How to use the tracking error calculator
From return series gives the full picture:
- Paste the portfolio’s returns in percent, oldest first. The example holds 36 monthly returns of an actively managed stock portfolio, the same data as our alpha calculator.
- Paste the benchmark’s returns for the same periods. Use the index the fund names as its benchmark, as a total return series that includes dividends.
- Choose the frequency, which sets the annualization factor.
From annual figures is the shortcut. Enter the two annual returns and either the tracking error from a factsheet or, if you do not have it, the two volatilities and their correlation to estimate it.
The formulas
Tracking error = stdev(at) × √NRp,t and Rb,t are the portfolio and benchmark returns in period t. The standard deviation is the sample version (dividing by n − 1). N is the number of periods in a year: 12 for monthly data.
Hit rate = periods with at > 0 ÷ all periodsThe numerator is the average active return, annualized. The hit rate counts how often the portfolio beat the benchmark, whatever the size of the gap.
When only volatilities are available, tracking error can be estimated from them:
A worked example
Over 36 months, the example portfolio’s monthly return differed from the benchmark’s with a standard deviation of 1.85%. Multiplied by √12, that is an annualized tracking error of 6.43%.
The portfolio beat the benchmark by 2.70% a year on average, so the information ratio is 0.42. It came out ahead in 20 of the 36 months, a hit rate of 56%. By the end, money in the portfolio was worth 5.55% more than the same money in the benchmark.
What tracking error tells you, and what it does not
Tracking error measures how independent a portfolio is from its benchmark. It is the risk an investor takes by choosing an active manager instead of the index, and it says nothing about whether that risk paid off. A fund can have a high tracking error and beat its index handsomely, or trail it badly; the information ratio is what connects the two.
As a loose guide:
- Index funds aim for a tracking error close to zero. What remains comes from fees, cash held for flows, sampling (holding only part of a large index) and the timing of dividends.
- Enhanced index and low-tracking-error funds deliberately allow a little more, in exchange for a chance at modest outperformance.
- Diversified active funds run noticeably higher tracking error, and concentrated or style-tilted funds higher still.
If a fund that charges active fees shows a tracking error close to that of an index fund, it is probably holding something very close to the index, a pattern often called closet indexing.
Why correlation matters so much
Tracking error falls quickly as the correlation with the benchmark rises. With the quick tool’s volatilities of 18% and 16%:
| Correlation with the benchmark | Estimated tracking error | Information ratio at a 1.50% active return |
|---|---|---|
| 0.90 | 7.85% | 0.19 |
| 0.95 | 5.73% | 0.26 |
| 0.99 | 3.12% | 0.48 |
Two funds with the same volatility as the index can therefore have very different active risk. The estimate is sensitive to the correlation input, so treat it as a rough figure and prefer tracking error computed from actual return differences when you have them.
Arithmetic and compound active return
The information ratio uses the average of the periodic differences, annualized by multiplying by N. That is the standard convention, but it is not the same as the difference between the two compound annual returns, which the calculator shows separately: +2.70% against +2.07% in the example. The gap comes mostly from the difference in volatility, because the more volatile series loses more of its average return to compounding. When you compare information ratios from different sources, check which convention they use.
What this calculator does not include
The calculator measures past, or ex-post, tracking error from the returns you supply. Fund managers also use ex-ante tracking error, forecast from the current holdings with a risk model, which can differ a lot when the portfolio has changed. Results depend on choosing the right benchmark: measured against the wrong index, a fund looks riskier and its information ratio less meaningful. Returns should be after fees if you want the investor’s experience. Short histories give unstable estimates, and the information ratio in particular needs many years of data before it says much about skill. To separate skill from market exposure, see the alpha and beta calculators.