From Linear Regression to Lasso: Fast, Interpretable Baselines for Market Prediction
In a world obsessed with transformers and "foundation models," linear and regularized regressions still do a lot of quiet, serious work in finance.
1. Why Linear Models Still Matter
The hype cycle has moved on to transformers and “foundation models,” but linear and regularized regressions still do a lot of quiet, serious work in finance. Three reasons they earn their keep:
- They are fast: you can run a full equity universe in seconds.
- They are interpretable: coefficients read like a factor exposure sheet.
- They provide a clean benchmark for more complex models.
That last point is why the linear family makes such a useful baseline. Before a tree ensemble or neural net is worth the extra complexity, it should clear what a well-regularized linear model already gives you out-of-sample. In volarixs you run both as experiments on the same datasets, feature sets, and target horizon, so the comparison is apples-to-apples on the metrics each run records.
2. The Core Ideas: From OLS to Elastic Net
We use four core variants:
- OLS / Linear Regression: minimize squared error, no regularization.
- Ridge (L2): penalize large coefficients, shrink them towards zero.
- Lasso (L1): penalize absolute values, force many coefficients to zero (feature selection).
- Elastic Net: combination of L1 and L2; more stable than pure Lasso in correlated features.
Model Family Overview
The objective functions:
min ||y - Xβ||²min ||y - Xβ||² + λ||β||²min ||y - Xβ||² + λ||β||₁min ||y - Xβ||² + λ₁||β||₁ + λ₂||β||²Interactive Coefficient Shrinkage Playground
| Factor | Coefficient | Sign |
|---|---|---|
| Market Beta | 0.409 | |
| Size | -0.291 | |
| Value | 0.255 | |
| Momentum | 0.136 | |
| Volatility | -0.200 | |
| Quality | 0.164 | |
| Macro | 0.109 |
Example: Suppose you predict 5-day forward returns for AAPL using factors like market beta, size, value, momentum, volatility, macro surprises.
- • OLS might use everything and overfit.
- • Ridge shrinks exposures, making the model more robust out-of-sample.
- • Lasso might drop some factors entirely if they don't help.
- • Elastic Net gives a balance: selective but stable.
3. Application to Financial Time Series
Key points:
- We transform price data into cross-sectional features at each date (returns, realized vol, rolling betas, etc.).
- We run cross-sectional regressions (all tickers at a given date) or time-series regressions (one asset over time) depending on the setup.
- Regularization helps with:
- • Noisy factors
- • High collinearity (value vs quality vs carry, etc.)
- • High-dimensional feature sets (text, macro, technicals)
4. How volarixs Uses This Family
In volarixs, the linear models sit alongside trees, boosting, neural nets, time-series and volatility models in the experiment wizard:
- They serve as a baseline you select in an experiment and as cheap, fast candidates for the prediction factory.
- Each run records:
- • Train and test R² (
r2_train/r2_test), so you can see the gap between in- and out-of-sample fit at a glance - • The model, datasets, feature sets and target horizon that produced it, plus run status
- • The regime context the run was made under — the macro state and historical analogues that let you read a result against the environment it came from
- • Train and test R² (
That train-vs-test R² gap is exactly where regularization earns its keep: a Ridge or Elastic Net run that holds up out-of-sample is the kind of baseline a heavier model has to beat to justify itself.