Swiss bonds: how well do you really understand tracking error?

At first glance, tracking error (TE) might seem like a straightforward gauge of how closely a portfolio follows its benchmark. But dig a bit deeper, and you’ll find a complex interplay of factors that can significantly influence how TE is calculated, interpreted and applied.

Whether evaluating past performance or forecasting future risk, a deeper understanding of TE can lead to more informed investment decisions.

Volatility of relative returns

Most investors consider both absolute and relative returns when assessing performance. The absolute view focuses on how much profit is generated by a portfolio, while the relative view focuses on how a portfolio performs against a benchmark.

Risk-aware investors seek to understand how much absolute or relative performance might fluctuate in the future. The standard risk measure for estimating the variability of returns is volatility. It indicates how much absolute or relative returns deviate from their expected value, but not the direction of the deviation.

TE is the term commonly used to refer to the volatility of relative returns (or excess returns), showing how much portfolio returns fluctuate around benchmark returns. While passive investment solutions should aim for a minimal TE, active strategies often use TE limits to control the level of active risk a portfolio takes on.

Given that TE measures the fluctuations of excess returns, a portfolio that consistently outperforms its benchmark by a fixed amount will still show a low TE, despite significant deviations from the benchmark.

The concept of a maximum TE of 1% for an active strategy may seem straightforward. Yet the details warrant a closer look, highlighting important questions about how the figure is calculated:

• What is the frequency of the underlying return series (daily, monthly, etc.)?
• Over what time period is the volatility of excess returns calculated? How many data points are needed?
• How should TEs be compared?

Read also: A superior credit exposure: how CDS can help solve performance problems in high yield

Return series frequency

Monthly returns are often used in practice, and an annualised TE is calculated over a specific number of past data points for better comparability. For example, an annualised TE based on monthly data over three years would use 36 data points.

The shorter the time series used, the more sensitive the TE becomes to individual performance outliers. For instance, if the portfolio experienced an unusually large performance swing during the onset of the Covid crisis, this data point would distort the TE for 36 months in a three-year series before it returned to its ‘normal’ level.

In a five-year series, the outlier would still have an effect, but the distortion would be smaller because of the larger sample size (60 instead of 36 data points). Therefore, longer time series are advisable to reduce the impact of outliers on TE.

FIG 1. Rolling ex-post TE over different time horizons (Swiss Franc Credit Bond strategy vs the SBI A-BBB Index)¹

Ex-ante versus ex-poste

Another important practical question: how can you control the TE limit when launching a new actively managed portfolio that lacks any performance history? If, for example, investment guidelines specified a maximum annualised TE of 1% based on monthly data over the past five years, wouldn’t you have to wait five years before you could calculate the first realised TE?

The answer is yes – but only if you were using ex-post (or realised) TE. This is the type we have discussed so far. Ex-post TE is by definition backward-looking, based on actual, realised excess returns.

Ex-ante TE, on the other hand, allows for a risk assessment before the investment is made. It’s a forward-looking measure based on how the portfolio is built and the types of risks it’s exposed to. Let’s break down how it works.

Risk model calculations

Ex-ante TE can be interpreted as the expected TE and is based on a risk model. This model defines the specific risk factors (fₙ) used to describe the returns (either of individual securities or a portfolio).

Ex-ante TE depends directly on the risk model used, and they can vary widely. To calculate the ex-ante TE for a given model, you need the portfolio’s exposure to the benchmark (ω) and the covariance matrix of the risk factors (C).

Ex-ante TE

This calculation shows that ex-ante TE responds both to changes in portfolio exposure and to changes in the covariance matrix. For example, if the volatilities of the risk factors decrease over time, the ex-ante TE will also decrease – even if the portfolio exposure remains unchanged.

Read also: Fixed income in the new macro world order

Which measure to use?

Given the nature of ex-ante TE, it offers a more timely assessment of current active risk. For example, if a skilled active portfolio manager has achieved a stable monthly outperformance of 0.1 percentage point over the past three years, the ex-post TE would be 0%. But that doesn’t mean the portfolio took no active risk over that period.

If you want to know how much risk a portfolio manager is taking, ex-ante TE is the preferred measure. For evaluating a manager’s past performance, ex-post TE is more appropriate.

In theory and practice, the ex-ante TE is usually lower than the ex-post TE seen over time. This is because ex-ante TE assumes that portfolio exposure remains constant over time. In reality, exposure changes continuously (due to market movements and monthly benchmark rebalancing). These changes introduce more variability, which is why the actual tracking error often ends up higher than what was estimated.

Swiss bonds and tracking error

When it comes to Swiss bonds, passive products usually have a TE of less than 0.2% p.a. The allowed TE is often closer to 1.0% p.a. for active products that focus on the investment grade segment and don't take significant active interest rate risks.

A TE target of 2%, on the other hand, means the portfolio needs more flexibility in the investment guidelines. This might include being able to invest in riskier bonds (sub investment grade), use a wider range of instruments (including derivatives) or take more pronounced active interest rate risks.

In summary, ex-ante TE works best for assessing active risk in a portfolio, while ex-post TE is more suitable for evaluating the past performance of active portfolio managers.

Ultimately, understanding both types of tracking error, and when to use them, offers a more complete view of active portfolio risk and performance, helping investors make decisions with greater confidence.