Lesson 1: Financial Markets, Risk & the Mathematics of Value

Financial markets — basic architecture

• Primary vs secondary markets — issuance of new securities vs trading of existing ones.
• Equities — ownership claims; residual claim on earnings and assets.
• Bonds / fixed income — contractual debt claims with stated coupons and maturity (or other structures).
• Risk and return — higher expected return is generally associated with higher risk; diversification can reduce idiosyncratic risk.
• Information and prices — market prices aggregate dispersed information; the efficient-market hypothesis (in its various forms) is a benchmark theory, not an uncontested fact.

Core quantitative ideas (linked to STEM / maths)

• Time value of money — present value, future value, discounting. Requires understanding of exponential growth and geometric series.
• Expected value and variance — basic probability applied to uncertain payoffs.
• Compound growth — the mathematics behind long-horizon returns: \( (1+r)^n \).
• Diversification — portfolio variance depends on covariances, not only individual variances (a direct application of statistics).
• Indexes and benchmarks — market-capitalisation and other weighting schemes.

These ideas connect directly to the Alpha School mathematics and statistics tracks (algebra, precalculus, probability, AP Statistics, etc.) and to the free MIT OCW / MITx calculus and probability materials listed in the STEM resource guide.