Professor John ZietlowMBA 621

Risk And Return: CAPM And Beyond

Chapter 6

Chapter 6: Overview

• 6.1 Introduction to Asset-Pricing Models• 6.2 Efficient Risky Portfolios

–The Efficient Frontier with two assets–The Efficient Frontier with many assets

• 6.3 Riskless Borrowing and Lending–Portfolios of Risky and Riskless Assets–Finding the Optimal Portfolio

• 6.4 Equilibrium and the Market Portfolio–The Market Portfolio–The Capital Market Line

Chapter 6: Overview (Continued)

• 6.5 The Capital Asset Pricing Model–The Security Market Line–Estimating Betas

• 6.6 Empirical Evidence on the CAPM–Early Tests–The Fama-French Challenge

• 6.7 Alternatives to the CAPM–The Fama-French Three-Factor Model–Arbitrage Pricing Theory

• 6.8 Summary: The Current State of Asset-Pricing Theory

Efficient Risky Portfolios--The Efficient Frontier With Two Assets

• Though high volatility assets historically have high return, variance of return a poor measure of risk for asset pricing– Investors can easily diversify away firm-specific risk

• Investors will only be willing to “pay for” systematic risk– Asset pricing models aim to define & quantify systematic risk– Asset pricing models assume investors hold assets in p/f

• Begin developing pricing model by asking: “Are some p/fs better than others?” – Clearly, yes: p/f of Microsoft & Berkshire beats either alone

• Figure next slide makes p/f with two generic stocks, A & B– Visually, A&B seem imperfectly correlated: -1< AB <+1– Curve connecting A&B called the feasible set of p/fs– Only p/fs from minimum variance p/f (MVP) to B are efficient

E(RP)

A

MVP (75%A, 25%B)

C (50%A, 50%B)

inefficient portfolios

P

efficient portfolios

•

••

•B

Expected Return And Standard Deviation For Portfolios Of Two Assets

The Efficient Frontier With Many Assets

• Since investors have many assets to choose from, must also show that efficient frontier exists for many assets– Next figure: how individual stocks plot in risk-return space– Each dot represents individual security; Feasible set

consists of all possible p/fs• Only p/fs on upward sloping edge from MVP are efficient

– A,B,C are inefficient: p/fs on frontier offer higher return for same risk or same return for lower risk

• Figure “The Effect Of Expanding The Feasible Set On The Efficient Frontier” shows how expanding universe of investment assets expands efficient frontier– Include non-equity assets: bonds, real estate, art, gold– Include international assets as well as U.S.

• Basic point: Investors always stay on efficient frontier– Appetite for risk determines exactly where

E(RP)

A

C

P

efficient portfolios

•

••

•

B

The Efficient Frontier With Many Assets

• • •• •

•

•

••

•

• •••

MVP

E(RP)

P

The Effect Of Expanding The Feasible Set On The Efficient Frontier

EF including domestic & foreign assets EF including domestic

stocks, bonds, and real estate

EF for portfolios of domestic stocks

Illustrating The Efficient Frontier Using P/Fs Of Berkshire, Microsoft, 3M & Praxair Stocks

• Why do assets that are not themselves on the efficient frontier (Point A in Figure “The Efficient Frontier With Many Assets”) survive in the capital market?– Answer: their value in a p/f with other assets – If negatively correlated, stock A may reduce p/f variance

• Demonstrate p/f construction using four stocks from chapter 5: Berkshire Hathaway, Microsoft, 3M & Praxair – Table next slide shows 16 p/fs; four with 100% in each stock

• Portfolios 5, 7, 10, 12, 16, plot the efficient frontier – All but #16 (100% Praxair) are p/fs of at least two stocks

• Microsoft (#1) plots very low by itself, but is part of five of the six efficient p/fs. – Reason: negatively correlated with other three stocks.

