In a quantitative-research data-analysis round, you are asked a methodology question. No coding is required — the interviewer wants you to reason like a statistician, and will interject with pointed sub-questions that have objectively right or wrong answers (about standard errors, biases, and test validity). You believe stocks that have performed well over the past year tend to keep outperforming in the near term — a momentum effect. Suppose you are handed a long history of daily prices for a broad equity universe. **How would you rigorously test whether momentum is a genuine alpha signal — that is, whether it has statistically and economically significant predictive power for future returns that is not explained by known risk factors?** Walk through your full methodology: how you would define the signal, design the tests, choose the test statistics, guard against biases, and decide whether the alpha would survive in practice. Prefer classical statistics and linear models over black-box machine learning. ```hint Frame it as a hypothesis test State a null hypothesis — the signal has **no** predictive power for future cross-sectional returns — then pick statistics that measure the signal-to-future-return relationship: the period-by-period **information coefficient (IC)**, the mean return of a **long-short decile portfolio**, or the slope in a **cross-sectional regression**. Each produces a time series you can t-test. ``` ```hint Standard errors are a trap A 12-month formation window with monthly rebalancing means consecutive observations overlap heavily, so the test-statistic series is **autocorrelated** and naive t-stats overstate significance. Think about HAC (Newey–West) corrections — and about the multiple-testing problem if many signal variants were tried before this one. ``` ```hint Alpha vs. risk premium A profitable signal is not alpha if it merely loads on known factors. Regress the strategy's return series on standard factor returns (a **linear model**) and test whether the intercept is significantly positive. ``` ### Constraints & Assumptions - Assume a broad, liquid equity universe (a few thousand names) with 10+ years of daily point-in-time prices, adjusted for splits and dividends, and including delisted stocks. - "Momentum" is yours to define precisely; a common convention is the trailing 12-month return skipping the most recent month, but you should justify your choice. - No code is required — the interviewer wants the methodology, the statistics, and the reasoning behind each choice. - Stick to classical statistics and linear models; complex ML models are out of scope for this round. ### Clarifying Questions to Ask - What universe and region are we testing (large-cap US, global, something else), and over what sample period? - At what horizon should the signal predict returns (days, one month, one quarter), and how often would the strategy rebalance? - Is the bar "statistical predictability" or "implementable alpha" — should the test be gross or net of transaction costs? - Which known risk factors am I expected to control for (market, size, value, and so on)? - Is the momentum definition fixed, or am I free to specify the formation window, skip period, and cross-sectional vs. time-series construction? - Do we care about long-short performance or long-only excess return against a benchmark? ### What a Strong Answer Covers ```premium-lock What a Strong Answer Covers ``` ### Follow-up Questions - Your long-short momentum portfolio has a t-statistic of about 2.2 over the full sample. Do you conclude the alpha is real? What evidence would change your mind? - You used a 12-month formation window with monthly rebalancing, so consecutive observations share 11 months of formation data. How exactly does this bias your inference, and what do you do about it? - After adding standard factors to the regression, the intercept shrinks and loses significance. What are the possible interpretations, and what would you test next? - How does your methodology change if the signal will be traded at meaningful size — what additional analyses matter before deploying real capital?