Design an experiment to launch fractional shares

Context

You're working on an investing/brokerage product. The team is weighing whether to roll out fractional share trading, meaning customers could purchase or sell portions of a stock or ETF rather than only whole units.

Task

1. Set out the benefits you'd expect fractional shares to deliver for the business and for users.
2. Put forward an experimentation plan for assessing the launch:
   • Which metric serves as the primary success metric?
   • Which diagnostic metrics help clarify why that metric moved?
   • Which guardrail metrics keep users or the business from being harmed?
   • Specify the randomization unit (user, account, household, etc.) and describe what the treatment and control groups experience.
   • Flag the main risks: interference/network effects, novelty effects, seasonality, and any selection bias.
3. Sample size / power
   • Demonstrate how you would work out the sample size required for the primary metric (stating assumptions like baseline rate/variance, MDE, $\alpha$, and power).
   • If the sample size must be adjusted while the experiment is running, describe a statistically sound way to do it.
4. Constraint scenario
   • If the required sample size is beyond what you can obtain (not enough traffic or time), what do you do? Give at least three practical options (design, metrics, variance reduction, ramp strategy, or alternative inference methods) and weigh their tradeoffs.

Output

Produce a structured written plan that covers metric definitions, the assumptions underlying your power/MDE calculations, and a closing recommendation on whether and how to launch.

Overview: This question gauges a candidate's competence in experimentation design, product analytics, statistical power and sample-size calculation, causal inference, and risk identification in the context of a brokerage product.