Why Low-R² Return Predictions Can Still Inform Trading

Summary

The document asks how a return model with low R² could still support profitable decisions. It considers using predicted returns as expected returns for directional trades and Kelly sizing, then raises two concerns: predictions may cluster near zero, and small estimates can have uncertain signs. It asks whether the prediction should instead be used differently or whether a proxy target would be more useful.

The text offers no answer, empirical evidence, or proposed alternative, so it serves mainly as a framing of the problem. It does not establish that a low-R² model is profitable or explain how to assess profitability. Readers would need to examine out-of-sample performance, forecast calibration, trading costs, and uncertainty before drawing conclusions about a strategy or position size.

Key ideas

• Low R² alone does not explain how a return forecast should be turned into a trade.
• The author questions whether predictions concentrated near zero are useful as expected returns.
• Small predicted returns may have uncertain signs, complicating directional decisions.
• The document poses possible alternatives, including using predictions differently or forecasting a proxy, but does not evaluate them.

Tags

# Low R2, Profitable


# Low R2, Profitable












I have read quite a lot that models with R2 of 0.02 are profitable, and R2 of 0.1 is beyond incredible.

With such a small explained variance, how is the model utilized to make decisions?

Assuming one tries to predict returns at time now+t.

One can use the predicted value as a mean, trade on the direction of the predicted mean and bet Kelly using the predicted mean and the RMSE as std (adjust for uncertainty).

But, with 0.02 R2, the predictions are concentrated around 0, which prevents from using the prediction as a mean (too absolute small).

Also, the MSE is symmetrical which means that 0.001 could have easily been -0.001, which completely changes the direction of the trade.

So, maybe we can utilize the prediction in a different way. How?

Or, we can predict some proxy. What?

Or, probably, I do not know and understand something.

I would love to have a bit of guidance :)

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