Introduction

A common issue in performance attribution analysis is the treatment of securities that are present in the portfolio but not in the benchmark. Should the return contribution of such securities be assigned to stock selection or to asset allocation? The arguments run along the following lines:

• The use of this off-benchmark stock implies that the investor wanted to invest from a sector that was not present in the benchmark. Therefore, this was an asset allocation decision. • The investor chose this particular stock over all others. Therefore, this was a stock selection decision.

FIA allows the return of off-benchmark stocks to be assigned to either category. However, it is important to clear what this actually means, as there are typically several sources of return in play when reallocating return. For instance, a Brinson analysis can include the following sources of return:

• Asset allocation, at one or more levels • Stock selection return • Interaction return • Price return • FX return

Definition of off-benchmark stocks

We follow the usual convention that lower-case variables (w, r) refer to the portfolio, and upper-case variables (W, R) to the benchmark.

Security i is treated as off-benchmark if (i) $w_i<>0$ and (ii) $W_i=0$.

For such securities, stock selection return $r_{SS}$ is always zero, since it is defined as

For the case where interaction is combined with stock selection, we have

which can be non-zero.

Lastly, asset allocation return may be defined at the security level as where $R_S$ is the benchmark sector return, and $R$ is the overall benchmark return.

Treatment in FIA

The OffBenchmark switch is provided in FIA version 2.4 and above to handle these cases. The switch has three settings (not case sensitive): • None • AA • SS Assigning any other value will generate an error.

The OffBenchmark switch only applies to securities that have zero holding in the benchmark but non-zero holding in the portfolio. It need not be included or set, in which case its value is ’None’ by default.

OffBenchmark=AA

This setting directs all all return generated by stock selection decisions for off-benchmark securities to to asset allocation. The contribution from off-benchmark stock selection decisions is decreased to zero, and the contribution to off-benchmark asset allocation decisions is increased by the same amount. If interaction return is calculated separately, it is not changed. If it is combined with a stock selection term, the combined contribution is allocated to asset allocation. If there is more than one level of asset allocation, stock selection return is directed to the lowest AA level, with upper levels being unaffected.

OffBenchmark=SS

In this case, all return generated by asset allocation decisions for off-benchmark securities is directed to stock selection. If interaction is calculated separately, it is not affected by this redirection.