June 26, 2018 by Travis Morgan

A GIPS^{®}-compliant presentation contains a number of required statistics. One such metric is the internal dispersion of individual portfolios within a composite. The GIPS standards do not prescribe a specific methodology (as long as the measure that is selected is applied consistently) and thus many firms struggle with this calculation. The following is a best effort attempt at explaining one option: asset-weighted standard deviation.

The asset-weighted standard deviation of portfolio returns is a popular selection among investment managers for representing internal dispersion. It is, however, difficult to explain and sometimes even to interpret when presented alongside annual composite performance.

A common misconception is that the composite’s internal dispersion is intended to measure the standard deviation of the underlying accounts’ returns around the composite return. In fact though, the reported composite return does not factor into the formula and is unrelated to the asset-weighted standard deviation of portfolio returns within the composite. The standard deviation is, however, factoring the asset-weighted mean return for only those portfolios that have been in the composite for the full year. This mean return can be quite different from the composite’s asset-weighted return.

Another misconception is that the standard deviation is based simply on the mean return when in fact it is determining what the asset-weighted average return is. By using the asset-weighted average returns, the calculation is indicating that larger portfolios are more reflective of the intended strategy and as a result, the calculated mean should be weighted more heavily towards those portfolios returns.

In summary, the asset-weighted standard deviation reflects the dispersion of portfolio returns around the asset-weighted average of the returns for portfolios that have been in the composite for the full year. This all makes great in theory, but tends to be very difficult to understand and interpret.

To interpret what this means when compared to a composite return, please see the following example:

| Annual return | Beginning Market Value |
---|---|---|

1 | 10.50% | 1,000,000 |

2 | 15.00% | 15,000,000 |

3 | 10.45% | 1,000,000 |

4 | 10.65% | 1,000,000 |

5 | 10.35% | 1,000,000 |

6 | 10.68% | 1,000,000 |

Asset-Weighted Return | Asset-Weighted Standard Deviation | Equal-Weighted Standard Deviation |

13.88% | 1.94% | 1.67% |

For illustrative purposes, assume that the six portfolios above were the only portfolios in the composite and were included for the full year. In light of the reporting requirements found within a GIPS-compliant presentation (which include annual composite returns and a measure of internal dispersion), it is reasonable to assume that a prospective client would expect the majority of portfolio returns to fall within 1.94% of the asset-weighted return, but this isn’t the case. All but Portfolio 2 fall right around two standard deviation points away. This is because the whole calculation revolves around asset size and Portfolio 2 comprises the majority of the assets. This is neither intuitive nor meaningful given that a prospect would need to know the composition of the underlying portfolios to really have an idea on how to apply this information. While not ideal, it still seems to make more intuitive sense than the equal weighted standard deviation measure which indicates that five of the six portfolios’ returns fall further away from the asset-weighted return, as measured by standard deviation points. Equal-weighted standard deviation assumes an equal-weighted mean is presented for comparison purposes but this statistic is rarely reported.

Even with proper understanding of what an asset-weighted standard deviation statistically represents, it is not always feasible to accurately interpret the dispersion of underlying portfolio returns. Because this calculation uses an asset-weighted mean, a prospective client can reasonably assume that the majority of the composite assets, if not the majority of composite constituents, fall within one standard deviation of the composite return. Unfortunately, a prospective client will not know how evenly divided the composite assets are among all of the portfolios or if, as in the example, the majority exists within one portfolio. There are alternative methods that a firm could utilize to present this required statistic, but each comes with unique shortcomings.

Given that a firm is required to present asset-weighted performance, an asset-weighted dispersion calculation, even with its shortcomings, seems to provide a prospective client with the best view into the underlying assets and how closely the firm has managed the composite’s portfolios in a similar fashion.

## About the Author

**Travis Morgan, CFA, CIPM**, is a managing director with ACA Performance Services, a division of ACA Compliance Group. His primary responsibilities include overseeing GIPS compliance verifications and other performance-attestation engagements. Travis works from ACA’s Jacksonville, Oregon office. His client base includes firms across the US. These vary across many different asset classes and types, which gives him diverse experience in helping companies of all shapes and sizes come into compliance. Travis holds the Chartered Financial Analyst (CFA) designation. He also holds the Certificate in Investment Performance Measurement (CIPM) from the CFA and is a member of the CFA Society of Los Angeles.