The question
Forward Distributions is the flagship of OpenK, and the question behind it is narrow on purpose:
Using price data alone, do a market's historical state and path sharpen the forward-return distribution beyond what simple baselines already deliver?
Every part of that question carries weight. State and path mean where the market sits and how it arrived. The forward-return distribution is the full range of what has tended to happen next in the real world, not the option-implied distribution priced for hedging. Baselines mean I hold the work against honest, simple alternatives. Price alone means exactly that: no direct macroeconomic inputs.
The premise is that price history is already a compressed record of the cycle, and that the structure I care about can be recovered from price itself if it is described correctly.
Why a single price is not enough
A price tells you what one instrument costs right now. It does not tell you where that price sits against the market's own history, whether it arrived through a slow climb or a violent drop, or how that context shaped the outcomes that followed.
Markets and the economy operate as a two-way loop. Over shorter windows, investors can overweight the current event and underweight the history around it. Fear and optimism run through the entire cycle, not only at its extremes.
Forward Distributions puts that missing context back in. Instead of asking only what the price is, I ask a fuller question:
Given where the market sits relative to its own past, and given the path it took to get here, what has the full distribution of future returns tended to look like?
How I represent state and path
STATE describes where the market sits relative to its own history. It is measured across several memory lengths rather than against one fixed anchor. A single moving average or look-back period may be informative, but it forces one version of memory onto every part of the cycle. Reading across several memories allows recent context and structural context to exist at the same time.
The K curve, OpenK's moving long-run reference, plays an important role in that description. It provides an anchor that can change with the market rather than assuming that one historical average remains correct forever.
PATH describes how the market reached its current position. It captures the shape, speed, and character of the journey rather than only the endpoint. Two markets can sit at the same level after arriving in completely different ways, and those different paths may carry different information about what follows.
STATE says where the market is. PATH says how it got there. Both are read from price, and the internal construction remains private.
What the model outputs
The output is not one number. It is a distribution.
For a given horizon, the model describes the full shape of forward returns: the center, the width of the range, the balance between upside and downside, and the odds of the large moves that matter most.
It does this across several horizons because the context that matters over one month may not be the context that matters over several years. Predictability changes with time, so the forecast has to change with it.
A point estimate hides the two things an investor most needs to understand: how uncertain the estimate is and how severe the downside could be. Two markets can have the same expected return while carrying completely different risks.
A heavy left tail marks vulnerability, not timing. It says the market is fragile. It does not say the market will turn tomorrow.
The distortion is also asymmetric. It is often most visible in the downside before or during stress, and in the upside distribution after a crash. A separate OpenK program on fear and promise develops that asymmetry in full.
The published lineage
The pieces behind this program are published, and I name them because they are both the lineage and the standard OpenK measures itself against.
Corsi showed that volatility is best understood across several time horizons at once. That multi-horizon principle is central to how OpenK represents market state. Guyon and Lekeufack demonstrated that volatility is strongly path-dependent, providing published evidence that the road a market traveled contains information beyond its current position.
Other research supports modeling the full shape of future returns rather than only the average. Amaya, Christoffersen, Jacobs, and Vasquez showed that realized skewness contains information about future equity returns. Harvey and Siddique established that conditional skewness is priced in the cross-section. Kelly and Jiang showed that tail risk is both time-varying and priced in asset markets.
Those papers establish separate parts of the problem: multiple time horizons, path dependence, skewness, and tail risk. OpenK asks what happens when those pieces are brought together in one physical forward distribution, read entirely from price and anchored to a moving long-run reference.
The published ideas are the foundation. The synthesis is mine.
How I test it honestly
A method that quietly uses future information is worthless, and most of the ways to fool yourself are subtle. The validation design is therefore strict.
The data is divided chronologically into training, validation, embargo, and test periods. It is never randomly shuffled. The embargo is a deliberate gap that prevents overlapping future returns from leaking information across the boundaries.
Every transformation is prior-only, meaning it is calculated using only the information that would have been available at the historical decision time. Nothing is normalized using statistics drawn from the future.
Every result is also measured against simple baselines. Better than nothing is not the standard. Better than the plausible alternative is.
What holds up, and what stays hard
The results are not uniform, and they should not be.
The value of STATE and PATH changes with the horizon and the condition of the market. There are places where the added context sharpens the forward distribution beyond the baselines, and there are places where the simpler approach is genuinely as good. I treat both as findings.
The program fails if the added context cannot improve out-of-sample forecasts beyond those simpler alternatives, or if the apparent advantage disappears under chronological testing.
The downside tail remains the hardest part of the distribution to forecast well. It is also the region investors care about most. Crashes are rare, their causes differ, and the limited number of examples makes the left tail especially easy to overfit.
That is the honest frontier of the work. The places where added context does not help are as informative as the places where it does.
Limitations and status
The limitations are real.
Markets are nonstationary, so the relationships learned from the past can shift. The crash periods that dominate downside risk are scarce. The work currently focuses on broad indexes, so its conclusions should not automatically be extended to individual securities or other markets.
An improved distribution is also a sharper map, not a strategy. There is no automatic path from a better forecast to a profitable trade. Position sizing, execution, costs, timing, and risk management remain separate problems.
Status: Forward Distributions is the OpenK flagship and is currently in live testing. The published foundations are strong, but the value of the program will be determined by what survives honest out-of-sample comparison.
The parts that resist testing are teaching me as much as the parts that hold.