Ashark would not be a good index fossil because

The shark cannot be considered as a good indicator for fossil study. Because the species is known to have survived for a very long period of time.  

Explanation:

Fossil studies are done by determining the age of the fossil preserved strata or rock. This is done in order to determine the period of time in which a species found as fossil presence.

Sharks have been known to have survived for a very long duration of time. And, therefore, do not corroborate to a specific period of time.  Graptolites and Ammonites are considered as the best index fossils.