Interpretation Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio’s active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per cent of the mean excess return. Examples Index funds are expected to have minimal tracking errors. Inverse exchange-traded funds are designed to perform as the inverse of an index or other benchmark, and thus reflect tracking errors relative to short positions in the underlying index or benchmark. Index fund creation Index funds are expected to minimize the tracking error with respect to the index they are attempting to replicate, and this problem may be solved using standard optimization techniques. To begin, define to be:where is the vector of active weights for each asset relative to the benchmark index and is the covariance matrix for the assets in the index. While creating an index fund could involve holding all investable assets in the index, it is sometimes better practice to only invest in a subset of the assets. These considerations lead to the following mixed-integer quadratic programming (MIQP) problem:where is the logical condition of whether or not an asset is included in the index fund, and is defined as: References External links Tracking Error - YouTube Tracking error: A hidden cost of passive investing Tracking error What is the Tracking Error? Financial risk management Convex optimization