with indifference pricing — the point at which a specific investor, with their specific constraints, is equally content to hold or walk away.
- Their two-stage model separates the allocation decision from the balancing act, capturing the non-linear way risk compounds when you're holding something you cannot easily sell — a subtlety traditional methods consistently miss.
- The researchers are already looking ahead, planning to incorporate tokenization of private assets and to formally disentangle market risk, model risk, and pure uncertainty into distinct, treatable categories.
Private equity has become too large to ignore and too complex to price honestly. Billions pour into these investments each year, yet the people deciding how much of a portfolio to commit have long operated without reliable mathematical tools — no continuous price, no transparent market, no clear signal of whether they are overpaying for something they cannot easily sell.
Alexander Lipton and Marcos Lopez de Prado, who lead research and development at Abu Dhabi Investment Authority, argue that the industry has been applying the wrong framework. Arbitrage pricing theory — the dominant approach borrowed from public markets — assumes investors can hedge and exit freely. Private assets offer no such luxury, and when those assumptions fail, the math fails with them.
Their proposed alternative centers on utility maximization and indifference pricing. Rather than searching for a single fair value that applies universally, the framework asks a more honest question: at what price would this particular investor be equally willing to hold or forgo this asset? A pension fund with a 30-year horizon and a family office with tighter liquidity needs will rationally arrive at different answers for the same investment, and the model accommodates that reality.
The structure is deliberately clean. It works with three assets — a risk-free instrument, a liquid public benchmark, and the illiquid private holding — and unfolds in two stages: first, determining how much of a portfolio should enter private assets at all; second, balancing the remaining holdings accordingly. This sequence captures a non-linearity that traditional methods overlook, reflecting how risk compounds differently when exit is not freely available.
Both researchers have long track records in financial mathematics and were named buy-side quants of the year by Risk magazine in 2021. They regard the current paper as a foundation rather than a conclusion. Future work will explore how digitization and tokenization might reshape private asset markets, and will attempt to formally separate three distinct sources of uncertainty — market risk, model risk, and irreducible unknowns — each of which demands its own treatment.
The significance of the work lies in its timing. Private equity is no longer a niche. The capital is real, the institutions managing it are enormous, and the allocation decisions are made daily. This framework offers those decision-makers something the field has lacked: mathematics built for the world private assets actually inhabit.
Private equity has become impossible to ignore. Billions flow into these deals every year, and when the companies eventually go public, the market watches closely. Yet for the people actually deciding whether to invest in private assets—and how much of their portfolio to commit—the math has always been fuzzy. There is no continuous price, no transparent market, no clear way to know if you're overpaying or underpaying for something illiquid and difficult to sell.
Alexander Lipton and Marcos Lopez de Prado, who lead research and development at Abu Dhabi Investment Authority, have spent the last several years thinking about this problem. Their conclusion: the financial industry has been using the wrong tools. Private equity valuations have borrowed methods from public markets, where stocks trade constantly and prices adjust in real time. But private assets don't work that way. You can't instantly buy or sell them. You can't hedge them easily. The traditional approach—arbitrage pricing theory—assumes you can do all of those things. When you can't, the math breaks down.
Their paper proposes something different: a framework built on utility maximization, which is a fancy way of saying it accounts for what individual investors actually care about. Instead of hunting for a single "fair market value" that applies to everyone, the framework produces what they call indifference pricing—the price at which a specific investor would be equally happy holding the asset or not holding it. This matters because private equity isn't one thing to everyone. A pension fund with a 30-year horizon and a family office with different liquidity needs will rationally value the same investment differently.
The model itself is elegant in its simplicity. It assumes three assets: something risk-free, something liquid and publicly traded (like an index), and the illiquid private investment. The approach unfolds in two stages. First, you decide how much of your portfolio should go into private assets at all—a question that depends entirely on your risk tolerance and time horizon. Second, once you've made that allocation decision, you figure out how to balance the rest of your holdings between the liquid and illiquid pieces. This two-step process catches something traditional methods miss: the non-linearity of how risk compounds when you're holding assets you can't easily sell.
Lipton describes it as a quantitative tool for answering qualitative questions. The framework doesn't replace judgment or gut instinct. Instead, it disciplines those instincts with mathematics. A portfolio manager might have a strong conviction about a particular private equity fund, but the framework forces them to articulate why—and to see how that conviction interacts with everything else they're holding.
Both researchers have spent years publishing on different corners of financial mathematics, and they've already won recognition for their work: Risk magazine named them buy-side quants of the year in 2021 for a paper on optimal trading using heat potentials. But they see the private equity work as unfinished. Their next moves involve layering in digitization and tokenization—the idea that private assets might eventually be represented and traded in new ways—while keeping the quantitative rigor intact. They're also focused on what they call "disentangling risk," breaking down the sources of uncertainty into three buckets: market risk, model risk, and pure uncertainty. Each requires different treatment.
What makes this work significant is timing. Private equity has grown so large that it can no longer be treated as a niche corner of finance. The assets are real, the capital is real, and the decisions about how much to allocate are being made every day by institutions managing trillions. Until now, those decisions have rested on methods borrowed from a different world. This framework offers something better: a way to think about private assets on their own terms, with mathematics that acknowledges what makes them different.
Citas Notables
The paper is trying to discipline judgment with a coherent mathematical framework, not replace discretionary views— Marcos Lopez de Prado
You can think of this model as a quantitative tool to answer qualitative questions— Alexander Lipton
La Conversación del Hearth Otra perspectiva de la historia
Why does private equity valuation matter so much right now? It's always been opaque.
Because the money is enormous now, and it's not staying private anymore. These companies go public, and suddenly everyone realizes how much capital was committed to them. Portfolio managers need to know if they should be in this game at all.
But couldn't they just use the same valuation methods that work for public companies?
That's exactly what they've been doing, and it doesn't work. Public market methods assume you can buy and sell instantly. Private assets don't move that way. You're stuck with them. The math breaks down when you remove that assumption.
So what does utility maximization actually do differently?
It stops pretending there's one right price for everyone. Instead, it asks: at what price would *this specific investor*, with *their specific time horizon and risk tolerance*, be indifferent between holding the asset and not holding it? The answer is different for a pension fund than for a hedge fund.
That sounds more honest, but also more complicated.
It is more complicated. But it's honest in a way the old methods weren't. And the framework gives you a structure for thinking through the complications instead of just guessing.
What happens next? Is this going to change how people actually allocate capital?
That's the real question. The framework exists now. Whether institutions adopt it depends on whether they trust the math more than they trust their instincts. The researchers are already thinking about tokenization and digitization—ways to make private assets more tradable. That could change everything.