Active portfolio management - characteristic portfolios derivation

In the book Active Portfolio Management by Grinold and Kahn, on page 30, when it derives the characteristic portfolio $$h_a$$ for some characteristic vector $$a$$, the problem is set up as $$\min h^TVh$$ s.t. $$h^ta=1$$

Why do we not need to add the constraint that $$1^Th=1$$ ($$h$$ should be a weight vector of a portfolio) here?

Characteristic portfolios are not necessarily fully invested. They can include long and short positions and have significant leverage. Take the characteristic portfolio for earnings-to-price ratios. Since typical earnings-to-price ratios range roughly from 0.15 to 0, the characteristic portfolio will require leverage to generate a portfolio earnings-to-price ratio of 1. $$[\ldots]$$
In essence, he argues there is no need for the full investment constraint, hence $$1^Th =1$$ is excluded.