Tracking error

Imagine a month when your product returns 2 % and its benchmark returns 2.10 %. The product has lagged by 0.10 percentage point; a percentage point here is simply the difference between two percentage returns. That gap is called an active return, even if the product is not actively managed. It is written a=Rp−Rb, where Rp is the portfolio return and Rb the benchmark return for the same period. Repeat this for later months. TE then examines how these differences vary around their average. It is neither a single gap nor the volatility of prices themselves. [1]

In our illustrative example, three monthly active returns are −0.10; 0.00; +0.10 percentage point. The product lags once, matches the benchmark once and beats it once. The average difference is 0.00. To calculate the sample standard deviation, square each distance from that average; their sum is 0.02. Because we use a sample, divide by n−1=2, where n is the number of observations, then take the square root: √(0.02/2)=0.10 percentage point. This is monthly TE before annualization. Three observations explain the calculation; they do not provide a reliable assessment of a real product. [1]

Change the series to −0.10; −0.10; −0.10 percentage point. The product lags by the same amount each time. Nothing varies around its own average, so TE=0. Yet the investor received less than the benchmark in every month. This is why we also examine Tracking difference, the difference between product and benchmark returns over a chosen horizon. For the entire period, monthly returns compound: each new change applies to a value already changed by the preceding months. The simple average of monthly gaps is therefore not automatically the difference between compounded returns. [1] [2]

TE is often annualized, meaning expressed on an annual basis, to help comparison. For monthly TE of 0.10 percentage point, the usual multiplication by √12 gives approximately 0.346 percentage point a year. But this conversion rests on assumptions: variability must be sufficiently stable, with uncorrelated periodic deviations, meaning no linear relationship between deviations in different periods. It is not a prediction of a certain annual result. Daily and monthly series, or observation windows of different lengths, may not be directly comparable without knowing the method. [1]

The benchmark, currency, valuation date and time must match. Also distinguish price return from total return: the latter accounts for distributions to investors according to its methodology. NAV is the net value of assets after liabilities, here expressed per share. If you use NAV returns, check which costs they already include. Missing trading days, different closing times or a different currency share class can produce discrepancies simply because the inputs do not align. A number obtained that way does not by itself prove the manager has done a poor job. [1] [2]

TE calculated from NAV returns against an index assesses how the product’s assets follow that benchmark. But the investor buys and sells shares at a market price. It can sit above NAV, a premium, or below it, a discount. Changes in that gap add another influence on market-price returns. A one-off premium of 2 % is not TE = 2 %. A single price gap cannot show how return differences varied over time; that requires a series of consistently measured periods. [3]

A product may not hold assets in exactly the same proportions as its index. Some use sampling: rather than holding every constituent, they select a group intended to reproduce its performance. Rebalancing means adjusting holdings when the target composition changes, and those trades cost money. Taxes and other expenses can matter too. However, not every cost affects TE in the same way. In a purely mathematical model, subtracting the same constant from every active return shifts the average but leaves variability around it unchanged. Do not assume a real fee produces precisely that constant return difference without checking. [2]

Ex-post TE is calculated retrospectively from a chosen set of past data. A forecast of future TE instead depends on a model and its assumptions; it is not the same measure. Even low historical TE does not protect against a market decline. If portfolio and benchmark both lose exactly 20 % in every observed period, all active returns are zero. Tracking is perfect in this example, but the investment keeps losing value. Read tracking difference and actual absolute losses alongside TE. Tracking accuracy and investment safety are separate questions. [1] [2]