Expected Return And Standard Deviation For Various Portfolios

12.091.9110000016

5.71.2105015355

71.630901007

7.991.7425750010

11.141.8990100012

8.430.540001004

7.661.44402020203

6.131.2702550252

16.511.170010001

StandDev %

ExpectedReturn %

% Praxair% 3M% Microsoft% BerkshirePortfolioNumber

#1: 100% Microsoft

#16: 100% Praxair

#4: 100% Berkshire

#8:100% 3M

Efficient Frontier

Riskless Borrowing And Lending

• Cannot yet say which p/f a particular investor would choose– Risk aversion determines specific p/f on efficient frontier

• Adding riskless asset changes everything and makes one p/f alone efficient risky asset.– Assume mutual fund MF on efficient frontier in next figure– And that investors can borrow and lend at risk-free rate Rf

• All investors will hold combination of riskless asset and MF– Between Rf and MF, allocating existing wealth (point A)– Above MF, borrowing at Rf, investing proceeds in MF (pt B)

• Ray from Rf through MF called Capital Market Line (CML)– P/Fs on CML dominate all previous efficient p/fs

• Figure “Portfolios Of Risky & Risk-Free Assets” shows that CML becomes new efficient frontier– Every investor chooses combination of portfolio M and riskless

asset: called two-fund separation principle

Portfolios Of Risky & Risk-Free Assets

•

•

•

•RF=6%

0 30%

9%

12%

16.5%

A

B

M

E(RP)

P

old efficient frontier

new efficient frontier

L1

•X

Portfolios Of Risky & Risk-Free Assets: The Capital Market Line (CML)

•

•

•

•RF=6%

0 15% 30% 52%

9%

12%

16.5%

A

B

MF

E(RP)

P

CML

Finding the Optimal Portfolio

(17%, 3%)

(14%, 6%)

(12%, 9%)

(15%, 12%)

(19%, 16%)

(24%, 21%)(30%, 23%)

0

3

6

9

12

15

18

21

24

27

0 3 6 9 12 15 18 21 24 27 30 33 36

Portfolio Standard Deviation, %

Port

folio

Exp

ecte

d R

etur

n,%

Assume investor plots seven p/fs in risk-return space, as shown below:

Now assume investor can also borrow and lend risk-free at 3%. This creates tangency p/f (24%, 21%) and a CML from Rf through this p/f.

Equilibrium And The Market PortfolioThe Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is the primary model for determining the required return on risky assets– Developed in mid-1960s, it is still used today—at least at a

conceptual level The CAPM says that Figure “Portfolios Of Risky & Risk-

Free Assets” (repeated next slide) cannot represent an equilibrium result for assets not in portfolio M– Prices of assets in portfolio M would be bid up – Prices of all other assets would decline

Each asset will change in price until it offers an expected return that is commensurate with its risk – Equilibrium occurs when an asset’s expected return places it

on the capital market line.• But how does risk influence an asset’s expected return?

Portfolios Of Risky & Risk-Free Assets(Reproduced For Example)

•

•

•

•RF=6%

0 30%

9%

12%

16.5%

A

B

M

E(RP)

P

old efficient frontier

new efficient frontier

L1

•X

Equilibrium And The Market Portfolio

• Investors have access to similar sources of information, so economists say they have homogeneous expectations– Suggests everyone agrees on risk & return of specific assets– They will agree on efficient frontier, and will all hold same p/f

• With homogeneous expectation, p/f M receives a special title, the market portfolio, with “market” risk, expected (R)– Proxy by expected return and risk on, say, S&P 500 Index

• Line connecting M to Rf is the true Capital Market Line– Have been using the term rather loosely thus far

• CML quantifies the risk-return tradeoff for p/fs of M and Rf

– Eq 6.2 says E(Rp) equals Rf plus the market price of risk (term in brackets) times the p/f’s standard deviation, P:

pm

fmfp

RRERRE

))(()( (Eq. 6.2)

Systematic Risk And Expected (Required) Return In The CAPM

• Already know that only an asset’s nondiversifiable risk impacts the return variability of a well-diversified portfolio– Only the asset's systematic risk matters to an investor.

• The CAPM defines systematic risk as the asset's return covariance with the market portfolio of risky assets– Specific risk measure used is called Beta, [next slide]

• Investors will only hold high-beta assets if offered high E(R)– Inclusion of high-beta assets raises p/f’s systematic risk– Inclusion of low-beta assets lowers p/f’s systematic risk

• Equilibrium occurs when all assets’ expected return plots on the Security Market Line (SML) in next figure A&B– SML plots trade-off between E(R) and Beta, not std dev– SML connects Rf ( =0) and point [E(RM), =1]

• In equilibrium, all assets must plot on the SML

The Security Market Line

i

E(RP)

RF=6%

SML

slope = E(Rm) - RF = Market Risk Premium (MRP)

•

•A

B

•

•

•RM

=1.0

Calculating Required Return Using The Security Market Line

i

E(RP)

