Factor Portfolio Selection as a Portfolio Optimization Problem

Summary

The question asks how to choose a subset of factor portfolios to maximize Sharpe without testing every possible combination. The response frames the task as portfolio optimization and emphasizes first defining what “best” means, since minimum variance, maximum Sharpe, and maximum return are distinct objectives.

It states that minimum variance has a closed-form solution for weights, while suggesting that a maximum-Sharpe closed form may exist under restrictions such as no short selling. The answer is tentative and gives no derivation, algorithm, or evidence, and it does not resolve the specific maximum-Sharpe selection problem. Its main practical lesson is to formulate the objective and constraints before choosing an optimization method.

Key ideas

• Selecting factor portfolios can be formulated as a portfolio optimization problem.
• Minimum variance, maximum Sharpe, and maximum return are different objectives.
• The response identifies a closed-form solution for minimum-variance weights.
• It leaves the maximum-Sharpe solution uncertain and potentially dependent on constraints.

Tags

# Combination of factors


# Combination of factors












Let's say I have 10 factors and I want to find a combination (basically sum of exposures) of factors (of any length) from this set which has max sharpe. Is there an easy way to find this out rather than running simulations of all 2^10 combinations?

## Answer by KaiSqDist (score 0, accepted)

https://quant.stackexchange.com/a/78594

This seems like a portfolio optimization problem, but with factor portfolios. What do you mean by best performing? Do you refer to:

- Minimum variance

- Maximum Sharpe

- Maximum returns

From what I recall, only minimum variance has a closed-form solution to find the weights and therefore there is no need to run simulations. There might be a variation of the maximum Sharpe where you have a closed form solution but I think it does not involve short-selling - honestly not sure for the maximum Sharpe part.

You can go into some portfolio optimization books or literature to find out, it should not be that hard. Good luck!

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