1 chapter 3 mean-variance analysis, capm, apt. 2
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Chapter 3
Mean-Variance Analysis, CAPM, APT
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B.Many Assets Portfolio1. Minimum Variance Opportunity Set
The locus of risk and return combination offered by portfolio of risky assets that yields the minimum variance for a given rate of return
2. Efficient Set (Efficient Frontier)
The set of mean-variance choices from the investment opportunity set where for a given variance no other investment opportunity offers a higher return.
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C.Capital Market Line(CML)
1. Optimal Portfolio Choice(The efficient set) for a risk averse investor
» B:Equilibrium Point?» E:Equilibrium Point?Efficient Portfolio?» D:Equilibrium Point?» C:Equilibrium Point? EE MRTMRS
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C.Capital Market Line(CML)
2. Optimal Portfolio Choice for a different risk averse investors
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C.Capital Market Line(CML)
» A:Utility Maximization?
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D.Capital Asset Pricing Model (CAPM)Treynor[1961], Sharpe[1963], Lintner[1965], Mosson[1966]
1. Assumptions1) Risk-averse investors, expected utility maximization
2) Price-taker investor, Homogenous expectation, Joint-Normal distribution
3) Risk-free rate
4) Marketable and Perfectly divisible assets.
5) Frictionless market and No information costs
6) No market imperfections.
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D.Capital Asset Pricing Model (CAPM)
2. Derivation of CAPM
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D.Capital Asset Pricing Model (CAPM)In equilibrium,
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D.Capital Asset Pricing Model (CAPM)
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D.Capital Asset Pricing Model (CAPM)– Two-fund Separation Theorem
• Each investor will have a utility-maximization portfolio that is a combination of the risk free asset and a portfolio of risky assets that is determined by the line drawn from the risk free rate of return tangent to the investor’s efficient set of risky assets
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D.Capital Asset Pricing Model (CAPM)
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» Basu [1977]:P/E
» Litzenberger & Ramaswamy[1979]:Dividend
» Banz[1981]: Size Effect
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E.Arbitrage Pricing Theory(APT)1. Assumptions : Ross[1976]
1) Risk-averse Investors
2) Homogeneous expectation of k-factor return generating process
3) Perfect Market
4) Number of assets,N > Number of factors,k
5) Idiosyncratic risk, is independent of all factors and
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1) Arbitrage portfolio in Equilibrium No Wealth change
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E.Arbitrage Pricing Theory(APT)2) Derivation of APT
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E.Arbitrage Pricing Theory(APT)
3) Advantages of APTA. No assumption of normal distribution
B. No efficient market portfolio
C. Asset pricing is dependent on many factors
4) Empirical of APT: Chen, Roll and Ross (1983)A. Industrial Production
B. Changes in default risk premium
C. Twists in the yield curve
D. Unexpected inflation
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