Explain derivatives, YTM, and core statistics

You are interviewing for a quantitative/data role and are asked a mix of markets + 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/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 $\mathbb{E}[T]$ using a Markov chain / state-based recursion.
3. Variance & covariance algebra: Derive $\mathrm{Var}(A+B)$ in terms of $\mathrm{Var}(A)$ , $\mathrm{Var}(B)$ , and $\mathrm{Cov}(A,B)$ .
   • 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 $R^2$ and explain what it means in a regression context, including at least one limitation/pitfall.