[{"content":"When you train a neural network and a gradient boosting model on the same stock return data, they don\u0026rsquo;t just give you different numbers — they disagree in structured ways. The neural network picks up on nonlinear interactions between firm characteristics. The boosted tree finds threshold effects and feature interactions that linear models miss entirely. And the regularized linear model? It sees a cleaner, lower-dimensional version of the same data.\nThis isn\u0026rsquo;t a bug. It\u0026rsquo;s information.\nThe setup In my current research, I train models from six different classes — ridge regression, elastic net, random forests, XGBoost, LightGBM, and neural networks — on the same panel of US stock returns spanning 1957-2024. Each model produces a set of \u0026ldquo;factors\u0026rdquo; (managed portfolios formed from its predictions). When you stack these factors together into a zoo and look at their covariance structure, something surprising happens.\nThe eigenvalue spectrum is bimodal. The linear models produce high-variance factors that cluster together. The nonlinear models produce lower-variance factors that are nearly orthogonal to the linear ones — subspace angles exceeding 70 degrees.\nI call this spectral segregation.\nWhy it matters Most ensemble methods treat model disagreement as noise to be averaged away. But if the disagreement is geometrically structured — if different model classes are literally pointing in different directions in return space — then blind averaging destroys information.\nThe key insight: a model\u0026rsquo;s deviation from the ensemble mean is only valuable if it aligns with the stochastic discount factor (the pricing kernel that tells you which directions in return space are compensated with risk premia). The cosine of the angle between a model\u0026rsquo;s deviation vector and the SDF explains 64% of cross-model variation in deviation quality.\nThe practical upshot Instead of equal-weighting your ensemble or using generic stacking, you can weight models by how well their unique signals align with the pricing kernel. In out-of-sample tests, SDF-aligned ensembles roughly double the Sharpe ratio compared to uniform shrinkage.\nThe deeper lesson: model disagreement isn\u0026rsquo;t just statistical variance. It reflects genuine differences in how architectures decompose the data-generating process. Understanding the geometry of that disagreement turns a liability into an edge.\nThis post summarizes ideas from my working paper, \u0026ldquo;Which Directions Pay? A Geometric Theory of Model Disagreement in Asset Pricing.\u0026rdquo; The full paper is in progress.\n","permalink":"https://ajsquestions.github.io/blog/why-ml-models-disagree-about-stock-returns/","summary":"Model disagreement in asset pricing isn\u0026rsquo;t noise — it\u0026rsquo;s geometry. A look at what happens when you point different ML architectures at the same return prediction problem.","title":"Why ML Models Disagree About Stock Returns"},{"content":"When I TA\u0026rsquo;d Financial Econometrics at Booth, students would ask: why does ridge regression improve out-of-sample performance? The standard answer — \u0026ldquo;it reduces variance at the cost of some bias\u0026rdquo; — is correct but unsatisfying. It doesn\u0026rsquo;t explain what ridge is actually doing to your portfolio.\nHere\u0026rsquo;s a more useful way to think about it.\nThe portfolio view Every linear regression on stock returns implicitly constructs a portfolio. The coefficients are weights. The predicted return is the portfolio\u0026rsquo;s expected payoff. When you add a ridge penalty, you\u0026rsquo;re not just shrinking numbers toward zero — you\u0026rsquo;re rotating your portfolio toward the directions of highest variance in the data.\nRidge penalizes the norm of the coefficient vector. In the eigenspace of the covariance matrix, this means high-variance principal components get preserved while low-variance ones get killed. The shrinkage isn\u0026rsquo;t uniform in economic terms — it\u0026rsquo;s uniform in statistical terms, which has very non-uniform economic consequences.\nWhy this matters for asset pricing In asset pricing, the low-variance directions are often where the interesting signals live. Small anomalies, conditional patterns, nonlinear interactions — these show up in eigenvectors that ridge shrinkage aggressively dampens.\nThis is exactly the spectral segregation problem I study in my research. When you mix linear and nonlinear factors in a zoo, the nonlinear factors tend to have lower eigenvalues. Ridge shrinkage, calibrated on the full zoo, systematically kills these directions — even when they carry genuine risk premia.\nThe result: your \u0026ldquo;regularized\u0026rdquo; model isn\u0026rsquo;t just simpler. It\u0026rsquo;s encoding a very specific belief — that the high-variance, linear directions are the ones worth betting on. Sometimes that\u0026rsquo;s right. Often it\u0026rsquo;s not.