Daucus carrota Professor André Farber Solvay Business School Université Libre de Bruxelles

February 5, 2016 Daucus carota |2 Theory of asset pricing under certainty Fisher Theory of Interest Williams Theory of Investment Value Hirshleifer Theory of Optimal Investment Decisions

February 5, 2016 Daucus carota |3 Theory of asset pricing under uncertainty Markowitz Portfolio theory Sharpe Lintner CAPM Black Scholes Merton OPM Arrow State prices Cox Ross Rubinstein Binomial OPM Arrow Debreu General equilibrium Cochrane – Campbell: p = E(MX) Vasiceck Term structure Ross Risk neutral pricing Ross APT Lucas Asset Prices Harrison Kreps Martingales

February 5, 2016 Daucus carota |4 Three views of asset pricing Adapted from Cochrane Figure 6.1 General equilibrium Stochastic discount factors Mean variance efficiency Complete markets No arbitrage (NA) Law of one price (LOOP) Beta pricing State prices linear pricing rule Factor model + No arbitrage Risk-neutral pricing

February 5, 2016 Daucus carota |5 Review: valuing uncertain cash flows Mean Variance Pricing CAPM Sharpe Lintner APT Ross Law of one price No arbitrage opportunities State prices Risk neutral pricing

February 5, 2016 Daucus carota |6 Data CompanyPriceFuture payoff (m€) Rain Proba = 0.40 Sun Proba = 0.60 Mkt Portf Gov. Bond Type of weather RainSun Payoff45m€35m€ Market Project Investment = 30m

February 5, 2016 Daucus carota |7 1.Market portfolio - statistics CompanyPriceFuture payoff (m€) Rain Proba = 0.40 Sun Proba = 0.60 Mkt Portf Returns-19.54%28.61% Expected return: r M = 9.35% Market risk premium r M – r f = 4.35% Variance Price of covariance risk

February 5, 2016 Daucus carota |8 2. Project Type of weatherRain (0.40)Sun (0.60) Payoff C45m€35m€ Return Mkt Portfolio-19.54%28.61% Expected cash flow Covariance with mkt port. Certainty equivalent:

February 5, 2016 Daucus carota |9 Details of previous calculations Sun (0.60)Rain (0.40) Mkt Portfolio28.61%-19.54% Project3545

February 5, 2016 Daucus carota |10 3. Net Present Value of the project. PV (Payoff) NPV = 38 – 30 = +8 >0 Expected return = 2.62% Beta Sun % Rain %

February 5, 2016 Daucus carota |11 4. State prices valuation

February 5, 2016 Daucus carota |12 5. Risk neutral pricing

February 5, 2016 Daucus carota |13 John Campbell Asset Pricing at the Millenium Journal of Finance 55,4 (Aug. 2000)

February 5, 2016 Daucus carota |14 Stochastic Discount Factors Stochastic discount factor