Chapter 3 MeanVariance Analysis CAPM APT 1 2

Chapter 3 Mean-Variance Analysis, CAPM, APT 1

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A. Two Asset Portfolio 3

A. Two Asset Portfolio 1. 4

A. Two Asset Portfolio 5

A. Two Asset Portfolio 2. 6

A. Two Asset Portfolio 7

A. Two Asset Portfolio 3. 8

B. Many Assets Portfolio (Rf. Markowitz, Portfolio Selection, 1992) 9

B. Many Assets Portfolio L 10

B. Many Assets Portfolio 1. 2. 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 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. 11

C. Capital Market Line(CML) 1. Optimal Portfolio Choice(The efficient set) for a risk averse investor » » B: Equilibrium Point? Efficient Portfolio? D: Equilibrium Point? C: Equilibrium Point? 12

C. Capital Market Line(CML) 2. Optimal Portfolio Choice for a different risk averse investors 13

C. Capital Market Line(CML) » A: Utility Maximization? » B: Utility Maximization? No Capital Market? With Capital Market? » C: Utility Maximization? 14

D. Capital Asset Pricing Model (CAPM) Treynor[1961], Sharpe[1963], Lintner[1965], Mosson[1966] 1. Assumptions 1) 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. 15

D. Capital Asset Pricing Model (CAPM) 2. Derivation of CAPM 16

D. Capital Asset Pricing Model (CAPM) In equilibrium, 17

D. Capital Asset Pricing Model (CAPM) 18

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 19

D. Capital Asset Pricing Model (CAPM) – Capital Market Line and Mutual Fund Theorem • If investors have homogenous beliefs, then they all hold the same mutual fund and • They all have the same linear efficient set called the CML 20

D. Capital Asset Pricing Model (CAPM) » » Basu [1977]: P/E Litzenberger & Ramaswamy[1979]: Dividend Banz[1981]: Size Effect Keim[1983]: January Effect 21

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 22

E. Arbitrage Pricing Theory(APT) 2. Model 1) Arbitrage portfolio in Equilibrium No Wealth change No additional return No additional risk A. No change in wealth B. No additional return 23

E. Arbitrage Pricing Theory(APT) C. No additional risk (No systematic risk, No unsystematic risk) condition a. Unsystematic Risk (Average residual variance) (∵ Law of large number) 24

E. Arbitrage Pricing Theory(APT) b. Systematic Rick 25

E. Arbitrage Pricing Theory(APT) 2) Derivation of APT 26

E. Arbitrage Pricing Theory(APT) 27

E. Arbitrage Pricing Theory(APT) 3) Advantages of APT A. 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. B. C. D. Industrial Production Changes in default risk premium Twists in the yield curve Unexpected inflation 28