\nThe teaching takeaway When I explain regularization in class, I start with geometry, not formulas. Draw the ellipse (the constraint set). Draw the contour lines (the loss surface). Show where they touch. Then ask: what did we just assume about reality by choosing this shape?\nEvery regularizer is a prior. The question is whether it\u0026rsquo;s the prior you actually believe.\n","permalink":"https://ajsquestions.github.io/blog/what-regularization-actually-does-to-your-portfolio/","summary":"Ridge regression doesn\u0026rsquo;t just shrink coefficients — it encodes a prior about which directions in return space are worth betting on.","title":"What Regularization Actually Does to Your Portfolio"},{"content":"FootieM8 started as a class exercise: can the probabilistic models we study in econometrics actually predict football matches? The answer turned out to be yes — and also no, depending on what you mean by \u0026ldquo;predict.\u0026rdquo;\nThe architecture The system combines two families of models. The first is probabilistic: Poisson regression and Dixon-Coles models that estimate goal-scoring rates for each team and derive match outcome probabilities from those rates. The second is machine learning: LightGBM and logistic regression trained on Elo ratings, recent form, and historical bookmaker odds.\nThe ensemble weights these families together using cross-validated calibration. Walk-forward evaluation prevents data leakage — the system never sees future data during training, not even implicitly through feature engineering.\nCovering 25+ leagues across 30+ seasons means dealing with messy data: team name changes, league restructurings, missing fixtures, and the fact that Accrington Stanley in 1996 is not the same entity as Accrington Stanley in 2024.\nWhat actually worked The Poisson and Dixon-Coles models are surprisingly robust. They capture the base rates well — home advantage, defensive strength, scoring trends — and produce well-calibrated probabilities. When they say a team has a 40% chance of winning, that team wins roughly 40% of the time.\nElo ratings, despite their simplicity, are the single best feature for ML models. Better than recent form, better than goals scored, better than anything derived from betting odds. The LightGBM ensemble adds marginal lift on top of the probabilistic models, mainly by capturing nonlinear interactions between team quality and venue effects.\nWhat didn\u0026rsquo;t Beating the market is a different problem than predicting outcomes. The models are well-calibrated, but prediction markets (Kalshi, in my case) are also well-calibrated. The edge, when it exists, is small — typically 1-3% on specific match types. After transaction costs and the platform\u0026rsquo;s spread, most of that edge evaporates.\nThe honest conclusion: the models work as a prediction system. They don\u0026rsquo;t work as a money machine. That\u0026rsquo;s actually the more interesting finding — it\u0026rsquo;s evidence that these markets are reasonably efficient, even for relatively obscure leagues.\nThe meta-lesson Building FootieM8 taught me more about model evaluation than any class. When you have skin in the game — even play money on Kalshi — you start caring about calibration, not just accuracy. You learn the difference between a model that\u0026rsquo;s impressive on a test set and a model you\u0026rsquo;d actually bet on.\nThat distinction matters just as much in asset pricing, where the \u0026ldquo;bet\u0026rdquo; is a portfolio allocation and the \u0026ldquo;evaluation\u0026rdquo; is whether your Sharpe ratio survives out of sample.\n","permalink":"https://ajsquestions.github.io/blog/building-a-football-prediction-system/","summary":"Building a research-grade match prediction system taught me more about model evaluation than any textbook.","title":"What I Learned Building a Football Prediction System"},{"content":"Email — aryamaan.jena.phd@anderson.ucla.edu LinkedIn — linkedin.com/in/aj‑jena Links CV (PDF) GitHub ","permalink":"https://ajsquestions.github.io/contact/","summary":"\u003cp\u003e\u003cstrong\u003eEmail\u003c/strong\u003e — \u003ca href=\"mailto:aryamaan.jena.phd@anderson.ucla.edu\"\u003earyamaan.jena.phd@anderson.ucla.edu\u003c/a\u003e\n\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLinkedIn\u003c/strong\u003e — \u003ca href=\"https://www.linkedin.com/in/aj-jena-13b738172/\" target=\"_blank\"\u003elinkedin.com/in/aj‑jena\u003c/a\u003e\n\u003c/p\u003e\n\u003ch3 id=\"links\"\u003eLinks\u003c/h3\u003e\n\u003cp\u003e\u003ca href=\"/AJ_CV_Feb26.pdf\"\u003eCV (PDF)\u003c/a\u003e\n\u003c/p\u003e\n\u003cp\u003e\u003ca href=\"https://github.com/ajsquestions\" target=\"_blank\"\u003eGitHub\u003c/a\u003e\n\u003c/p\u003e","title":"Contact"}]