The All-Ones Vector in a Minimum-Variance Portfolio Formula

Summary

The document clarifies the meaning of the vector often denoted by u in a matrix expression for minimum-variance portfolio weights. A student initially wonders whether it represents expected returns, but distinguishes it from the separately named return vector in the formula. The accepted reply confirms that u is the unit vector of all ones, with one entry corresponding to each asset or portfolio component.

In minimum-variance portfolio formulas, this vector can encode the full-investment constraint: weights sum to one. The document itself provides only a brief confirmation and points to an external answer; it does not reproduce the full expression, derive the weights, or discuss alternative constraints such as allowing short positions. Its explanation is consequently limited to notation, and the precise role of u depends on the formula in which it appears.

Key ideas

• In the cited minimum-variance expression, u denotes a vector whose entries are all one.
• The vector is distinct from the expected-return vector, which the question identifies separately.
• An all-ones vector commonly expresses the constraint that portfolio weights sum to one.
• The document confirms notation but does not derive the portfolio formula or cover other constraint choices.

Tags

# What is the u vector in the expression for the weights of the min variance portfolio


# What is the u vector in the expression for the weights of the min variance portfolio












I was working on my finical math homework where I need to find the minimum variance portfolio. I need to use the following matrix expression.

Nowhere in the class notes does the instructor say what the u vector in the above expression is. At first I thought it was the expected returns of each portfolios (however that would be the m vector). I reverse engineered the result of an example and it appears the u is just a vector of all ones. Not sure if this is a finance thing or a matrix algebra thing. Does u stand for unit vector as in a vector of all ones? What does it mean?

## Answer by foshizzle (score 2, accepted)

https://quant.stackexchange.com/a/26154

yes u is the unit vector of all ones

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