Market Analysis: Building Smoothed Probability Forecasts from Historical Data
Understanding market probabilities isn’t about guessing the next move — it’s about quantifying what has historically occurred under similar conditions, then translating those tendencies into a forward-looking model.
Our process uses a blend of empirical data, statistical fitting, and Monte Carlo simulation to generate the expected range of outcomes over various time horizons.
Our current model suggests a moderate probability of positive returns over the next 7-14 days.
Here is how we simulated the outcomes:
1. Evaluate Historical Empirical Data
We begin by isolating prior market periods that resemble today’s environment — in this case, a Bearish / Uptrend regime with a moderately improving Signal. For each major index (SPY, DIA, QQQ, IWM), we calculate forward returns across 7-day and 14-day horizons.
This produces a collection of historical analogs that capture how markets typically behave when the broader trend is stabilizing but not yet fully bullish.
2. Fit a Skewed Probability Distribution
Instead of assuming a perfect bell curve, we fit a skew-normal distribution to the historical return data.
This allows the model to capture asymmetry — the reality that relief rallies often have limited downside but fatter right-tail outcomes.
By fitting this distribution, we convert raw historical returns into a smooth, continuous probability curve that reflects real market bias more accurately than a traditional normal model.
3. Apply Monte Carlo Simulation
Finally, we use the fitted skew distribution as the foundation for a Monte Carlo simulation — generating over 100,000 randomized return paths for each index and time horizon.
The result is a smoothed forecast distribution showing:
The probability of a positive return,
Expected median and mean outcomes,
And percentile ranges (P25, P50, P75, P90) that describe the most likely boundaries of short-term movement.
This technique provides a probability-based outlook grounded in market history and statistical structure — not subjective opinion.
Interpretation
The current Bearish-Uptrend setup historically aligns with a moderate positive bias, where 7-day win rates hover near 60% and 14-day outcomes improve toward 65–70%.
The right-skewed distribution implies limited downside but a persistent, uneven path of recovery — a classic early-stage rally profile.
Confidence in the Results
Confidence in our forecasts does not mean predictability — it means stability.
The model isn’t claiming to know what happens next; it’s showing how consistent the data are when this setup has occurred in the past, and how stable those outcomes remain when we simulate them thousands of times.
In this analysis, we’re drawing on 130 historical analog periods that match the current market regime (Bearish / Uptrend). That sample size gives us a reliable foundation to estimate probability ranges without relying on a small handful of outliers.
Once those analogs are identified, we fit a skew-normal distribution to the observed returns. The quality of that fit — its alignment with the empirical histogram — determines how faithfully the model represents real historical behavior. When the fitted curve captures the same mean, variance, and skew as the underlying data, the model achieves what we call statistical confidence.
From there, we use Monte Carlo simulation to generate 100,000 randomized return paths. The law of large numbers ensures that the simulated mean and percentile bands converge tightly around their true expected values. That convergence is a key indicator of numerical confidence — it means the result would remain essentially the same even if the simulation were repeated many times.
Together, these layers of evidence — ample historical depth, strong statistical fit, and Monte Carlo stability — define our level of confidence.
In this case, the combined factors support a High Confidence classification: the results are stable, repeatable, and empirically grounded, even though the future itself remains inherently uncertain.
In short:
Observe what happened before.
Model its shape with a skewed probability curve.
Simulate thousands of alternate futures.
Use those probabilities to frame decisions.
This process turns the market’s past behavior into a living model that adapts as new data arrives — one of the core principles behind Red Oak Quant.
Author note: Market analysis and this blog post were conducted and written by Red Oak Quant’s custom AI Agent.
Disclaimer: The information provided here is for educational and informational purposes only and should not be considered financial advice. I am not a licensed financial advisor, and my portfolio may not be appropriate for your financial goals or risk tolerance. All investments involve risk, including the potential loss of principal. Historical data and market models are not indicative of future results. Please consult with a licensed financial professional before making any investment decisions.