Combining Alphas by Adjusting Weights Until Marginal Alpha Is Zero

Summary

The document asks how to combine many statistically significant in-sample signals and whether historical covariance with mean-variance optimization is the best approach. Its answer offers a portfolio-balance intuition: add an asset or alpha exposure while its estimated alpha relative to the current portfolio remains positive, and reduce the weight if that alpha turns negative.

A regression is used to illustrate the idea, first measuring an asset’s alpha against a market portfolio and then recalculating it against a portfolio that includes the asset. The answer claims that this process leads to the same allocation as a mean-variance portfolio problem. It does not specify how to estimate alpha, account for transaction costs, handle estimation error, or manage constraints and risk; nor does it describe a practical procedure for 100 correlated signals. The illustration is therefore conceptual rather than a complete industry method, and its regression notation is imprecise.

Key ideas

• The answer frames portfolio construction as adjusting an exposure until its alpha relative to the portfolio reaches zero.
• The estimated alpha can change as the portfolio changes, so it should be recalculated after adding an exposure.
• A negative marginal alpha suggests reducing the weight, while a positive one suggests increasing it.
• The document asserts equivalence with mean-variance optimization but gives no detailed derivation or implementation guidance.

Tags

# What is industry best practice to combine alphas?


# What is industry best practice to combine alphas?












Say I have 100 different alphas that all have statistically significant returns in-sample.

Is the best practice to use historical covariance matrix plus Markowitz portfolio theory to create an optimal weighting for each alpha?

I have to imagine that there is a way at forecasting covariance that is better than just using historical?

Also I'd imagine there is a better algorithm to weight each alpha?

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/71450

You add each of those securities to your portfolio until the alpha is zero.

Imagine that I hold the market portfolio and I am considering adding real estate to my portfolio.

I run a regression: $$r_{realestate} = r_f= \alpha_{realestate} + \beta_{realestate}(r_m - r_f) + \epsilon_{realestate} $$

If the alpha is positive I add the security to my market portfolio. Imagine that I add 50% so that I have 50-50 portfolio. Then I run the regression again:

I run a regression: $$r_{realestate} = r_f= \alpha_{realestate} + \beta_{realestate}(r_{50,50} - r_f) + \epsilon_{realestate} $$

If the alpha is negative I need to decrease the weight, if it is positive I need to keep adding.

If you run a mean-variance portfolio problem (forget alphas) you will get the exact same answer.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.