ML in Signal Generation

Hard·25 min read

Statistical / ML for QuantsMachine LearningAlpha SignalsRegularisationCross-Validation

Quick Quiz

1. Predicting 21-day forward returns from daily data with ridge, why is standard

k

-fold cross-validation invalid, and what minimum purge gap is needed?

Test folds can precede training folds and adjacent 21-day labels overlap; purge = 21 daysInvalid because returns are non-normal; purge gap of 21 days fixes the distributionInvalid because of heteroskedasticity; purge gap of 1 day sufficesInvalid only for tree models; ridge is fine with

k=10

2. For ridge

\hat\beta=(X^\top X+\lambda I)^{-1}X^\top y

, how do its bias and variance compare to OLS, and when does ridge beat OLS in MSE?

Same bias as OLS but higher variance from the penaltyZero bias and lower variance, so it always dominates OLSBeats OLS only when

X^\top X

is exactly singularAdds bias, lowers variance; wins in MSE for a small penalty

\lambda

3. A boosted-tree signal has in-sample IC = 0.12 and purged out-of-sample IC = 0.02. What does the ratio indicate and how should you respond?

The model needs more features to generaliseThe signal is robust; the low OOS IC is just transaction costs0.17 is normal for trees; raise n_estimators to lift OOS ICSevere overfitting — reduce capacity (shallower trees, larger leaves)

4. Impurity-based (Gini/gain) feature importance in gradient boosted trees is an unbiased estimate of each feature's true predictive contribution, even when features differ in cardinality or are correlated.

TrueFalse

5. Why is 12-1 momentum (12-month return excluding the most recent month) standard, and what is the danger of including the last month?

It is a regulatory requirement; using the last month is a look-ahead biasIt is only a computational convenience; both formulations are equivalent signalsIt reduces transaction costs by avoiding high-turnover short-term signalsIt excludes the last month to avoid 1-month short-term reversal contaminating the signal

6. By the Fundamental Law of Active Management,

\text{IR}\approx\text{IC}\sqrt N

. With IC = 0.05 and

N=2400

independent bets/year, the theoretical IR — and why is realised IR usually lower — is:

\approx2.45

; realised equals it provided the IC estimate is unbiased

0.05\times200=10

; realised lower because of margin requirements

0.05\sqrt{2400}\approx2.45

; realised lower from costs and correlationIR = IC = 0.05; the

\sqrt N

factor applies only to binary bets

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