We act as though we are in a linear world because it is easier to calculate behavior in the linear world. It does not matter if the linear model does a poor job, we can make the calculations. Nevertheless, the machine learning explosion has led to better and easy to apply non-linear models which allows researchers to make better forecasts. The latest AQR paper, "Can machines build better stock portfolios? The virtue of complexity in the cross-section of stocks" shows what kind of improvement you can get from using non-linear techniques. While modeling should always strive for simplicity, adding complexity can have significant benefits.
Surprisingly some techniques are easy to implement and just adjust for non-linear relationships at the extremes, yet using these techniques will generate significant improvement in Sharpe ratio. The two exhibits from the paper show the improvement with nonlinear models and provide a simple picture of what it means to have a non-linear relationship. In this case, the AQR folks use ridge regression as the technique to gain the Sharpe improvement. These improvements can come even when looking at simple value and momentum factors.
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