Other exposures
Some market participants like to keep track of other hedges, such as industry or sector risk, or exchanges and factor risk.
Sector exposure
Keeping diversified sector exposure is good practice. Typically, you do not want your entire long/short sector exposures to look like technology long in 1999, short in 2000. Some market participants like to fully hedge their sector exposure to mitigate industry risk. This introduces another unnecessary layer of complexity. In practice, entire sectors dominate or trail the markets. A case in point: In 2008, one would have been hard-pressed to find any stock in the financial sector on the long side.
Sector neutrality works with only pairs trading or arbitrage strategies. Not all the stocks within the same sector travel at the same speed. Sector neutrality introduces an interesting capital allocation problem: Should sector allocation reflect the market capitalization of the underlying sectors or the disparity among constituents...