Chapter 6Risk and Return: The CAPM

and Beyond

Professor XXX

Course Name / #

22

Efficient Risky Portfolios

Variance of return - a poor measure of risk

Investors can only expect compensationfor systematic risk

Asset pricing models aim to define andquantify systematic riskBegin developing pricing model by asking:Are some portfolios better than others?

33

E(RP)

P

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

44

Two – Asset Portfolios

E(RP)

P

Stock A•

• Stock B

MVP (75%A, 25%B)

C (50%A, 50%B)

inefficient portfolios

efficient portfolios

•

•

Are Some Portfolios Better Than Others?

efficient portfolios

•MVP

D

F•

•

E

• • •• •

• ••

•

• ••

•

N – Asset Portfolios

Efficient portfolios achieve the highest possible return for any level of volatility

What happens when we add a risk-free asset to the picture?

55

Expected Return (per month) and Standard Deviation for Various Portfolios

66

Riskless Borrowing And Lending

Return: 6%Risk-free asset Y

Buying asset Y = Lending money at 6%

interestHow would a portfolio with $100 (50%) in asset X and

$100 (50%) in asset Y perform?

Portfolio has lower return but also less volatility than 100% in XPortfolio has higher return and higher volatility than 100% in risk-free

Three possible returns:

-10%; 10%; 30%

Risky asset X

Expected return = 10%Standard deviation =16.3%

$100 Asset X

$100 Asset Y

Three possible returns:

-2%; 8%; 18%

Expected return = 8%Standard deviation =8.16%

77

Riskless Borrowing And Lending (Continued)

What if we sell short asset Y instead of buying it?Borrow $100 at 6%Must repay $106

Invest $300 in XOriginal $200 investment plus $100 in borrowed funds

%18$200

$200-$106-$270 Investment $200on Return Net When X Pays –

10%

%12$200

$200-$106-$330 Investment $200on Return Net When X Pays 10%

%42$200

$200-$106-$390 Investment $200on Return Net When X Pays 30%

Expected return on the portfolio is 12%. Higher expected return comes at the expense of greater volatility

88

Riskless Borrowing And Lending (Continued)

PortfolioExpected Return

Standard Deviation

50% risky, 50% risk-free 8% 8.16%

100% risky, 0% risk free 10% 16.33%

150% risky, -50% risk free 12% 24.49%

The more we invest in X, the higher the expected return

The expected return is higher, but so is the volatility

This relationship is linear

99

Portfolios Of Risky & Risk-Free Assets

•

••

•RF=6%

0 30% 52%

12%

16.5%

E(RP)

P

9%

15%

A

MF

B

1010

New Efficient Frontier

1111

The Market Portfolio

Only one risky portfolio is efficient

Equilibrium requires this to be the Market Portfolio

Suppose investors agree on which portfolio is efficient

Market Portfolio: value weighted portfolio of all available risky assets

The line connecting Rf to the market portfolio - called the Capital Market Line

1212

Finding the Optimal Risky Portfolio

If investors can borrow and lend at the risk-free rate, then from the entire feasible set of risky portfolios, one portfolio will emerge that maximizes the return investors can expect for a given standard deviation.

To determine the composition of the optimal portfolio, you need to know the expected return and standard deviation for every risky asset, as well as the covariance between every pair of assets.

1313

Finding the Optimal Portfolio

1414

The Capital Market Line

The line connecting Rf to the market portfolio is called the Capital Market Line (CML)

CML quantifies the relationship between the expected return and standard deviation for portfolios consisting of the risk-free asset and the market portfolio, using

1515

Capital Asset Pricing Model (CAPM)

Only beta changes from one security to the next. For that reason, analysts

classify the CAPM as a single-factor model, meaning that just one variable explains differences in returns across securities.

1616

The Security Market Line

Plots the relationship between expected return and betas

In equilibrium, all assets lie on this lineIf stock lies above the line

Expected return is too highInvestors bid up price until expected return

fallsIf stock lies below the line

Expected return is too lowInvestors sell stock, driving down price until

expected return rises

1717

The Security Market Line

i

E(RP)

RF

SML

Slope = E(Rm) - RF = Market

Risk Premium (MRP)

•A - Undervalued

•

•

•RM

=1.0

•B

•A

• B - Overvalued

1818

Beta

2m

imi

The numerator is the covariance of the stock with the market

The denominator is the market’s variance

In the CAPM, a stock’s systematic risk is captured by beta

The higher the beta, the higher the expected return on the stock

1919

Beta And Expected Return

Beta measures a stock’s exposure to market risk

The market risk premium is the reward for bearing market risk:

• Rm - Rf

E(Ri) = Rf + ß [E(Rm) – Rf]

• Return for bearing no market risk

• Stock’s exposure to market risk

• Reward for bearing market risk

2020

Calculating Expected Returns

E(Ri) = Rf + ß [E(Rm) – Rf]• Assume

• Risk–free rate = 2%• Expected return on the market = 8%

If Stock’s Beta Is Then Expected Return Is

0 2%

0.5 5%

1 8%

2 14%When Beta = 0, The Return Equals The Risk-Free ReturnWhen Beta = 1, The Return Equals The Expected Market

Return

2121

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

Sh

arp

er Im

age

Wee

kly

Ret

urn

Slope = Beta = 1.44

R-square = 0.19

2222

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

Co

nA

gra

We

ek

ly R

etu

rn

beta = 0.11

R-square = 0.003

2323

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

Cit

igro

up

We

ek

ly R

etu

rn beta = 1.20

R-square = 0.50

2424

r%

12.4%

10

5

Rf = 2%

1 2GEP&G

SML

6.8%

Using The Security Market Line

15

•

slope = E(Rm) – RF =

MRP = 10% - 2% = 8% = Y ÷ X

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

2525

r%

11.1%

10

5

Rf = 2%

1 2GEP&G

SML1

6.2%

Shifts In The SML Due To A Shift In Required Market Return

15

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

••

SML2

2626

r%

14.4%

10

5Rf = 4%

1 2GEP&G

SML1

8.8%

Shifts In The SML 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

2727

Alternatives To CAPM

Arbitrage Pricing Theory

Fama-French Model lowhigh3bigsmall21 RRRRRRRR iifmifi

Betas represent sensitivities to each source of riskTerms in parentheses are the rewards for bearing each type of risk.

2828

The Current State of APT

Investors demand compensation for taking risk because they are risk averse.

There is widespread agreement that systematic risk drives returns.

You can measure systematic risk in several different ways depending on the asset pricing model you choose.

The CAPM is still widely used in practice in both corporate finance and investment-oriented professions.