Work

Quantitative Methods · UC3M · November 2025

Bank branch profitability

What drives the ordinary margin across 129 branches after a merger

Reward the residual, not the size.

Course
Quantitative Methods for Management, Master in Management, UC3M
Data
129 branches, 8 financial predictors, branch origin
Model
Log-log OLS, best-subsets selection
Mark
Distinction

01/The brief

Bank C has just absorbed two banks, A and B. Management wants to know what actually drives a branch's ordinary margin, whether the absorbed branches perform differently, and how to pick eight branch directors for a bonus without simply rewarding the biggest branches.

The data covers 129 branches: commissions, mortgages, loans to property developers, investment funds, SME loans, consumer loans, unpaid loans and deposits, plus the bank each branch came from.

02/The model in numbers

  • 129

    Branches in the sample

  • 84.2%

    Adjusted R² of the optimal model

  • 5

    Drivers kept, all significant at p < 0.003

  • 2.03

    Durbin-Watson: no residual autocorrelation

  • −33.4%

    Margin of Bank A branches against Bank B, all else equal

  • +28.4%

    Margin of Bank C branches against Bank B, all else equal

03/The five drivers

Elasticities from the optimal model: a 1% rise in each driver goes with this percentage change in the ordinary margin, holding the others constant.

  • Commissions0.355
  • SME loans0.165
  • Deposits0.127
  • Property-developer loans0.121
  • Consumer loans0.118

ln(margin) = 0.259 + 0.355 ln(commissions) + 0.165 ln(SME) + 0.121 ln(developer) + 0.118 ln(consumer) + 0.127 ln(deposits)

04/Try the model

Change each driver and see what the fitted model predicts for a branch's ordinary margin. Commissions move it most: a 10% rise adds about 3.4%.

  • 0%

    β = 0.355

  • 0%

    β = 0.165

  • 0%

    β = 0.127

  • 0%

    β = 0.121

  • 0%

    β = 0.118

Predicted change in ordinary margin

0.0%

Uses the fitted elasticities. Changes compound: each driver contributes (1 + change)^β. A model prediction, not a forecast for any real branch.

05/What the analysis found

  1. 01

    Logs first

    The margin was heavily skewed (standardised skewness 7.02, kurtosis 8.94), and so were most predictors. A log transform of every continuous variable brought them close enough to normal for OLS, and turned the coefficients into elasticities.

  2. 02

    Collinearity, handled

    All eight predictors were significant on their own, but together they inflated each other's standard errors. A best-subsets search showed adjusted R² flattening after five variables; investment funds was dropped (p = 0.37), leaving a stable five-driver model.

  3. 03

    Real estate: developers yes, mortgages unclear

    Forcing both property variables in, as the division director asked, a 1% rise in developer loans goes with a 0.070% higher margin (p < 0.001). Mortgages turn insignificant (p = 0.52) because they move with developer loans, so their own effect cannot be isolated.

  4. 04

    Investment funds add nothing

    With the main drivers in the model, the investment-funds elasticity is 0.0066: economically and statistically zero.

  5. 05

    Where a branch came from matters

    Holding the portfolio constant, branches from Bank A earn a 33.4% lower margin than Bank B branches, and Bank C branches 28.4% more (p < 0.0001 for both).

06/Who gets the bonus

Ranking branches by raw margin rewards size and location, not management: a large branch in a wealthy area wins by default.

Instead, use the model to predict what each branch should earn given its portfolio, then rank by the residual, the gap between actual and predicted margin. The eight branches with the largest positive residuals beat their own circumstances. They get the bonus.

07/What I would do next

  1. 01Re-estimate on the central 90% of branches to check whether the stars are genuinely better or just a different population.
  2. 02Standardise every predictor before comparing effects.
  3. 03Fit Lasso and Ridge regressions, which handle collinearity by shrinking weaker coefficients instead of dropping them.

08/Team

Francisco Cordeiro Batista, Gonçalo Carinhas Marques, André Mourão D. Moreira, Maria Francisca Silva

My part: the statistical analysis, the model selection and the interpretation of the coefficients for management, co-written with the team.

Academic coursework. Figures come from the case data, not from any employer.