In the Schweser note, underweighting a pharmaceutical stock in order to overweight another pharmaceutical stock will certainly increase active share because the weights of the portfolio will be different to the weights in the benchmark. However, if the two pharmaceutical stocks are highly correlated, the portfolio will not behave markedly different from the benchmark, hence active risk is not likely to substantially increase. On the other hand , underweighting a pharmaceutical company and overweighting a security with a low correlation to the pharmaceutical company, such as a consumer discretionary company, will likely increase both active share and active risk
The Example indicates that high correlation pair trade would have lower active risk than the low correlation pair trade.
Another question from the book,
Question: After further research, Nichols adds Portfolio D’s manager in the list of managers approved for use by JAG. One of the appeals of manager D was the manager’s use of paired trades. For example, in the most recent quarter the manager had in place a pairs trade between an industrial and a consumer durables stock. The industrial was overweighted by 1.5% and the consumer durable was underweighted by 1.5% versus the portfolio’s benchmark. The trade was not successful and the manager reversed the trade by restoring both positions to an equal weight versus the benchmark. In its place the manager initiated a new pairs trade between two different consumer staples companies. This time the over and underweights were only 1.0%.
Determine whether the active risk of Manager D most likely increased or decreased as a result of the two pairs trade actions taken.
The effect on active risk is unclear:
- Decreasing the over/underweights would decrease the active risk.
- But active risk is also affected by covariance within the pair and the covariance likely went up, increasing the active risk. The covariance (and correlation) should increase because the manager went from a pair of stocks in different sectors to a pair in one sector.
The answer indicates that the higher correlation pair trade would lead to higher active risk.
Is it a contradiction between two examples?