Card-Based Trading Game: Valuation Updates, Trade Choice, Position and P&L

In the first technical round for a trading role, after a short introduction, most of the hour is an interactive trading game played with the interviewer, followed by a review of the game. The game resembles trading on a card game: some information is public, and each participant also holds private information. Several bots quote prices, and on each quote you decide whether to trade, whether to buy or sell, and how many lots. Information is revealed step by step, so you keep updating your valuation while remembering your position and your profit and loss (P&L). The interviewer probes throughout and asks you to justify almost every decision: how you arrived at the current valuation, why new information changed it, why you traded with that bot, why that quantity, and whether your existing position affects your next move. Later the discussion turns to the value of information and to estimating P&L. The report gives no exact rules or numbers, so settle the rules first, then work through the parts below as you would aloud during the game. ### Clarifying Questions - What is traded, and how does it settle: for example, the sum of a set of cards? - What is in the deck, and are cards drawn without replacement? - Which cards are public, which are private to you, and what private information do the bots hold? - In what order is information revealed, and how many trading rounds are there? - How many lots can you trade on each quote, and is there a position limit? - Do the bots' quotes follow a fixed rule, or can they react to their own information and to your trades? ### Part 1 — Value the contract and update it State your fair value from the public information and your private card, then show how it changes when a new card is revealed. In one or two sentences, explain why the new information moved your estimate in that direction and by that amount. ```hint Price each unseen card Ask what a card you cannot see is worth on average, given every card you have already seen, including your own. ``` #### What This Part Should Cover - The expected settlement value conditional on everything seen, with draws without replacement handled correctly - How a revealed card replaces its earlier expectation and shifts the expectation of the cards still hidden - The remaining uncertainty, not only the point estimate - Mental arithmetic stated aloud at each step ### Part 2 — Choose the trade The bots post bids and asks. Explain how you decide whether to trade, which bot to trade with, whether to buy or sell, and how many lots, and what a bot's quote might tell you about its private information. ```hint Price against value, then ask why Compare each bid and ask with your fair value first; then ask why a bot that has seen a card you have not would offer you that price. ``` #### What This Part Should Cover - Edge per lot against each quote, and the choice of counterparty - A size tied to edge, uncertainty, the quantity offered and the position limit - Adverse selection: what a quote may reveal about a bot's card, and how robust the trade is to it - Checking whether two bots' quotes cross ### Part 3 — Carry the position and the P&L After some trades you hold a position, and new information arrives. Explain how you track position, cash and P&L as you go, what your expected P&L is now, and whether and how your existing position should affect the next trade. ```hint Keep a ledger Write down position and cash after every trade, then ask what your P&L would be if the contract settled at your current fair value. ``` #### What This Part Should Cover - A running record of position and cash, and P&L marked at the current fair value - Deciding the next trade from the current value rather than from earlier prices - How the existing position changes risk and the room left under the limit ### Part 4 — The value of information Explain how you would estimate what a piece of information is worth before it is revealed: for example, the right to see one more hidden card before the next round of trading. ```hint When does it pay Ask in which outcomes the extra card would make you trade differently from how you would trade without it. ``` #### What This Part Should Cover - Value of information as the expected improvement of the best decision with it over the best decision without it - Why information that changes no decision is worth nothing - How quotes, sizes and limits cap that value ### What a Strong Answer Covers - Correct conditional expectations, recomputed as each card appears - Every trade justified by edge against fair value, with a defensible counterparty and size - Awareness that the bots hold private information that their quotes may carry - Accurate bookkeeping of position and P&L across rounds - Clear, brief narration under constant questioning, with trades that match the reasoning given ### Follow-up Questions - In the review after the game, which trade would you change, and was it a bad decision or a bad outcome? - One bot seems to be on the winning side of every trade you make with it. What do you conclude, and how do you adjust? - How would your sizing change if a large loss were penalized, rather than being judged on expected P&L alone?