Research case studies

6 lessons · 3 equations. Each lesson below gives its formulas and key rules; open the lesson for the full explanation.

A method for open-ended research cases

Key rules

When was each field actually knowable? Publication date, not period end.
Is the universe point-in-time, or does it contain only survivors?
Have the values been revised since first release?

Prediction cases: demand, pricing and the traps in each

How much to stock: the newsvendor rule

q^* = F^{-1}\!\left(\frac{c_u}{c_u + c_o}\right)

Stock the quantile of the demand distribution given by the critical ratio: the cost of having one unit too few ( $c_u$ , lost margin) over the total of that and the cost of one unit too many ( $c_o$ , waste). It is why a demand model must forecast a distribution, not just a mean.

Remember

Sales are censored demand; flag stock-outs and model the censoring.

Causal cases: treatment effects, confounding and surprising results

How many users an experiment needs

n_{\text{per arm}} = \frac{2\,(z_{1-\alpha/2} + z_{1-\beta})^2\,p(1 - p)}{\delta^2}

For a conversion rate near $p$ and an absolute lift $\delta$ to be detected with significance $\alpha$ and power $1 - \beta$ . The $\delta^2$ in the denominator is the whole story: small effects need enormous samples.

Remember

A treatment effect needs a counterfactual that is never observed.

Market-data cases: short-horizon prediction from the order book

Did the market maker keep the spread?

\text{effective} = 2d\,(P - M_t),\quad \text{realised} = 2d\,(P - M_{t+\Delta}),\quad \text{impact} = \text{effective} - \text{realised}

For a trade at price $P$ with direction $d = +1$ for a buy and $-1$ for a sell, $M_t$ the mid at the trade and $M_{t+\Delta}$ the mid a short while later. The realised spread is what the liquidity provider kept after the price moved; the impact is what informed flow took back.

Remember

Predict the microprice change, over a horizon you can actually act on.

Data quality: missingness, outliers, regimes and leakage

Key rules

Plot every series over the full history and look at it.
Count missing values by date and by asset, and ask why the pattern is what it is.
Check that timestamps are in the timezone and convention you think.

Communicating: structuring an answer and defending an assumption

Key rules

Signpost before you reason, so the interviewer can redirect you early.
State assumptions explicitly and rank them by how much damage each would do.
Under pushback, ask what specifically is disputed, then adjust for a stated reason.