Quant Concepts

Before a trading signal can be evaluated, we need a mathematical object for what we expect on average.

The expected value of a return $R$ is the probability-weighted average of all possible outcomes.

A strategy can be wrong more often than it is right and still have positive expected value.

For example, a strategy with frequent small losses and rare large wins can still be profitable if the payoff distribution is asymmetric.

A profitable strategy is not defined by being right often. It is defined by having positive expected value.

A trading feature matters only if observing it changes the expected return.

In quant research, the relevant object is not just expected return, but conditional expected return.

The incremental value of a signal can be written as the difference between conditional and unconditional expectation.

If this difference is close to zero, the feature may be interesting — but it is not edge.

Examples of $X_t$ include momentum, value, volume, volatility, and analyst revisions.

A feature becomes a signal only when it shifts the conditional return distribution.

A predictive model in quant research is not a machine for certainty.

It is a function that approximates the relationship between observed features and expected future returns.

Under squared error loss, the best prediction function is the conditional expectation.

This is why regression and many machine learning models can be interpreted as approximation tools for expected return estimation.

Changing the model class changes the approximation method — not the underlying object.

In quant research, models are not magic predictors. They are approximation tools for conditional structure.

A positive conditional expectation in a backtest is not sufficient.

In quant research, the deeper question is whether the effect remains stable outside the environment in which it was first observed.

A stronger formulation asks whether the learned expectation remains consistent from training to testing.

This is why out-of-sample testing matters: a true signal should not disappear once it leaves the original backtest window.

Research quality also depends on whether the effect survives transaction costs, turnover, regime changes, and overfitting risk.

Alpha is not the formula. Alpha is the stable conditional expectation that remains after reality tests it.