How is logistic regression used in finance and how does it differ from linear regression?

Logistic regression is a classification technique used when the dependent variable is binary (yes/no, default/no-default, buy/sell). This is fundamentally different from linear regression, which predicts continuous outcomes.

Why not use linear regression for binary outcomes?

Linear regression can predict values outside the [0, 1] range — a probability of -0.2 or 1.4 is meaningless. Logistic regression uses a sigmoid function to constrain predictions between 0 and 1:

P(Y=1) = 1 / (1 + e^(-z))

where z = β₀ + β₁X₁ + β₂X₂ + ...

Financial applications:

1. Credit default prediction: Will this borrower default? Input: debt/equity, interest coverage, current ratio → Output: probability of default
2. Earnings surprise prediction: Will the company beat estimates? Input: analyst revisions, insider buying, earnings momentum → Output: probability of beat
3. Merger completion prediction: Will a proposed deal close? Input: regulatory risk, financing certainty, premium offered → Output: probability of completion

Interpreting coefficients — Odds ratios:

In logistic regression, coefficients are interpreted as log odds:

• If β₁ = 0.5 for debt/equity ratio, then each 1-unit increase in D/E multiplies the odds of default by e^0.5 = 1.65 (65% higher odds)
• A negative coefficient reduces the odds

Example: Sentinel Credit Analytics builds a logistic model for corporate default:

For a company with D/E = 2.0, Interest Coverage = 1.5, Cash/Assets = 0.05:

z = -3.0 + 0.82(2.0) + (-0.45)(1.5) + (-1.20)(0.05) = -3.0 + 1.64 - 0.675 - 0.06 = -2.095

P(default) = 1/(1 + e^2.095) = 1/(1 + 8.13) ≈ 10.9%

Exam tip: CFA Level II tests interpretation of logistic regression output — know how to calculate predicted probabilities and interpret odds ratios. You won't need to derive the maximum likelihood estimation.

Practice quantitative methods in our CFA Level II materials.