# Understanding Tracking Error & R-Squared

Jocelyn Gilligan

July 23, 2024

Understanding Tracking Error & R-Squared

When evaluating the performance of an investment portfolio, it’s essential to consider metrics that help measure the portfolio’s consistency and alignment with its benchmark. Two critical metrics in this context are Tracking Error and R-Squared. These metrics provide insights into the portfolio’s performance and risk characteristics. Let’s explore what these metrics mean, how they are calculated, and their significance.

What is Tracking Error?

Tracking Error measures the deviation of a portfolio’s returns from its benchmark returns. It indicates how closely a portfolio follows the benchmark to which it is compared. A lower tracking error suggests that the portfolio’s returns are closely aligned with the benchmark, while a higher tracking error indicates greater deviation.

Tracking Error Formula

Tracking Error= standard deviation of (P-B)

where:

• P = Portfolio return
• B​ = Benchmark return

Annualized Tracking Error

When using monthly data, tracking error is annualized by multiplying the result by the square root of 12.

What is a Good Tracking Error?

A “good” tracking error depends on the investment strategy. For passive funds that aim to replicate a benchmark, a lower tracking error is desirable. For active funds that seek to outperform the benchmark, a higher tracking error might be acceptable, reflecting the manager’s active bets.

What is R-Squared?

R-Squared (R²) measures the proportion of the portfolio’s movements that can be explained by movements in its benchmark. It ranges from 0 to 100%, where a higher R-Squared indicates a greater correlation between the portfolio and its benchmark.

R-Squared Formula

R² = (Correlation of portfolio and benchmark returns)²

What is a Good R-Squared?

A higher R-Squared (closer to 100%) indicates that the portfolio’s returns are highly correlated with the benchmark. For passive funds, a high R-Squared is preferred. For active funds, a lower R-Squared might indicate that the manager is taking independent positions relative to the benchmark.

How to Interpret Tracking Error and R-Squared

• Tracking Error: Indicates the consistency of the portfolio’s returns relative to the benchmark. A lower tracking error is desirable for passive strategies, while active strategies might tolerate higher tracking errors.
• R-Squared: Shows the degree of correlation between the portfolio and benchmark returns. A high R-Squared suggests strong alignment, suitable for passive strategies, while a lower R-Squared might indicate active management.

While both Tracking Error and R-Squared are good measures to understand how closely a track record is managed to a benchmark, they should be analyzed with other available performance metrics. A high or low Tracking Error and R-Squared does not indicate if the performance was good or not. Therefore, using Tracking Error in combination with other metrics like Alpha or the Sharpe Ratio can help provide additional information on whether the strategy performed well while analyzing how closely it was managed to a benchmark. Any selected performance metric should also cover the same time periods as the calculated Tracking Error and R-Squared for the most relevant comparison.

Why are Tracking Error and R-Squared Important?

Both metrics are crucial for assessing portfolio performance and understanding the risk-return profile. They help investors gauge how well a portfolio is managed relative to its benchmark and assess the effectiveness of active versus passive management strategies.

Conclusion

Tracking Error and R-Squared are essential tools for evaluating portfolio performance. Understanding these metrics can help investors make informed decisions about their investment strategies and better manage their portfolios.