Sharpe Ratio
PublishedEfficiency: how much pace does a driver extract per unit of chaos?
Mathematics & Statistics · Purdue · Class of 2027
Prabhat M
Quantitative research: rigorous models that explain why, not just predict that.
Most recently: a pre-registered, six-week study of how prediction markets priced the 2026 World Cup. It found a real 600ms lead between venues, then showed that none of it survives contact with the order book. Read the write-up.
- Focus
- Quant Research · Prediction Markets
- Based
- West Lafayette, IN
- Status
- Open to FT 2027
104World Cup matches priced tick-by-tick, both venues, one wall clock
11Predictions pre-registered before kickoff, graded in public after: 6 pass, 2 fail, 3 inconclusive
01
About
Currently
Writing up xResidual, a six-week live study of how prediction markets priced the 2026 World Cup: pre-registered in June, graded in public on July 19. Finalizing the QuantF1 methodology paper for arXiv submission.
I'm a Math and Statistics senior at Purdue, graduating May 2027. My work sits at the intersection of quantitative finance, sports analytics, and applied machine learning. What interests me most is the mechanism behind a result: models whose predictions come with reasons attached.
Over the past two years I've self-built an implementation library covering the core syllabus of a graduate-level quantitative finance program: option pricing through exotics, credit risk models, factor models, portfolio optimization, time series analytics. More recently, I've been developing QuantF1: a hierarchical Bayesian study of how far a Formula 1 driver's skill can be separated from their machinery. The methodology paper is in preparation for arXiv.
Co-founder of UltraRice, fiscally sponsored by The Hack Foundation (d.b.a. Hack Club), a 501(c)(3) nonprofit. UltraRice works on ultrasonic rice fortification for malnutrition in India, started at 17 and funded with $20,000+ in non-dilutive grants from Tyler Cowen's Emergent Ventures India (Mercatus Center, George Mason University) on the strength of independent research. Public financials at bank.hackclub.com/ultrarice. Before that, The Knowledge Society (2022), where UltraRice began as an end-of-year moonshot. Selected for the 2026 IMC Trading US Chess Academy, one of 20 brackets nationwide, finishing 7th in the qualifier.
Languages
- Python
- C++
- SQL
- R
Quant Methods
- Hierarchical Bayesian (PyMC)
- Market Microstructure
- Monte Carlo & Exotics
- Time Series (ARIMA/GARCH)
- Factor Models & Optimization
- Walk-Forward Validation
- Kelly Sizing
Infrastructure
- Azure · AWS
- Docker
- systemd
- CI/CD · GitHub Actions
- SQLite
- Git
02
Research
FlagshipThree threads of one instinct: rigorous models that explain why, not just predict that: risk-adjusted sports analytics, prediction-market efficiency, and systematic quantitative finance.
Sports Analytics
QuantF1
FlagshipA hierarchical Bayesian study of 76,000 F1 laps (2022–25, PyMC/NUTS, AR(1) Student-t) examining how far a driver's skill can be separated from their machinery. Championship-points variance decomposes into roughly 70% pace, 26% conversion, 4% luck, isolating conversion as a measurable within-team skill; the cross-team split is only weakly identified, swinging 47–71% on the removal of a single team switch. Paper: arXiv, in preparation.
What surprised me. The within-team comparison is the part that identifies cleanly: teammates share machinery, so conversion separates as a measurable skill. The cross-team split does not. Removing a single mid-season team switch swings the variance share from 47% to 71%, which means the headline "how much is the driver" number rests on a handful of driver moves rather than on 76,000 laps. The honest version of this study reports that fragility instead of picking the flattering number, and that constraint shaped the whole paper.
The Series
- The Sharpe Ratio of a Driver: What Quant Finance Can Teach Us About Formula 1 Performance
- The Sortino Ratio of a Driver: Measuring Controlled Aggression in F1
- The Execution Profile of a Driver: Measuring Performance Beyond the Results Table
- The Alpha of a Driver: Separating Skill from Machinery in Formula 1
- The Physics of Failure: Measuring Drawdown and Recovery in Formula 1
Analytical Framework
Sortino Ratio
PublishedControlled Aggression: which mistakes actually matter?
Execution Profile
PublishedBehavior: how is performance delivered?
Alpha
PublishedSkill vs Machinery: separating the driver from the car.
Drawdown and Recovery
PublishedResilience: what happens when things go wrong?
Regime Sensitivity
Forthcoming · arXivContext: when does a driver's execution work?
Consistency
Forthcoming · arXivRepeatability: is this structural skill or situational brilliance?
