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.

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% ?单项选择题

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