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Financial Economics — lecture notes

Lec 04 #

Arbitrage opportunity

Pice bounds for options

Put-call parity

Binomial model

Blackscholes

Lec 05 #

Pricing by arbitrage

We have multiple linear independent assets (think of polymarket contracts)

Arbitrage portfolio

Lec 06 #

Economic analysis of asset markets

  • Pareto-optimal allocations

  • Contract curve

  • Market clearing condition: everything sold by one is bought by another

  • Comotinicity

  • Price responce to risk changes

Lec 07 #

Uncertain environments:

  • compound lottery $λL+(1−λ)L′$

  • Preference relation

    • Complete $for any L and L′∈L(Z ) we have L ⪰L′or L′⪰L$

    • Transitive $(L1 ⪰L2 and L2 ⪰L3) ⇒L1 ⪰L3$

  • VNM (Von Neumann and Morgenstern) Expected Utility Theory

    • Independence

    • Continuity

Risk Averse

  • Utility Index u

  • Expected utility function v

  • VNM preferences is risk averse if and only if her utility index is concave

Risk increase

  • SOSD: Second-order stochastic dominance: if dominant then less risky than other

    • $EL[x] ≥EL′[x]$

    • $\int_{-\infty}^{y} F_L(x)dx \leq \int_{-\infty}^{y} F_{L'}(x)dx$ less weight on smaller returns

  • Mean preserving spread -> more risk

  • White noise: mean 0, can be seen as risk

Quantifying Risk Aversion

  • Certainty Equivalant: uncertain lottery utility compared to a certain lottery

  • Risk Premium: Expectation - certainty equivalant $\pi_L = E_L[x] - e_L$

  • Risk Aversion coefficient

Lec 10 #

CAPM: combination of risk free asset and tangent portfolio

Sharpe Ratio: Slope of riskfree + risky of efficient frontier = sharpe ratio

Tangent Portfolio has the highest sharpe ratio among risky assets