Capital Asset Pricing Model CAPM Security Market Line CAPM and Market Efficiency Alpha (  ) vs. Beta (  )

Investments 112 CAPM  Capital Asset Pricing Model  An equilibrium model underlying modern finance theory  Based on diversification principle and simplified assumptions  Who developed it?  Markowitz: Nobel Prize  Sharpe: Nobel Prize  Treynor, Lintner and Mossin

Investments 113 CAPM  Assumptions  Individual investors are price takers  Individual’s action inconsequential to stock prices  Single-period investment horizon  Investors maximize expected utility  Homogeneous expectations  Investors do not know the actual outcome  Investors agree on the likelihood of each outcome  Investors risk aversion may be different  Market is frictionless  No taxes, and transaction costs

Investments 114 CAPM  Resulting Equilibrium Outcome  All investors will hold the same portfolio for risky assets – the 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

Investments 115 CAPM  Capital Market Line E[r P ] E[r M ] rfrfrfrf M CML MMMM PPPP

Investments 116 CAPM – a Single Factor Model  CAPM is just a single factor model!

Investments 117 CAPM  Expected return on individual security  The risk premium on individual securities  is equal to its expected return above the risk free rate of return  depends on its contribution to the risk of the market portfolio  depends on its level of systematic risk  The systematic risk  is a function of the covariance of returns with the assets that make up the market portfolio  is equal to one for market portfolio

Investments 118 Security Market Line (SML)  Math and Graphical Representation E(r i ) E(r M ) rfrfrfrf SML iiii MMMM = 1.0

Investments 119 Security Market Line (SML)  Sample calculations  Market risk premium is 8%, risk free rate is 3%, security x and y have beta of 1.25 and 0.6, what is the expected return of each based on CAPM?  Solution:  Security x:  Security y:

Investments 1110 Security Market Line (SML)  Graph of Samples E(r) r x =13% SML   M =1.0 r M =11% r y =7.8% r f =3%  x =1.25  y =0.6 Market risk premium: 8%

Investments 1111 CAPM Estimation  How to find beta?  Find the return data of individual stocks  Find the market return data  Find the T-bill data  Calculate the excess return of  Individual stocks  Market  Run the regression

Investments 1112 CAPM Estimation  GM Example (is it such a good stock?)

Investments 1113 CAPM and Market Efficiency  If markets are perfectly efficient, there would be no non-zero alphas!  Did this stop people in search for alpha?

Investments 1114 What about Alpha? Where can we see Alphas (and how to tell them from Betas)? Alpha production on top of benchmark Benchmark Return  Alpha of strategy Residual beta of strategy (may be zero)  2) “Pure Alpha” sources: Hedge Funds  The product is the alpha, with or without some residual market beta Alpha and Beta are integrated in strategy 3) “Embedded Alpha” Sources: Private Investments  The alpha is inseparable from the beta, but dispersion of returns among managers suggests that alpha exists and can be large 1) Traditional sources: Active Managers  Alpha is integrated into the product, but is easily identifiable

Investments 1115 Investments - It Is All about Alpha!  Investments – Active vs. Passive  Alpha (  ) vs. Beta (  )  Beta is easy – it is the market  Beta should be free  Hedge Funds manage to charge for  (and not just a token)…  Alpha is hard, but does it require frequent trading?  Not necessarily – it is about taking right long-term positions, and identifying underpriced factors  Good old “Buy Low – Sell High” always works!!!  Not having too many constraints helps

Investments 1116 Application - Disequilibrium Example  Suppose a security with  = 1.25 is offering expected return of 15%, what’s your decision?  Solution:  According to SML (CAPM), it should offer 13%   = 15% – 13%=2%  Under-priced: offering too high a rate of return for its level of risk, what to do?  What is then over-priced? – It is the market index!!!  Long a portfolio C of similar stocks and short a market portfolio!

Investments 1117 Arbitrage – How to Get It Done  How does it work?  Market portfolio: α M = 0, and β M = 1  If portfolio C has α C = 2%, β C = 1.25  Show me the money  Long $100 of portfolio C  Short $125 of the market portfolio  Net payoff  Risk-free two bucks? I’ll take it anytime!

Investments 1118 Application  Graph of disequilibrium E[r i ] 15% SML 1.0 r m =11% r f =3% 1.25  = 2% 

Investments 1119 Wrap-up  What is CAPM?  Market risk premium  beta  What does CAPM tell us?  How to capture the excess risk adjusted return (non-zero  )?