Prediction Markets
xResidual
Complete · Graded Jul 19, 2026A six-week live study of how the sharpest forecasts on earth (prediction markets like Kalshi and Polymarket, benchmarked against bookmaker consensus) priced all 104 matches of the 2026 World Cup. Eleven falsifiable predictions were pre-registered before kickoff on June 11 and graded in public when the tournament closed on July 19. Every published figure resolves from the data artifact through generated macros, guarded by regression tests that fail on drift. The full record, predictions, code, and grading, stays up.
What the Study Found
81.0%Polymarket's Gonzalo-Granger information share: it leads price discovery, on de-vigged mids with ADF-gated VECM
61/63Matches where that leadership held
12.0¢Median cross-venue dislocation at a 600ms lead. Gate it on depth actually resting in the book and the median match yields no harvestable goal at all
~0.5%Depth resting at the dislocated price, as a share of normal, and it stays collapsed for the 3–4 seconds the gap exists
The headline result is a negative one, and it is the point: a visible, statistically clean 12-cent lead exists between venues, and adverse selection eats all of it. Measuring that honestly mattered more than reporting an edge that would not survive contact with the book.
What nearly went wrong. My first pass at the ledger returned +10.2¢ on 100% of goals. A number that good is not a discovery, it is a bug you have not found yet, and it was: the ledger credited a follower with the full price move while assuming the quote it was lifting would still be resting there. At the instant of a goal it is not. I had measured the size of an opportunity without checking whether anyone could take it. Gating the same ledger on real depth inverted the result, and that correction is the whole finding. The write-up walks through it.
How the Pre-Registered Calls Landed
6 / 2 / 3Pass, fail, inconclusive across eleven predictions. Both named primaries passed; the two failures are published below, not quietly dropped
0.487Final market Brier over 72 scored matches vs. my pre-committed model's 0.503, reliability slope 1.07 against my 0.87. The market was better calibrated than I was
+0.020Nats per match the de-vigged market beat me by on log score (0.825 vs 0.845). It won 35 of 72 matches outright: the gap is margin, not frequency, and is not significant (p = 0.34)
59%Of 222 directional calls closed with positive CLV, median +0.68pp. But the mean is −2.81pp: a minority of large adverse moves swamps it
The two that failed. P3 predicted the raw cross-venue title gap would stay inside 1pp; graded at the close it was 3.98pp, because once teams resolve, Kalshi's winner field stops being a probability distribution at all. P10 predicted the documented goal-overreaction fade would net positive; it returned −0.285pp per trade. That edge is arbed away on these venues, and I said in advance that publishing either result was the point.
Where the CLV actually came from. Split by market, the advance-to-knockout lane closed 74% positive at +4.03pp mean; the deeper reach-round lanes ran near coin-flip with badly negative means (reach-QF: 50%, −7.06pp). The simulated paper-trading book agreed independently, ending +$148 on a notional $1,452, no capital at risk, with the entire gain in that same advance lane and −$117 given back in lanes where I had no modelled edge. One robust edge, several expensive ways to lose it: that split is the finding, and it only shows up because the losing lanes were logged too.
The Pipeline
Expectation Baseline
BaselineWorld Football Elo over 49k historical results, paired with a Skellam goal model.
Monte Carlo Engine
SimulationFormat-aware tournament sim: 40k iterations, FIFA best-thirds rules, Transfermarkt squad-value blending, and an empirical-Bayes confederation-bias correction.
Residual Analysis
CoreLog-score and standardized z-scores with honest sigma discipline: expectation vs. outcome.
Market Microstructure
MarketsOrder-book depth, spreads, imbalance, and cross-venue price discovery across Kalshi and Polymarket.
Calibration
ValidationCORP isotonic reliability diagrams with consistency bands and three devig methods: falsifiable predictions pre-registered, graded in public on Jul 19.
In-Play Capture
In-PlayMillisecond-stamped websocket capture of both order books throughout every match, with auto goal-shock detection and the goal-overreaction fade test (P10).
Built to Be Trusted
Always-on collection
Price logging ran 24/7 on an always-on Azure VM via systemd timers for the full six weeks. No kickoff was ever lost to a sleeping laptop.
Content-hash provenance
Every build stamps the git SHA, model parameters, and input fingerprints, and flags any published card that has drifted from the model behind it.
112 unit tests
Across the math core, calibration, microstructure, simulation invariants, the confederation-bias correction, and data-integrity guards.
Systematic Trading & Derivatives
Quantitative Finance
Implementation work spanning derivatives, portfolio construction, and systematic trading, including a production prediction-market forecasting system currently paper-trading via daily GitHub Actions.
Quant-Finance Repository
Quant-Finance
End-to-end research and implementation library covering Black-Scholes, Monte Carlo for Asian/Barrier/Lookback/Rainbow exotics, Merton credit model, factor models, portfolio optimization, and time series analytics.
