Asset Pricing Theory in One Lecture

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Video 2

• Asset Pricing Theory in One Lecture
• Eric Falkenstein

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MBA Course in 45 Minutes

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

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What Causes Profits? What Causes Returns?
Puzzle.

• Monopoly power
• Uncertainty (Frank Knight)
• Entrepreneur (Schumpeter)
• Return on Capital
• Profits should go to zero over time (Das Kapital)
• Modern Portfolio Theory Return for bearing risk

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Two Basic Ideas

• Diversification, Diminishing Marginal Utility
• Processes
• Arbitrage
• Equilibrium

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Marginal Utility

• 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

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Marginal Revolution 1860s

• Jevons, Menger, Walras noted diminishing marginal
  utility could explain pricing

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Diminishing Marginal Utility Necessary and
Sufficient Condition for Risk Aversion
Johnny Von Neumann and Oscar Mortgenstern 1941
Theory of Games Milton Friedman and Savage 1947
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Markowitz

• 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

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Law of Large Numbers
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Convex Hull of Investment Possibilities
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Only Covariance Matters for large portfolios
?
Total risk U
Idiosyncratic Risk
Systematic Risk
n
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Markowitz Should Invest in Portfolios, not
single asets
risk is variance of return
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Why utility cares about variance, not volatility
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Iso-Utility Curves for Return and Volatility
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Why we like efficient portfolios
No points plot above the red line
100 investment in security with highest E(R)
Expected Return
All portfolios on the red line are efficient
100 investment in minimum variance portfolio
Standard Deviation
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'New' ideas there from start

• 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 1952

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Normality?

• 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

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Tobin Two-Fund Separation Theorem
Exp Return
Port-1
U1
U2
Port-2
U3
U4
Port-3
Volatility
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There exists a unique portfolio of risky assets
that maximizes utility
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Regardless of risk preference, everyone uses same
risky portfolio
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Always hold some cash liquidity preference
Expected Return
C
B
Rf
A
Standard Deviation
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Sharpe How do asset returns relate to efficient
frontier?
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The Capital Asset Pricing Model
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Security Market Line (SML)
Market Portfolio
Expected Return
E(R)
Rf
1.0
Beta
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General Equilibrium aka Stochastic Discount
Factor ? CAPM
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APT and SDF use similar logic to generate
arbitrary factors
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
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Arbitrage Pricing Theory

• 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

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APT and Behavioral Finance

• 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

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Asset Pricing Theory

• 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 Rm-Rf , whatever matters
  to people, linear pricing in factors

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Hope for Final Theory

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