Performance Perspectives Blog

Expert Level – Common Themes #1: Standard Deviation, Downside Deviation and Tracking Error

by | Apr 18, 2010



It may seem that the list of formulae to memorize for the CIPM Expert Level exam is quite long, but three of the risk measurement formulas are essentially three different applications of the same formula.

Expert level candidates are responsible for knowing the formulae for the following risk statistics:

  • standard deviation
  • downside deviation
  • tracking error

Consider the formulae for each of these:
If you accept and understand that the standard deviation formula measures variability in an account’s historical returns, then downside deviation and tracking error are variations of that idea:

  • Downside deviation uses the same formula as standard deviation, except that it measures variability in the downside (i.e., losing returns). Losing returns are defined as those that fall below the pre-defined target return T. Thus, T replaces the average return in the standard deviation formula. The other modification to the formula is that any observations that are at or above the target return are treated as having a distance from the target of zero. We still divide by the total number of observations, N.

  • Tracking error measures the variability of the historical excess returns. Thus, tracking error uses the same formula as standard deviation (because it is, in fact, a standard deviation), but we are using the excess return in each period rather than the account’s return in each period as the input data.

Given this, candidates have a couple of different ways to approach these formulae:

  1. You can memorize the individual formulae
  2. You can memorize the formula for standard deviation, and learn the three different applications for it.

Every candidate learns differently, but I recommend the latter approach be used, as it will give you a more comprehensive understanding of the material.

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