Folio Lab/Documentation

Benchmark Tracker

Build a long-only portfolio that maximises return subject to a tracking-error budget against a chosen benchmark — useful for enhanced-indexing strategies on Nifty / Sensex.

Overview

The Benchmark Tracker constructs a portfolio that aims to outperform a benchmark while constraining how much it deviates from it. Tracking error is defined as the standard deviation of the difference between portfolio and benchmark returns; the optimiser takes that as a budget and seeks the highest expected return within that budget.

This is the standard formulation for enhanced indexing: take measured active risk in proportion to your conviction, while keeping the portfolio anchored to the benchmark.

Mathematical Formulation

Let be the portfolio return and the benchmark return. The tracking error (TE) is:

The optimisation problem is:

Folio Lab implements this via skfolio's MeanRisk with objective_function = MAXIMIZE_RETURN and a tracking-error constraint. Default (1%); if the constraint is infeasible at the requested level the optimiser progressively relaxes to 0.01 then 0.02 and switches between CLARABEL and SCS solvers before raising.

When to Use

  • Enhanced indexing: You want benchmark exposure but with a tilt toward names you believe will outperform.
  • Mandate-driven portfolios: A client mandate sets a hard cap on tracking error against Nifty 50 or Sensex.
  • Tax / liquidity-driven sub-replication: You cannot hold all benchmark constituents but want to closely follow it.

Advantages & Limitations

Advantages

  • Mandate-friendly: Direct control over relative risk.
  • Convex problem: Reliable convergence.
  • Interpretable: Tracking error is a familiar number.
  • Long-only: Compatible with standard NSE/BSE mandates.

Limitations

  • Requires benchmark returns: No benchmark, no method.
  • Backward-looking: TE estimated from history may understate stress regimes.
  • Sensitive to expected returns: Garbage-in, garbage-out for the return signal.
  • Concentration risk: Strict TE may force you to mirror benchmark concentration.

References

  • Roll, R. (1992). "A Mean/Variance Analysis of Tracking Error." The Journal of Portfolio Management, 18(4), 13-22.
  • Jorion, P. (2003). "Portfolio Optimization with Tracking-Error Constraints." Financial Analysts Journal, 59(5), 70-82.
  • skfolio documentation — skfolio.optimization.MeanRisk.