Basis risk is the risk that Future contract and the underlying do not change in a similar fashion when exposed to the same factor.
Why is a bond portfolio hedge with a Treasury bond contract based on a single deliverable treasury bond exposed to basis risk? Would that risk be eliminated if we have several deliverable treasury bonds?
because in reality what you get might not be what you expect. you think your underlying is a 10 year treasury, but it could be a 20 year treasury with 10 years left.
Also a group of securities may correlate better if you compare it to a out of benchmark security. but not necessary better then a security in the benchmark that’s highly correlated already. it all depends.