Asset Pricing Theory in One Lecture Eric Falkenstein 1 Finding Alpha

Capital Asset Pricing Model (CAPM) Arbitrage Pricing Model (APT) Stochastic Discount Factor Model (SDF) General Equilibrium Theory 2 Finding Alpha

1. Monopoly power 2. Uncertainty (Frank Knight) 3. Entrepreneur (Schumpeter) 4. Return on Capital Profits should go to zero over time (Das Kapital) Modern Portfolio Theory: Return for bearing ‘risk’ 3 Finding Alpha

Diversification, Diminishing Marginal Utility Processes: Arbitrage Equilibrium 4 Finding Alpha E[Ret i ]=  +E  i f Diversification Decreasing marginal utility UtilityConsumption Portfolio Vol # assets

St. Petersburg Paradox (1738): what is value of $1 paid if you get a head in a coin flip, where the payoff is (number of times coin flipped)^2? Should be infinity Why not? Diminishing marginal returns 5 Finding Alpha

Jevons, Menger, Walras noted diminishing marginal utility could explain pricing 6 Finding Alpha

7 Johnny Von Neumann and Oscar Mortgenstern 1941 Theory of Games Milton Friedman and Savage 1947

Why not put all your wealth in one stock? “To suppose that safety-first consists in having a small gamble in a large number of different [companies] … strikes me as a travesty of investment policy.” Keynes 8 Finding Alpha

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Finding Alpha 11 Systematic Risk Idiosyncratic Risk n  Total risk; U

12 Finding Alpha ‘ risk’ is ‘variance of return’

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Finding Alpha 15 Standard Deviation Expected Return 100% investment in security with highest E(R) 100% investment in minimum variance portfolio No points plot above the red line All portfolios on the red line are efficient Why we like efficient portfolios

Portfolio Selection: Efficient Diversification of Investments (1959) Markowitz preferred ‘semi-variance’ in book Also examines: standard deviation, expected value of loss, expected absolute deviation, probability of loss, maximum loss ‘Prospect Theory’ in Finding Alpha

Levy and Markowitz (1979) show the mean-variance optimization is an excellent approximation to expected utility when not-normal ”[in the 1960s] there was lots of interest in this issue for about ten years. Then academics lost interest. “ Eugene Fama

Finding Alpha 18 Exp Return Volatility U1 U2 U3 Port-1 Port-2 Port-3 U4

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Finding Alpha 21 Standard Deviation Expected Return RfRf A B C

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24 Beta Expected Return RfRf Market Portfolio 1.0 E(R)

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26 Finding Alpha Total Ut Marginal Ut Wealth T-bills, MT Tbonds, LT Treasuries, Corp Bonds, Mortgages, Large Cap Stocks, Large-cap growth stocks, medium cap stocks, small cap stocks, non-US bonds, European stocks, Japanese stocks

If f is a risk factor, it must have a linear price to prevent arbitrage Can of beer: $1 6-pack of beer: $6 Case of beer (24 pack): $24 Price of beer linear in units, else arbitrage 27 Finding Alpha

28 For k number factors How many factors? 3? 5? 12? What are the factors? Empirical issue. Could be estimated just like a ‘bias’ Total Portfolio Volatility no longer the issue

Markowitz. Normative model: people should invest in efficient portfolios No residual aka idiosyncratic aka unsystematic, volatility Tobin: Efficient portfolio always combination of a single risky portfolio and the non-risky asset Sharpe : Given Tobin, covariance with the market dictate expected return Ross: add factors like R m -R f, whatever matters to people, linear pricing in factors 29 Finding Alpha

linear in risk factors not include residual risk include something very like the stock market as one of the prominent factors 30 Finding Alpha