Probability & the Return Model

Prerequisites

• SVI 101 Foundations of Market Statistics

Learning Objectives

• Explain how SVI 102 builds on 101 — from reading data honestly to modeling the probability that generates it.
• Define a random variable formally as a map from outcomes to numbers, and distinguish discrete (PMF) from continuous (PDF) variables.
• State the normal-log-return / lognormal-price model, write the normal density, and explain why prices are lognormal and floored at zero.
• Compute conditional probabilities and conditional expectations, and relate them through joint, marginal, and conditional distributions.
• Compute the close-to-close historical volatility estimator and annualize it with the square-root-of-time rule.
• Frame trend extraction as estimating the trend component of price = trend + noise, and see any moving average as a linear filter (a weighted mean whose weights sum to one).
• Compute a portfolio's expected return (wᵀμ) and the two-asset variance with its covariance cross-term, and explain why risk is not the weighted average of its parts.

Module Schedule