Tracking Error Minimization

Tracking error minimization is a key strategy in portfolio management, especially for index tracking or replicating a benchmark portfolio. It aims to construct a portfolio that closely follows the performance of a designated model portfolio. The central idea is to minimize the variance between the returns of the tracking portfolio and the returns of the model portfolio.

Mathematically, the tracking error (TE) can be defined as:

where:

This formula essentially captures the volatility of the difference in returns between the two portfolios. By minimizing this variance, the tracking portfolio seeks to stick as closely as possible to the benchmark's performance.

Note that constraints influence the optimal portfolio composition and can affect the achievable tracking error. For instance, a constraint limiting investment in stocks of a particular region might increase the tracking error if the benchmark has significant exposure to that segment. Conversely, constraints can also help manage risk and align the portfolio with specific investment objectives.

In essence, tracking error minimization with constraints involves finding the optimal portfolio weights that minimize the variance between the tracking portfolio's returns and the benchmark's returns, while simultaneously adhering to the specified limitations. This approach helps investors construct portfolios that closely track their desired benchmarks while incorporating practical investment considerations and risk management principles.

Here is an example of tracking the SMI index in USD (orange line) with a portfolio of 20 stocks: