Suppose that there are only two stocks, A & B, 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 Stock A will outperform stock B by 5%?

Question

Suppose that there are only two stocks, A & B, 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 Stock A will outperform stock B by 5%?

BlackTom AI · Accepted Answer

To tackle this question, we first restate the setup: there are two stocks A and B, and we want to encode a view in the Black-Litterman framework that A will outperform B by 5% using a P matrix row.
Option 1: P=[1, -1]. This row vector expresses a view on the difference between the two assets, namely that r_A - r_B is positive. A positive coefficient on A and a negative coefficient on B aligns with a view that A will outperform B by the amount indicated in the view (here 5%). The interpretation is that the expected excess return of A relative to B is 5%, which matches the stated view.
Option 2: P=[0, -1]. This would indicate a view solely on B without any weighting on A, effectively expressing a view that B is expected to underperform zero relative to A, or that only B matters with a negative weight. It does not encode a direct A minus B difference, so it cannot express A outperforming B by 5%.
Option 3: P=[0, 1]. This is the opposite sign of Option 2: it places weight only on B with a positive coefficient, which would imply a view tied to B outperforming some baseline, not a direct A minus B outperformance. It does not express A exceeding B by 5%.
Option 4: P=[1, 0]. This places all weight on A and none on B, effectively encoding a view about A in isolation, such as A having a positive excess return regardless of B. It does not explicitly convey the relative performance between A and B, which is required to express that A outperforms B by 5%.
In summary, the intent is to encode a view about the difference in performance between A and B. A row like [1, -1] cleanly captures the A minus B relationship, while the other options fail to express that specific relative view, either by omitting one asset, misplacing signs, or focusing on a single asset without referencing the comparison.

Fall 2025.FIN.5321.02 Final Exam

Suppose that there are only two stocks, A & B, 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 Stock A will outperform stock B by 5%?

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