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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?

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1 Answer 1

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Below proposition 1 (In the 2nd edition at p. 28?), at the beginning of the chapter, he specifically writes:

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.

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