and the expected active return. It is written as rjj) - P^^M X rx^~ian(t). The exceptional active return is one way that a portfolio manager adds value since it measures the performance of the active portfolio relative to what would be expected under normal market conditions. Since it is a measure of value-added performance, we are interested in finding sources of exceptional active return. To this end, we decompose this return into (1) market timing, (2) factor return contributions, and (3) stock selection (which is not the same as specific return contribution). Market timing is defined as the active beta, Pactive(£), times the difference between the realized market portfolio return over some historical period (e.g., prior six months), and the long-run expected return on the market, rm(t) - r^ong"run(?). Factor contributions were defined previously in equation (19.6). Stock selection refers to a portfolio manager's ability to choose stocks. Within the context of a factor model, stock selection may be defined as the exceptional active return minus the sum of (1) factor return contributions and (2) market timing. Note that stock selection is not the same as the contribution from specific return, which was defined in equation (19.7). Mathematically, we derive the decomposition of stock selection as follows (assuming the market return is the same as the benchmark return). First, rewrite the active return as *> = ^-^> , (19,1) Equation (19.11) shows that the active local portfolio return is the sum of the expected and exceptional return. Stock selection is defined as Stock selection= r^(t)- Pactlve (t)r^- (t)-Pactive (t)\rm(t)- r^'] {19A2) - Factor contribution The term stock selection should be used with caution, as it may not necessarily measure a portfolio manager's ability to select stocks. To better understand this point, note that stock selection is a function of factor contribution. Therefore, stock selection can vary depending on which factor model is used to measure return. As a result, what may be interpreted as stock selection may, in fact, simply measure a factor model's ability to explain portfolio returns. In review of this section, we started with a linear cross-sectional local factor model. This model explains the cross-section of returns in terms of a set of common factors. For a set of portfolio weights, the return on the active portfolio consists of the sum of factor and specific contributions. We decompose a portfolio's local return into an expected and exceptional return. The exceptional return is the sum of market timing, factor contribution, and stock selection. Stock selection is defined as the difference between exceptional return and the sum of market timing and factor contributions. Example Using PACE The various concepts outlined in the preceding section are illustrated in the following example using PACE (see Figure 19.1).