# Active Risk

## What it is:

Also called tracking error, active risk is the difference between a portfolio’s returns and the benchmark or index it was meant to mimic or beat.

There are two ways to measure active risk. The first is to subtract the benchmark’s cumulative returns from the portfolio’s returns, as follows:

Returnp - Returni = Active Risk

Where:
p = portfolio
i = index or benchmark

However, the second way is more common, which is to calculate the standard deviation of the difference in the the portfolio and benchmark returns over time. The formula is as follows:

## How it works (Example):

Let’s assume you invest in the XYZ Company mutual fund, which exists to replicate the Russell 2000 index, both in composition and in returns. If the XYZ Company mutual fund returns 5.5% in a year but the Russell 2000 (the benchmark) returns 5.0%, then using the first formula above, we would say that the XYZ Company mutual fund had a 0.5% active risk.

As time goes by, there are more periods during which we can compare returns. This is where the second formula becomes more useful. The consistency (or inconsistency) of the “spreads” between the portfolio’s returns and the benchmark’s returns are what allow analysts to try to predict the portfolio’s future performance. If, for example, we knew that the portfolio’s annual returns were 0.4% higher than the benchmark 67% of the time during the last five years, we would know that this would probably be the case going forward (assuming the portfolio manager made no major changes). The predictive value of these calculations gets even better when there are more data points and when the analyst accounts for how the portfolio’s securities move relative to one another (this is called covariance).

Several factors generally determine a portfolio’s active risk:

1. The degree to which the portfolio and the benchmark have securities in common
2. Differences in market capitalization, timing, investment style and other fundamental characteristics of the portfolio and the benchmark
3. Differences in the weighting of assets between the portfolio and the benchmark
4. The management fees, custodial fees, brokerage costs and other expenses affecting the portfolio that don’t affect the benchmark
5. The volatility of the benchmark
6. The portfolio’s beta

Further, portfolio managers must accommodate inflows and outflows of cash from investors, which forces them to rebalance their portfolios from time to time. This too involves direct and indirect costs.

## Why it Matters:

Low active risk means a portfolio closely follows its benchmark. High active risk indicates the opposite. Thus, active risk gives investors a sense of how “tight” the portfolio in question is around its benchmark or how volatile the portfolio is relative to its benchmark. It is important that some benchmarked portfolios are allowed more active risk than others -- this is why investors should understand whether their benchmarked portfolios are intended to either replicate a benchmark, invest in ways that mirror the spirit of the benchmark, or merely attempt to statistically recreate the behaviors of the benchmark.

Although some investors may be happy that the portfolio in our example outperformed the benchmark, the active risk actually suggests that the fund manager took on greater risk. This is not always what the fund’s investors want, and this is why active risk is in some ways a measure of excess risk.

Although the benchmark represents a feasible alternative to the portfolio in question, calculating active risk does not mean the wise investor must limit comparison to just the benchmark; he or she will also evaluate the active risk of other portfolios with the same objective.

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