You are reviewing a report by a portfolio manager that indicates that a fund's predicted (forward-looking) tracking error is 94.87 basis points

Furthermore, it is reported that the predicted tracking error due to systematic risk is 90 basis points and the predicted tracking error due to non-systematic risk is 30 basis points. Why doesn't the sum of these two tracking error components total up to 94.87 basis points?

The predicted tracking error is 94.87 basis points. The two major risk categories are systematic and non-systematic risks. For our portfolio, they are respectively 90 basis points and 30 basis points. Now this might seem confusing because adding these two risks we do not get to the predicted tracking error of 94.87 basis points for the portfolio. The reason is that these risk measures are standard deviations and therefore they are not additive. However, the variances are additive. The implicit assumption in this calculation is that there is no correlation or covariance between any of the two components of the risk factors.Consequently, the variance of the two major risk components is:

Predicted tracking error for systematic risks2 = variance for systematic risks = 902 = 8,100

Predicted tracking error for nonsystematic risks2 = variance for nonsystematic risks = 302 = 900

The total variance is 8,100 + 900 = 9,000 . The square root of the total variance is 94.86833 basis points, which rounded off to 94.87 basis points is equal to the predicted tracking error for the portfolio.