1 Why Models? Why Money?
Markets turn uncertain expectations into observable prices. A model offers a disciplined way to describe a small piece of that process. The key is knowing where the model helps and where it simplifies reality too aggressively.
1.1 A short map of the ideas
Modern Portfolio Theory (MPT) asks how risky assets can be combined. CAPM connects market-wide risk to an equilibrium expected return. The Efficient Market Hypothesis (EMH) asks how rapidly information is reflected in prices. Option pricing models translate contingent payoffs into prices under particular assumptions. Spreads arrange several options to create a chosen payoff profile.
Each advance solves a problem introduced by the preceding one—but does not make earlier limitations disappear.
1.2 A model is an instrument, not an oracle
A useful habit is to ask four questions each time you encounter a new equation:
- Purpose: What decision is it intended to support?
- Inputs: Which data and estimates does it require?
- Assumptions: What market behavior is excluded?
- Failure modes: How would we know it is giving a misleading answer?
An elegant formula is not evidence that its input estimates are accurate. Keep estimation risk separate from optimization risk.
1.3 Questions to carry forward
- Why can a portfolio of risky assets be less risky than some of its components?
- Under what assumptions can one risk factor explain expected returns?
- Why do option prices depend on time and volatility as well as the underlying price?
Living chapter. This is an initial working treatment. Derivations, examples, and references will be expanded in future editions.