I will start by coming back to the concept of alpha: it exists jointly with the concept of beta, and both terms are related to the coefficient of a linear regression of the returns of a strategy on "benchmarks" that are meant to be "non diversifiable risks" or "open source returns":
$$r(t) = \alpha(t) + \sum_k \beta_k F_k(t) + \epsilon(t).$$
The first "factor", corresponding to a non diversifiable risk is the *market factor: you make money on average (if you believe on capitalism via listed markets) if you invest on main indices like S&P500, FTSE100, DAX30 or CAC40. But you will suffer from large drawdowns if you invest on it.
The good news is that the non diversifiable risk is often easy to hedge with future, hence the remaining returns are easy to synthesise: keep your strategy as it is and hedge it with a future (I know it does not really make sense for intraday strategies because the transaction costs of such a hedge might be high).
Fama and French, and in fact the 300 factors listed in the excellent "... and the cross-section of expected returns" paper by Harvey, Liu, and Zhou are Open source strategies. Most often they have a lot of biases, have not been backtested with transaction costs (see "Stock market liquidity and the trading costs of asset pricing anomalies" by Raboun, Briere, Nefedova and L for details about transaction costs of FF factors.) but they are considered to be accessible to a lot of investors and traders, hence a "valuable" strategy should be orthogonal to them.
Or if you want to think about this differently: open source strategies may be overcrowded, and you do not want to be exposed to crowded strategies (see "Modeling Transaction Costs When Trades May Be Crowded: A Bayesian Network Using Partially Observable Orders Imbalance" in Machine Learning for Asset Management: New Developments and Financial Applications (2020) by Raboun, Briere, Nefedova and L again --yes, I recently developed an interest for these concepts ;{)}--).
What is the equivalent for intraday strategies?
- for should you have easily access to a market component that is the Future of the local cap weighted index: the E-mini for instance.
- you can even have access to ETFs tracking sectoral benchmarks; that may be good because at high frequency speed, I would rather think that a drop of a sector is easily diversifiable.
- you could also simulate for yourself "open source" intraday strategies like mean reversion or orderbook imbalance, as it is suggested in one comment, to be sure to not invest on crowded strategies.
It makes sense for intraday strategies, nevertheless you probably (and in any case you should) check the liquidity available for your intraday strategy in your backtests. Thus I suspect that you are already orthogonal to most open source and crowded strategies if your modelling of liquidity is good enough.
