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Estimate the Number of Florists in Sydney and Make a Market

Jane StreetQuantitative Trader · Technical Screen
MediumQuantitative TraderTechnical ScreenStatistics & Math

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Tests Fermi estimation, sanity checking via dual perspectives (demand vs. supply/geographic), quoting a two-sided market under uncertainty, and updating beliefs given market flow or new information.

Scenario

You are in a trading interview and the interviewer asks you to estimate a real-world quantity from scratch and make a market on it: the total number of brick-and-mortar florist shops operating in the Greater Sydney metropolitan area.

Your task is divided into three consecutive stages: estimation, market making, and Bayesian updating.

Part 1: Dual-Method Fermi Estimation

  1. Demand-Side Estimate: Construct a bottom-up model based on population, household flower consumption, average order size, and typical annual revenue required to keep an independent florist storefront open.
  2. Supply-Side / Geographic Cross-Check: Build an independent check using Sydney's geographic footprint, commercial hubs, shopping centers, or suburb counts.
  3. Reconcile both models to produce your single best point estimate (expected value).

Part 2: Quoting a Two-Sided Market

State a firm two-sided market (a [Bid, Ask] pair) on the true number of florist shops in Greater Sydney:

  • Your market must be wide enough to protect against estimation error, but narrow enough to be competitive.
  • Explain how your confidence interval maps to the spread.
  • State your preferred position (long/short/neutral) and identify the asymmetric risks.

Part 3: Responding to Flow and New Information

Suppose the interviewer says: "I buy 10 contracts from you at your Ask price. Furthermore, commercial registry data reveals that the City of Sydney council area (which houses roughly 5% of Greater Sydney's commercial retail density) has 42 registered florist businesses."

  1. Did you get adversely selected, or is this just noise?
  2. What is your new fair value estimate?
  3. What is your revised two-sided quote?

Hints

Hint 1

Start by establishing benchmark figures: Greater Sydney has a population of roughly 5.3 million people, or roughly 2 million households.

Hint 2

For the demand side, estimate how many flower purchases a household makes annually across holidays, events, and everyday gifts, and divide total retail spend by the average annual turnover of a small retail florist.

Hint 3

When updating after an aggressor lifts your ask, factor in both the trade flow signal (they likely know something or think your ask is cheap) and the hard data point provided.

Follow-up questions

  • If the counterparty could trade up to 100 contracts instead of 10, how does your spread widen as a function of size?
  • How would you account for non-traditional flower sellers (supermarkets, convenience stores, online-only warehouses) in the definition of your contract?
  • If you know the counterparty is an informed trader versus an uninformed retail participant, how does your Bayesian update on fair value differ?