Suppose that there are only 100 stocks in the stock market.

How do you express the view, in the context of the Black-Litterman asset allocation model with use of vectors, that the expected return of the first stock will be greater than 5% ?

Question

Suppose that there are only 100 stocks in the stock market.

How do you express the view, in the context of the Black-Litterman asset allocation model with use of vectors, that the expected return of the first stock will be greater than 5% ?

BlackTom AI · Accepted Answer

In the Black-Litterman framework, a view is expressed as P * mu = q, where P is a 1 by N vector that selects the combination of asset returns involved in the view, mu is the vector of expected returns, and q is the scalar value (or a vector of values) representing the view.

Option 1: P=[-1, 0,..., 0], a 1 by 100 vector. This P selects the first asset but with a negative sign, which would imply a view about the first asset with the opposite direction (i.e., a negative expected return interpretation if q were specified). Since the question asks specifically about the first stock having an expected return greater than 5%, this P is inconsistent with that intent.

Option 2: P=[1, 0,..., 0], a 1 by 100 vector. This P cleanly selects only the first stock and assigns a positive weight to it, which aligns with expressing a view about the first stock's return. To complete the view in BL, one would pair this P with a q value of 0.05 (i.e., 5%) to state that the first stock’s expected return is 5% or greater; the P part itself correctly encodes the asset selection for the view.

Option 3: P=[0, 0,..., 0], a 1 by 100 vector. A P of all zeros conveys no information about any asset’s return, effectively expressing no view. This cannot encode a belief that the first stock exceeds 5%, so it is incorrect for the stated purpose.

Option 4: P=[5%, 5%,..., 5%], a 1 by 100 vector. This P would imply the same 5% value for every asset in the P dot mu calculation, which does not isolate the first stock and does not correctly express a view about a single stock’s return relative to a 5% threshold. It also misuses the formulation, since P should be a selection vector (not a vector of the same numeric value for all assets).

In summary, the only option that correctly encodes the intention to express a view about the first stock’s return while keeping the structural form of P as a 1 by 100 selection vector is Option 2, with P = [1, 0, ..., 0]. The other options either misstate the direction, fail to express a view, or misuse the P matrix in the BL view specification.

Fall 2025.FIN.5321.02 Final Exam

Suppose that there are only 100 stocks in the stock market. How do you express the view, in the context of the Black-Litterman asset allocation model with use of vectors, that the expected return of the first stock will be greater than 5% ?

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