Fin 2802 Investments Spring 2010 Dragon Tang Lecture

Fin 2802: Investments Spring, 2010 Dragon Tang Lecture 17 Asset Pricing Theories March 25, 2010 Readings: Chapter 9 Practice Problem Sets: 1, 2, 3, 6 -20 FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 1

Asset Pricing Theories Objectives: • Use the implications of capital market theory to computer security risk premium • Construct security market line • Take advantage of an arbitrage opportunity with a portfolio that includes mispriced securities FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 2

Asset Pricing • Absolute pricing vs relative pricing • Positive view vs normative view FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 3

Capital Asset Pricing Model (CAPM) • Equilibrium model that underlies all modern financial theory • Derived using principles of diversification with simplified assumptions • Markowitz and Sharpe won Nobel prizes for this development FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 4

CAPM Assumptions • • • Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes, and transaction costs Information is costless and available to all investors • Investors are rational mean-variance optimizers • Homogeneous expectations FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 5

CAPM (Equilibrium) Results • All investors will hold the same portfolio for risky assets – market portfolio. • Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value. • Risk premium on the market depends on the average risk aversion of all market participants. • Risk premium on an individual security is a function of its covariance with the market. FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 6

Capital Market Line (CML) ing w rro Bo Rm ing d en L Rf M ML C Efficient Frontier Sharpe Ratio σm FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 7

The CML and the Separation Theorem • The CML leads all investors to invest in the M portfolio. The only difference is the location on the CML depending on risk preferences – Risk averse investors will lend part of the portfolio at the risk-free rate and invest the remainder in the market portfolio – Investors preferring more risk might borrow funds at Rf and invest everything in the market portfolio – Two-fund separation theorem or “mutual fund theorem” FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 8

The Market Portfolio • Because Portfolio M lies at the point of tangency, it has the highest portfolio possibility line • Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML • Therefore this portfolio must include ALL RISKY ASSETS • Because the market is in equilibrium, all assets are included in this portfolio in proportion to their market value • Therefore, Portfolio M must be the market portfolio FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 9

The Relevant Risk Measure for A Risky Asset • Its covariance with the market portfolio M: – Consider the stock of GM. Its inclusion in the market portfolio is going to increase the variance of the market portfolio by w. GMCOV(r. GM, r. M) – Marginally, for each unit of GM stock included, the amount of risk it brings to the market portfolio is COV(r. GM, r. M) – The risk premium each unit of GM stock provides is measured by r. GM-r. – The risk-return tradeoff can be measured by » (r. GM-r)/ COV(r. GM, r. M) » Also termed “market price of risk” » In equilibrium, market prices of risk for all traded asset should be the same! FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 10

Risk and Expected Return for A Risky Asset Expected Return = Rf + a*Risk Capital Asset Pricing Model (CAPM) FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 11

Capital Asset Pricing Model • Relates expected return of an asset to its exposure to the systematic risk as represented by b – The expected rate of return of a risky asset is determined by the RFR plus a risk premium for the asset – The risk premium, which can be negative (why? ), is determined by the systematic risk exposure of the asset (β) and the prevailing market risk premium (RM-RFR) • Security Market Line ( FIN 2802, Spring 10 - Tang ) Chapter 9: Asset Pricing Theories 12

Sample Calculations for SML If E(rm) - rf =. 08 and rf =. 03 bx = 1. 25 then E(rx) =. 03 + 1. 25(. 08) =. 13 or 13% by =. 6 then E(ry) =. 03 +. 6(. 08) =. 078 or 7. 8% FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 13

Graph of Sample Calculations E(r) SML. 08 Rx=13% Rm=11% Ry=7. 8% 3% . 6 1. 0 1. 25 ßy ßm ßx FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories ß 14

Determining the Expected Rate of Return for a Risky Asset • In equilibrium, all assets and all portfolios of assets should plot on the SML • Any security with an estimated return that plots above the SML is underpriced (w. r. t. CAPM) ( ) • Any security with an estimated return that plots below the SML is overpriced (w. r. t. CAPM) ( ) FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 15

The Security Market Line and Positive Alpha Stock FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 16

Practice Two investment advisers are comparing performance. One average a 19% return and the other a 16%. However, the beta of the first adviser was 1. 5, while that of the second was 1. 0. a. Can you tell which adviser was better? b. If the T-bill rate were 6%, and market return during the period were 14%, which would be better? c. What if T-bill rate were 3% and market return 15%? FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 17

b for Portfolios • Expected return of a portfolio • Beta is additive: Portfolio beta equals to portfolio weighted betas FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 18

Estimating the Index Model • Using historical data on T-bills (proxy for risk free rate), S&P 500 (proxy for market portfolio) and individual securities • Regress risk premiums for individual stocks against the risk premiums for the S&P 500 • Slope is the beta for the individual stock FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 19

Monthly Return Statistics for T-bills, S&P 500 and General Motors FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 20

Cumulative Returns for T-bills, S&P 500 and GM Stock FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 21

Characteristic Line for GM FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 22

Security Characteristic Line for GM: Summary Output FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 23

The CAPM and Reality • Is the condition of zero alphas for all stocks as implied by the CAPM met? – Not perfect but one of the best available • Is the CAPM testable? – Proxies must be used for the market portfolio • CAPM is still considered the best available description of security pricing and is widely accepted FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 24

Empirical Tests of the CAPM • Typical Tests – Time-series test (Black-Jensen-Scholes) – Cross-sectional tests (Fama-Mac. Beth) – Most tests are done in portfolios FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 25

Figure 9. 4 Frequency Distribution of Alphas FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 26

Empirical Tests of the CAPM • High beta portfolios do not necessarily generate high returns – Controversial results • Size and book-to-market value ratio seem to have explanatory power for returns – Fama and French • Momentum in returns – Relative strength FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 27

Why still the CAPM? • Is the CAPM wrong? – Problems with the proxy for market portfolio – Possible missing risk factors -> Multi-factor models – Relaxing assumptions • Important intuitions from the CAPM – Diversification – Only covariance with systematic risks matters FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 28

Extensions of the CAPM • Zero-Beta Model – Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks • Consideration of labor income and non-traded assets • Merton’s Multiperiod Model and hedge portfolios – Incorporation of the effects of changes in the real rate of interest and inflation FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 29

CAPM & Liquidity • Illiquidity Premium • Research supports a premium for illiquidity. – Amihud and Mendelson – Acharya and Pedersen • CAPM with liquidity FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 30

Figure 9. 5 The Relationship Between Illiquidity and Average Returns FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 31

Other Asset Pricing Models • CAPM is limited (true market portfolio is unobservable), nice idea though! • Other factors also matter, e. g. , Fama-French book-to-market and size factors • Arbitrage Pricing Theory (APT): no free lunch (for diversified portfolio)! FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 32

Puzzles (for any pricing model) • • • Stocks are excessively volatile Stocks are too rewarding Risk free rates are too low A lot people do not hold any stocks Even when people buy stocks, they buy too little FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 33

Summary • Assumptions for CAPM • Market portfolio and individual covariance with the market portfolio • The Security Market Line • CAPM and the Market Model • Multifactors and Arbitrage Pricing • Next Class: Optimal Portfolio FIN 2802, Spring 10 - Tang Chapter 9: Asset Pricing Theories 34