McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Return and Risk: The Capital Asset Pricing Model (CAPM) Module 5.4

11-1 Equilibrium risk pricing  Modules 2 and 3 largely followed the work of Markowitz.  Module 4 follows the work of Sharpe. Sharpe was going after a “holy grail” of finance. He was trying to figure out how to identify over- priced and under-priced stocks in a world where everyone could be well-diversified.  Both Markowitz and Sharpe won Nobel Prizes for their work

11-2 A key CAPM assumption  A key simplifying assumption that Sharpe uses is “homogeneous expectations.” This means all investors agree on the expected return, and risk of every asset, and agree on how each pair of assets will be correlated in the future! In essence, we are all sort of like robots that see the world in exactly the same manner.  Sharpe knows this is really not true, and in fact, is able to price risk by identifying exactly when we would stop acting “robotic” and choose to overweight or underweight a particular asset.

Market Equilibrium In a world with homogeneous expectations, M is the same for all investors. With the capital allocation line identified, all investors choose a point along the CML line—some combination of the risk-free asset and the market portfolio M. return PP efficient frontier rfrf M CML

11-4 Market Equilibrium Where the investor chooses along the Capital Market Line depends on his or her risk tolerance. The big point is that all investors have the same CML. 100% bonds 100% stocks rfrf return  Balanced fund CML

11-5 Risk When Holding the Market Portfolio  If everyone is holding a large market portfolio, then Sharpe showed that beta (  ) is the risk inherent in the security that is priced.  Beta measures the responsiveness of a security to movements in the market portfolio (i.e., beta is a measure of systematic risk).

11-6 Beta  You might recognize that expression for beta from your stats class.  Covariance(a,b)/Variance (b) = slope of an ordinary least squares regression of a on b. This is why it was quickly named ‘beta’ by financiers and statisticians.

11-7 Estimating  with Regression Security Returns Return on market % R i =  i +  i R m + e i Slope =  i Characteristic Line

11-8 The Formula for Beta Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio.

Relationship between Risk and Expected Return (CAPM)  Expected Return on the Market: Expected return on an individual security: Market Risk Premium This applies to individual securities held within well- diversified portfolios.

11-10 Expected Return on a Security  This formula is called the Capital Asset Pricing Model (CAPM): Assume  i = 0, then the expected return is R F. Assume  i = 1, then Expected return on a security = Risk- free rate + Beta of the security × Market risk premium

11-11 Relationship Between Risk & Return Expected return  1.0

11-12 Relationship Between Risk & Return Expected return  1.5

11-13 Using beta (1)  Suppose, using the previous example, that the security was actually priced to yield 12%. In this case the asset is priced to high. People should sell the asset until its price falls to a point where it would now expect to yield 13.5%  Suppose, using the previous example, that the security was actually priced to yield 15%. In this case the asset is priced to low. People should buy the asset until its price rises to a point where it would now expect to yield 13.5%

11-14 Using beta (2)  Suppose manager A is charged to manage a small-cap stock fund with portfolio beta of 1.6, and manager B is charged to manage a large-cap stock fund with portfolio beta 1.1. Also suppose the risk-free rate = 4% and market return=10%. The managers can only pick stocks within their respective sub-sets of small (manager A) and large (manager B) stocks. If manager A actually earned 15% and manager B earned 12.5%, which manager did better? “A” should have earned (.06)=13.6% “B” should have earned (.06)=10.6% A’s excess return or “alpha” = 1.4% B’s excess return or “alpha” = 1.9% We would say that manager B did better! Manager B had the greater “risk-adjusted” return.

11-15 Conclusion of risk pricing  CAPM is the first modern attempt to price risk. It employs one-factor called “market risk” and a stock’s quantity of market risk is measured with beta.  There are several other risk-pricing models in use today that employ more than one factor. These belong to a family of “multi-factor” pricing models. A topic of FINC852 “Investment Management”