RF=6%

SML

i =1.00.5 1.5

RM=14%

10%

18%

slope = E(Rm) – RF = MRP = 14% - 6% = 8% = Y ÷ X

Estimating Betas• CAPM makes theoretical sense, but many practical problems

– Does not uniquely identify market portfolio– Expresses relationship in (unobservable) expected return

• CAPM a single-factor model in that only beta changes from one security to the next:– Unfortunately, “fixed” parameters Rf and E(RM) actually vary– Makes beta estimation and testing of CAPM very difficult

• Fig A,B&C show beta estimations using weekly returns for three stocks versus a market index, Jan 2000-May 2001– Sharper Image; high-beta (1.44), moderate R-square (0.19)– ConAgra: low-beta (0.11), low R-square (0.003)– Citigroup: intermediate beta (1.20), high R-square (0.50)

• Differing levels of systematic & unsystematic risk cause differing R-squares– Systematic risk accounts for higher fraction of Citi’s total var

Figure A: Scatterplot for Returns on Sharper Image and S&P500

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

S&P500 Weekly Return

Shar

per I

mag

e W

eekl

y R

etur

n Slope = Beta = 1.44

R-square = 0.19

Fig B: Scatterplot for Returns on ConAgra and S&P500

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

S&P500 Weekly Return

Con

Agr

a W

eekl

y R

etur

n

beta = 0.11

R-square = 0.003

Fig C: Scatterplot for Returns on Citigroup and S&P500

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

S&P500 Weekly Return

Citi

grou

p W

eekl

y R

etur

n beta = 1.20

R-square = 0.50

Interpreting Beta Coefficients

Selected Beta Coefficients and Their InterpretationSelected Beta Coefficients and Their Interpretation

Beta Comment Interpretation

Move in same direction as market

Twice as responsive, or risky, as the marketSame response or risk as the market (I.e., average risk)

Only half as responsive, or risky, as the market

2.0

1.0

.5

0 Unaffected by market movement

Move in opposite direction as market

Only half as responsive, or risky, as the marketSame response or risk as the market (I.e., average risk)

Twice as responsive, or risky, as the market

- .5

-1.0

-2.0

Betas Of Individual Stocks

Beta Coefficients for Selected Stocks (January 2003)Beta Coefficients for Selected Stocks (January 2003)

Stock Beta Stock Beta

0.70Kimberly-Clark0.60Procter & Gamble1.35Martha Stewart Living1.00International Paper1.30USG Corp0.65Gillette 1.00Johnson Controls0.95SBC Communications1.35AT&T Wireless0.90American Electric Power

0.95Merck & Co0.30Newmont Mining1.10MetLife, Inc0.70Federal Realty Investmt Trust0.90Golden West Financial1.30Hewlett-Packard1.00Apple Computer1.25Intel 1.65JDS Uniphase1.30General Electric

Source: Value Line investment Survey (New York: Value Line Publishing, January 3, 10, 17 & 24, 2003)

Calculating Required Return, Given Beta And Expected Market Return

• Calculate Required Return, RR = Rf + ß(Rm - Rf)

• Must assume either that return on the market, Rm, known or that market risk premium, MRP = (Rm - Rf), is known

• Example: If the rate of return on U.S T-Bills (Rf) is 2.0% and equity risk premium (Rm - Rf) is 8.0%, what would be the required return for:– General Electric, ß=1.30– Procter & Gamble ß=0.60

General Electric

Procter & Gamble

Rf 2.0% 2.0%

Rm - Rf 8.0% 8.0%

ß 1.30 0.60

R 12.40% 6.80%

Can now plot SML using Rf =2.0%, ßGE=1.30 , ßPG=0.60 and Equity risk premium (Rm - Rf )=8.0%

r%

12.4%

10

5

Rf = 2%

1 2GEP&G

SML

6.8%

Using The Security Market Line

The SML and where P&G and GE place on it

15

•

slope = E(Rm) – RF = MRP = 10% - 2% = 8% = Y ÷ X

r%

11.1%10

5

Rf = 2%

1 2GEP&G

SML1

6.2%

Shifts In The Security Market Line Due To A Shift In Required Market Return

15

Shift due to change in market risk premium from 8% to 7%

••

SML2

r%

14.4%

10

5Rf = 4%

1 2GEP&G

SML1

8.8%

Shifts In The Security Market Line Due To A Shift In The Risk-Free Rate

15

•Shift due to change in

risk-free rate from 2% to 4%, with market risk

premium remaining at 8%. Note all returns

increase by 2%

SML2