Mapping Relative Stock Predictions to Portfolio Optimization Alpha

Summary

The document asks how to express forecasts of relative stock performance in a mean-variance portfolio optimizer for a medium-frequency strategy with holding periods of about a day to a week. It frames statistical arbitrage as trading relationships among stocks, often selected by sector or statistical similarity, with pairs trading relying on cointegration and an expectation that deviations will converge.

The author considers converting cross-sectional forecasts into ranks or deciles, assigning positive alpha to the strongest group and negative alpha to the weakest, then allocating those values to individual stocks. They also flag a practical issue: combining this ranked signal with other factors in one optimizer. The document poses these questions but provides no answer, empirical results, or implementation guidance. It therefore introduces the modeling problem rather than establishing that mean-variance optimization or a particular decile mapping is suitable; signal scaling, covariance estimates, constraints, and transaction costs remain unresolved.

Key ideas

• Statistical arbitrage can express forecasts about relative performance among stocks rather than absolute market direction.
• Pairs trading commonly looks for related stocks whose price relationship is expected to revert after a deviation.
• The author asks whether mean-variance optimization suits strategies with holding periods ranging from a day to a week.
• A proposed signal representation ranks stocks into deciles and assigns positive or negative alpha to the tails.
• The document leaves open how to scale ranked signals and combine multiple factors in an optimizer.

Tags

# Representing relative stock price predictions in portfolio optimization


# Representing relative stock price predictions in portfolio optimization












I wanted to ask a simple question in representing mathematical concepts/terms into the portfolio optimization utility functions.

I have never worked with these in production environment so I am very likely to be wrong, please feel free to disagree, provide some insights.

In Statistical Arbitrage, people are basically trying to bet based on the relative performance/relationship of the baskets of stocks (assume only in equities/Delta 1 space).

From pair's trading point of view, one attempts to find a pair of stocks that are in same sector/statistical clusters, and identify whether those selected pairs have cointegrated relationships, and bet that in the longer run these relationships will converge, as the pairs are identified to be stationary.

Extending this idea from a single stock - single stock pair, I was thinking of applying these relative performance alpha into the multiple stocks and representing them in "alpha" for mean-variance portfolio optimization purposes.

First of all, does applying mean variance optimization to medium frequency strategy (i.e., average holding period of a day to week) makes sense?

Also, how would one go about representing these predicted "relative price relationship among the stocks" into this optimization model? * some of the thoughts I had was, representing the relative stock predictions into decile, assign max alpha (e.g., 5%), and assign this 5% back to the stocks based on the decile. i.e., from 0-10% assign alpha of +5%, from 90-100% assign alpha of -5%, etc. But this brings another problem when I try to combine multiple factors into the optimization.

I appreciate your intuition and time in advance. Thank you.

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