R-Squared for Stock Return Models | Dataford Interview Questions

Your question is R-Squared for Stock Return Models. Take a moment with it on the right.

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Business Context

At NorthBridge Capital, a quant analyst is comparing two linear regression models for predicting monthly stock returns. The team wants to know why a model with more predictors can show a higher $R^2$ but still be a worse choice once model complexity is considered.

Problem Statement

You are given summary statistics for two regression models fit on the same 60 months of stock return data. Model A uses market excess return as the only predictor. Model B adds size, value, momentum, and short-term reversal factors. Explain the difference between $R^2$ and adjusted $R^2$ , compute both adjusted values, and determine which model is preferable based on goodness-of-fit after penalizing unnecessary predictors.

Given Data

Model	Observations	Predictors $(k)$	$R^2$
A: Market-only	60	1	0.082
B: Multi-factor	60	5	0.109

Assume both models include an intercept.

Requirements

Define $R^2$ and adjusted $R^2$ in plain language.
Compute adjusted $R^2$ for Model A.
Compute adjusted $R^2$ for Model B.
Compare the two models and explain why adjusted $R^2$ can decrease when new predictors are added.
State which metric is more appropriate for comparing these two stock return models.

Assumptions

Both models are estimated on the same response variable and same 60 monthly observations.
Predictors were added without changing the sample period.
The goal is in-sample explanatory comparison, not causal inference.
Ignore out-of-sample validation for this exercise, though you should mention it in interpretation.