4

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 ...


2

Your practical problem here is the insistence on non-negative weights, that sum to 1. There is no closed-form equation that solves this problem. However, it can be done via iterative methods. You weight each stock i by Ai that is unbounded, Its portfolio weight Wi is e(AI)/sum(e(Ai)). The weights sum to 1 and are all positive. SumW = sum(e(Ai)) dWi/dAi = Wi ...


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