Chapter 6

Risk And Return: CAPM And Beyond

Professor John Zietlow MBA 621

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 – Curve connecting A&B called the

feasible set

<+1 of p/fs – Only p/fs from minimum variance p/f (MVP) to B are

efficient

Expected Return And Standard Deviation For Portfolios Of Two Assets E(R P ) efficient portfolios

•

C (50%A, 50%B)

•

MVP (75%A, 25%B)

•

A inefficient portfolios

•

B



P

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

The Efficient Frontier With Many Assets E(R P ) efficient portfolios MVP

• • •

A

• • • • •

B

• • • • • • • • •

C

• 

P

The Effect Of Expanding The Feasible Set On The Efficient Frontier E(R P ) EF including domestic & foreign assets EF including domestic stocks, bonds, and real estate EF for portfolios of domestic stocks



P

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 Portfolio Number % Berkshire % Microsoft % 3M % Praxair Expected Return % Stand Dev %

1 2 3 4

5 7 10 12 16

0 25 20 100

35 0 0 0 0

100 50 20 0

15 10 0 0 0

0 25 20 0

50 90 75 10 0

0 0 40 0

0 0 25 90 100

1.17

1.27

1.44

0.54

1.21

1.63

1.74

1.89

1.91

16.51

6.13

7.66

8.43

5.7

7 7.99

11.14

12.09

2.5

2 1.5

1 0.5

0 0

Expected Return & Standard Deviation for Various Portfolios Efficient Frontier #8:100% 3M

5

#16: 100% Praxair

8 7 3 2 13 14 10 11 9 15 12 16

#1: 100% Microsoft

1 6

#4: 100% Berkshire

4 2 4 6 8 10 12

Monthly standard deviation (%)

14 16

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

R f

All investors will hold combination of riskless asset and MF

– Between

R f

and MF, allocating existing wealth (point A) – Above MF, borrowing at

R f

, investing proceeds in MF (pt B)

Ray from R

f

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 E(R P )

16.5%

new efficient frontier

12% 9%

R F =6%

• •

A

• X •

M

0 30% •

B

L 1

old efficient frontier



P

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

16.5% 12% 9%

R F =6%

• 0 • 15%

A

• 30%

MF

•

B CML

52% 

P

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

27 24 3 0 9 6 21 18 15 12 0 3 6 9 12 (15%, 12%) (12%, 9%) (14%, 6%) (17%, 3%) 15 18 (19%, 16%) 21 24 (24%, 21%) (30%, 23%)

Portfolio Standard Deviation, %

27 30 33 36

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

Equilibrium And The Market Portfolio The 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) E(R P )

16.5%

new efficient frontier

12% 9%

R F =6%

• •

A

• X •

M

0 30% •

B

L 1

old efficient frontier



P

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 R

f

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 R

f

– Eq 6.2 says

E(R p )

equals

R f

plus the market price of risk (term in brackets) times the p/f’s standard deviation, 

P

:

E

(

R p

) 

R f

   (

E

(

R m

) 

m



R f

)   

p

(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)

– SML connects

R f (



=0)

and point and

Beta

, not std dev

[E(R M ),



=1]

In equilibrium, all assets must plot on the SML

E(R P ) R M

•

R F =6% The Security Market Line

• •

B

 •

=1.0

SML A

•

slope = E(R m ) - R F = Market Risk Premium (MRP)



i

E(R P ) Calculating Required Return Using The Security Market Line slope = E(R m ) – R F = MRP = 14% - 6% = 8% =



Y ÷



X SML

18%

R M =14%

10%

R F =6%

0.5



i =1.0

1.5



i

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

R f

and

E(R M )

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

-0.3

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

0.3

Slope = Beta = 1.44

0.2

0.1

-0.2

-0.1

0 0 -0.1

-0.2

0.1

0.2

R-square = 0.19

-0.3

S&P500 Weekly Return

0.3

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

-0.15

-0.1

0.15

0.1

0.05

-0.05

0 0 -0.05

0.05

beta = 0.11

0.1

0.15

R-square = 0.003

-0.1

-0.15

S&P500 Weekly Return

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

0.2

0.15

0.1

beta = 1.20

0.05

-0.2

-0.15

-0.1

0 -0.05

-0.05

0 -0.1

0.05

0.1

R-square = 0.50

0.15

-0.15

-0.2

S&P500 Weekly Return

0.2

Interpreting Beta Coefficients Selected Beta Coefficients and Their Interpretation Beta Comment Interpretation 2.0

1.0

.5

- .5

0 -1.0

-2.0

Move in same direction as market Move in opposite direction as market Twice as responsive, or risky, as the market Same response or risk as the market (I.e., average risk) Only half as responsive, or risky, as the market Unaffected by market movement Only half as responsive, or risky, as the market Same response or risk as the market (I.e., average risk) Twice as responsive, or risky, as the market

Betas Of Individual Stocks Beta Coefficients for Selected Stocks (January 2003) Stock Beta Stock Beta American Electric Power AT&T Wireless SBC Communications Johnson Controls Gillette USG Corp International Paper Martha Stewart Living Procter & Gamble Kimberly-Clark 0.90

1.35

0.95

1.00

0.65

1.30

1.00

1.35

0.60

0.70

General Electric JDS Uniphase Intel Apple Computer Hewlett-Packard Golden West Financial Federal Realty Investmt Trust MetLife, Inc Newmont Mining Merck & Co 1.30

1.65

1.25

1.00

1.30

0.90

0.70

1.10

0.30

0.95

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, R

R = R f + ß(R m - R f )

Must assume either that return on the market, R

m

, known or that market risk premium, MRP = (R known

m - R f

), is Example: If the rate of return on U.S T-Bills (R

f

) is 2.0% and equity risk premium (R

m - R f )

is 8.0%, what would be the required return for:

– General Electric,

ß=1.30

– Procter & Gamble

ß=0.60

R f

General Electric

2.0%

Procter & Gamble

2.0%

R m -

R f

8.0% 8.0%

ß

1.30 0.60

R 12.40% 6.80% Can now plot SML using R

f

=2.0%,

ß GE =1.30 , ß PG

=0.60 and Equity

risk premium (

R m - R f

)= 8.0%

Using The Security Market Line r% 15 The SML and where P&G and GE place on it SML 12.4% 10

•

slope = E(R m ) – R F = MRP = 10% - 2% = 8% =



Y ÷



X 6.8% 5 R f = 2% P&G 1 GE 2



Shifts In The Security Market Line Due To A Shift In Required Market Return r% 15 SML 1 SML 2 11.1% 10 6.2% 5 R f = 2%

• •

Shift due to change in market risk premium from 8% to 7% P&G 1 GE 2



Shifts In The Security Market Line Due To A Shift In The Risk-Free Rate r% 15 14.4% SML 2 SML 1 10 8.8% 5 R f = 4%

•

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% P&G 1 GE 2

