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What is the relation between "Z-score" and "alpha "?
Pratyush Banad
posted

I understand that the z score is the number of standard deviations that a data point is away from the mean of the population and that alpha is the return of the strategy after adjusting for market risk factors. [This post][1] (line 157 ) seems to claim that alpha is defined by the negative of z-score.

# Our objective is to maximize alpha, where 'alpha' is defined by the negative of  
# recent_returns_zscore factor.  
objective = opt.MaximizeAlpha(-context.recent_returns_zscore)

I couldn't find any mention of a relation between the z-score and alpha when I tried to search for it.

How is the alpha defined by the z-score ?

Is it a function of the z score ?

Are there any sources where I can read about this?

[1]: https://www.quantopian.com/algorithms/5cb813755669f147e3c616e3

1 response
Dan Whitnable

There is absolutely no universal relationship between a negative z-score and alpha. The algorithm isn't making a 'claim' but rather making an 'hypothesis' stating there may an inverse relationship between 'recent returns' and alpha (ie excess gains). In this specific case (and I emphasize specific case) there is some basis that short term returns are inversely proportional to future gains. This is broadly termed 'short term reversal' and is one of the style exposures which Quantopian computes exposure in backtesting.

Again, there isn't a general relationship between z-core and alpha. Additionally, the 'z-score' isn't meaningful without stating 'z-score of what'. There probably isn't a relationship between the 'z-score of temperatures in New Zealand' and alpha for stocks in the US. However, there may be a relationship between the 'z-score of capex spending' and alpha.

Hope that makes sense.

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.

In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.