- Options pricing: Black-Scholes & Monte Carlo for Asian / Barrier / Lookback / Rainbow exotics
- Credit risk: Merton, Black-Cox, Jarrow-Turnbull
- Factor models: CAPM, Fama-French 3/5, Carhart, AQR style premia
- Portfolio optimization: Markowitz, Black-Litterman, reinforcement learning
- Sentiment-driven trading pipeline (VADER + FinBERT); backtesting engine with realistic transaction costs; live paper-trading bot
- Companion multi-asset signal track: walk-forward, out-of-sample validation; ~0.7 Sharpe on the Numerai signal competition
- Financial Models
- Portfolio Management
- Trading Strategy
- Time Series
- Live Paper Trading
ML@Purdue · Applied Prediction Markets
TSA Forecasting for Kalshi
Contributor on ML@Purdue team project (PM: Eubene In) building a production forecasting system for Kalshi's weekly TSA checkpoint contracts. Owned the ARIMA/SARIMAX baseline track and walk-forward benchmark harness; implemented quarter-Kelly position sizing.
- Best baseline (ENSEMBLE_BASIC, fold-wise retraining): R² 0.67 · MAE 142.7k · 95.88% PI coverage
- Empirical finding: retraining frequency matters more than model complexity for this problem
- Production track: AutoGluon ensembles with Newey-West HAC standard errors
- Paper-trading since March 2026 via GitHub Actions
03
Experience & Education
SLMs & Agentic AI Intern, Hexaware Technologies
Built a multi-detector statistical anomaly ensemble (robust MAD z-scores, Mahalanobis distance on shrinkage covariance, trajectory deviation), validated against held-out anomaly classes and reported honestly where it failed to generalize. Diagnosed a covariance-estimation bias mis-scaling the Mahalanobis statistic, halving the false-positive rate at constant recall.
Research Assistant, Purdue College of Liberal Arts Research Academy
Designed large-scale multi-agent simulation experiments for statistical analysis and hypothesis testing under partial information, with reproducible Python pipelines for out-of-sample evaluation. Modeled sequential decision-making under uncertainty, achieving a 25% improvement in task accuracy through data-driven intervention design.
Software Engineering Intern, Hotkeys Holding LLC
Engineered low-latency retrieval pipelines in Python using vector databases and Gemini APIs, cutting document-lookup latency ~90% and enabling sub-200ms real-time inference. Designed caching and batching workflows that reduced LLM response time 95% on cache hits, with end-to-end instrumentation for latency, throughput, and retrieval quality.
Education
Purdue University
B.S. Mathematics & Statistics
Quantitative Coursework
- Mathematical Probability
- Statistical Theory
- Introduction to Time Series
- Linear Algebra
- Vector Calculus
- Discrete Mathematics
- Data Structures
- Computer Architecture
- Assembly Language
Planned · Fall 2026 Foundations of Analysis · Elementary Stochastic Processes
Competitions & Honors
- Jump Trading Probability Cup: Top 20% (343 forecasts, +2.8 RBP vs. crowd)
- Putnam (2025)
- ICPC Regional (2024)
- IMC Trading US Chess Academy: 7th, Qualifier Bracket (2026)
- CICSE Chess Nationals: Tamil Nadu Rep (2023)
04
Writing
Eleven articles across four tracks. The flagship is the prediction-markets work: a negative result, published because a pre-registration you only report when it flatters you is not a pre-registration.
Prediction Markets
Cross-venue microstructure from xResidual: what tick data says about a speed advantage that does not become money.
QuantF1 Research
Separating driver skill from machinery. The full series is listed in section 02.
- The Sharpe Ratio of a DriverOct 2025
- The Sortino Ratio of a DriverOct 2025
- The Execution Profile of a DriverJan 2026
- The Alpha of a DriverJan 2026
- The Physics of FailureFeb 2026
Machine Learning
Neural networks, recommenders, and adversarial robustness.
- Adversarial Attacks on Neural NetworksMay 2024
- Hybrid Neural Network for Movie RecommendationsFeb 2023
The recommender write-up is cited in Lavreniuk and Potapova (2025), Applied Information Technologies, Vasyl' Stus Donetsk National University.
Neurosymbolic AI
Hybrid symbolic-neural systems, written before the wave.
Earlier work · applied ML and neurosymbolic AI, 2023–24
Repositories behind the articles above: a neurosymbolic disease-triage service (Flask, Dockerized, CI/CD), a study of adversarial attacks and defenses (FGSM, PGD, C&W), and the hybrid movie recommender that drew the citation above.
05
Let's Connect
I'm always interested in discussing research, collaborating on projects, or exploring new opportunities in quantitative finance, machine learning, and AI.