13-0 Return, Risk, and the Security Market Line Chapter 13 Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

Chapter Outline Expected Returns and Variances of Individual Securities Expected Returns and Variances of Portfolios Systematic and Unsystematic Risk Diversification Systematic Risk and Beta The Security Market Line & the Capital Asset Pricing Model (CAPM) 1

Expected Returns of Individual Securities The expected return is based on future returns and the probabilities of possible outcomes where 1, 2, 3…i = states p = probability that a state occurs R = future return 2

Variance of Individual Securities where 1, 2, 3…i = states p = probability that a state occurs R = future return E(R)= expected return 3

Example: E(R) and VAR of Individual Security Security A: StateR p E( R A ) = VAR A = Security B: State R p E( R B ) = VAR B = 4

Expected Portfolio Returns The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio where A, B, …j = securities 5

Example: Expected Portfolio Return You have a total of $15,000 to invest and have purchased $12,000 worth of security A and $3,000 worth of security B. Assume that E(R A )=.20 and E(R B ) =.173 What are the portfolio weights and what is the expected portfolio return E(R P )? 6

Variance of Portfolio Returns 1. Compute the future return of the portfolio for each state 2. Compute the expected portfolio return 3. Compute the portfolio variance where 1, 2, 3…i = states p = probability that a state occurs R = future return E(R)= expected return 7

Example: Variance of Portfolio Returns Assuming that 30% of the portfolio is invested in Stock A and 70% in stock B, what is the portfolio variance? State R A (w A =.3) R B (w B =.7)p R p % % E(R p )= VAR p = 8

Systematic & Unsystematic Risk Realized returns are generally not equal to expected returns There is the expected component and the unexpected component R = E(R)+U U = systematic (non-diversifiable) portion + unsystematic (diversifiable) portion 9

Diversification 10

Diversification 11

Systematic Risk and Beta We use the beta coefficient to measure systematic (non- diversifiable) risk What does beta tell us? –A beta of 1 implies the asset has the same systematic risk as the overall market –A beta < 1 implies the asset has less systematic risk than the overall market –A beta > 1 implies the asset has more systematic risk than the overall market 12

Sample Company Betas 13

Security Market Line & The Capital Asset Pricing Model (CAPM) In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market 14

Security Market Line & the CAPM The security market line (SML) is the representation of market equilibrium The slope of the SML is the reward- to-risk ratio 15

The CAPM The capital asset pricing model defines the relationship between risk and return E(R i ) = R f +  i (E(R M ) – R f ) 16

CAPM Example: Assume the risk-free rate is 3%, the return on the market is 9% and a particular stock has a beta of 1.5. What is the expected return of the stock? 17