Derivatives, Yield to Maturity (YTM), and Core Statistics

You are interviewing for a quantitative/data role and are asked a mix of markets and statistics fundamentals.

Part A — Markets & Instruments

1. Derivatives: Explain the difference between a forward, futures, and an option.
   • For each, describe: (i) who has the right vs obligation, (ii) how payoff works at expiration, (iii) typical trading venue (OTC vs exchange), (iv) margin/collateral, and (v) counterparty risk.
2. Compared to Stocks: How are forwards, futures, and options different from stocks?
3. Stock Basics: What are the basic characteristics of a stock? Mention at least:
   • What ownership/claim it represents.
   • What the ticker/symbol is used for.
   • Common rights/cashflows (e.g., voting/dividends) and limited liability.
4. Common Market Terms: Define YTM (Yield to Maturity) and give a concrete numeric example of how it is interpreted (you do not need to solve a full bond-pricing root-finding problem unless asked).

Part B — Probability & Statistics

1. Fair Coin Toss: Assume a fair coin with P(H) = P(T) = 0.5.
   • (a) For n tosses, what is the probability of getting exactly k heads?
   • (b) What are the expected value and variance of the number of heads X in n tosses?
2. Markov Chain Application (Coin Toss): Let T be the number of tosses needed to see two consecutive heads (HH) for the first time. Compute E[T] using a Markov chain / state-based recursion.
3. Variance & Covariance Algebra: Derive Var(A+B) in terms of Var(A), Var(B), and Cov(A,B).
   • Explain what covariance means.
   • What simplification occurs if A and B are independent?
4. Regression Interpretation:
   • What does variance represent in general, and how does it show up in linear regression (e.g., noise term, uncertainty, standard errors)?
   • Define R² and explain what it means in a regression context, including at least one limitation/pitfall.

Constraints & Assumptions

• Preserve the scope, facts, inputs, and requested outputs from the prompt above.
• If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
• Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.