Combining Alpha Signals and Choosing a Portfolio Objective

Summary

The document considers how to turn return-based factors into expected returns for portfolio optimization. The question proposes forming a long-short portfolio, perhaps from the highest and lowest ranked assets, and combining standardized returns with information coefficient and volatility. The response describes a prior approach: estimate expected returns from signals, then use historical return variances to form a Sharpe-optimized portfolio.

The author looks back critically on that method. They suggest that maximizing Sharpe may be a poor way to define the final alpha signal, pointing instead to Stochastic Portfolio Theory and the Continuous Kelly Capital Growth Criterion as possible frameworks for targeting long-run growth under risk. They also caution that historical variances may discard useful information that could help estimate future covariance. The discussion offers personal reflections rather than a tested comparison or a complete construction recipe; it does not specify how to estimate the proposed alternatives or validate them.

Key ideas

• A factor can be mapped to an expected return and combined with other signals.
• The response describes using historical return variances to construct a Sharpe-optimized portfolio.
• The author questions whether Sharpe optimization is the right objective for defining alpha.
• Stochastic Portfolio Theory and the Continuous Kelly Capital Growth Criterion are suggested as alternatives for long-run growth under risk.
• Forward-looking covariance estimates may contain useful information that historical variances omit.

Tags

# How does one create an alpha signal


# How does one create an alpha signal












I am curious and want to do some personal research into alpha signals, but I couldn't find much relevant information. What I think will be the way to is to start with a return series, build a long- short portfolio (e.g. top/bottom decile or some more refined ML techniques), take those returns calculate z-scores and do s.th like

```
z-score * IC * volatility
```

to get a real alpha signal that I can use in a portfolio optimisation context. Would be great to get more insight.

## Answer by David Addison (score 3, accepted)

https://quant.stackexchange.com/a/34551

I used to combine factors into an expected return per signal. I then used historical return variances to create a Sharpe-optimized weighted portfolio. In hindsight, I wish I had not used the Sharpe ratio to create the final alpha signal. I believe that more recent work in Stochastic Portfolio Theory and the Continuous Kelly Capital Growth Criterion provides better avenues for maximizing the long-run rate of return for a given amount of risk. I also regret using historical return variances since I think our data contained information that would have been useful in constructing forward-looking covariance matrices.

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