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

2. Theory of asset pricing under certainty
1930
Fisher Theory of Interest
Williams Theory of Investment Value
1940
1950
Hirshleifer Theory of Optimal Investment Decisions
1960
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3. Theory of asset pricing under uncertainty
1950
Markowitz Portfolio theory
Arrow State prices
1960
Arrow Debreu General equilibrium
Sharpe Lintner CAPM
1970
Black Scholes Merton OPM
Ross APT
Lucas Asset Prices
Ross Risk neutral pricing
Vasiceck Term structure
Cox Ross Rubinstein Binomial OPM
Harrison Kreps Martingales
1980
1990
Cochrane – Campbell: p = E(MX)
2000
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4. Three views of asset pricing
General equilibrium
Mean variance efficiency
Beta pricing
Stochastic discount factors
Factor model + No arbitrage
Risk-neutral pricing
State prices linear pricing rule
Complete markets No arbitrage (NA) Law of one price (LOOP)
Adapted from Cochrane Figure 6.1
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5. Review: valuing uncertain cash flows
CAPM Sharpe Lintner
Mean Variance Pricing
APT Ross
State prices
Law of one price
No arbitrage opportunities
Risk neutral pricing
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6. Data Market Project Investment = 30m Company Price Future payoff (m€)
Rain
Proba = 0.40
Sun
Proba = 0.60
Mkt Portf.
100
80.46
128.61
Gov. Bond
105
Market
Type of weather
Rain
Sun
Payoff
45m€
35m€
Project
Investment = 30m
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7. Market portfolio - statistics
Company
Price
Future payoff (m€)
Rain
Proba = 0.40
Sun
Proba = 0.60
Mkt Portf.
100
80.46
128.61
Returns
-19.54%
28.61%
Expected return: rM = 9.35% Market risk premium rM – rf = 4.35%
Variance
Price of covariance risk
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8. 2. Project Expected cash flow Covariance with mkt port.
Type of weather
Rain (0.40)
Sun (0.60)
Payoff C
45m€
35m€
Return Mkt Portfolio
-19.54%
28.61%
Expected cash flow
Covariance with mkt port.
Certainty equivalent:
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9. Details of previous calculations
Sun (0.60)
Rain (0.40)
Mkt Portfolio
28.61%
-19.54%
Project 35 45
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10. 3. Net Present Value of the project.
Sun %
Rain %
PV (Payoff)
NPV = 38 – 30 = +8 >0
Expected return = 2.62%
Beta
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11. 4. State prices valuation
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12. 5. Risk neutral pricing
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13. John Campbell Asset Pricing at the Millenium Journal of Finance 55,4 (Aug. 2000)
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14. Stochastic Discount Factors
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